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57dc3e3cbde35efc8ba63b639ae295a2abd94d9a | subsection | 23 | 34 | Body | The European Union has identified that context awareness is a crucial research area and specified a time-frame (2015-2020) for context-aware IoT computing R&D . Middleware solutions deals with heterogeneous devices and manages interoperability among them by understanding the sensory data collected besides providing sup... | {
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16844fa7eba55d4592674b7b56155da39f3de50a | subsection | 24 | 34 | Internet of Things Platforms | In IoT systems, messages can travel from one end-device to another application and/or device via the available WAN, PAN and platform layer. Recently, a number of platform layer standards have been suggested in some organizations to address fast delivery of messages between participating smart nodes and devices.OneM2M s... | {
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a1a29c2c87b89b0ac59f81c1f8ba747ec0a55d2e | subsection | 25 | 34 | System Model | Recent IoT services have been developed on a vertical system model in which each layer has been designed by an organization or a company. In turn, a recent trend of standardization considers horizontal system model to achieve scalable and interoprable operations in IoT's services . As the previous sections indicate, di... | {
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c053508679365ad6d2d91f8c8e3a87a03f64ed33 | subsection | 26 | 34 | Internet of Things Integration Practical Guidelines | A framework for sustainable interoperability in IoT is needed; this framework can (and should) learn from the best-of-breed interoperability solutions from related domains to take the good approaches while understanding the differences that the IoT poses . The below five steps can address some of the most common challe... | {
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5af233405ff5c91b7edb7e2b710af531267f247f | subsection | 27 | 34 | Internet of Things Software Development and Challenges | Emergence of IoT brings a new class of software and–or applications and additional efficiency constraints due to the limited resources of the things.
Software-specific requirements, communication and connectivity ability of devices have introduced new challenges for IoT systems' interoperability. With the ever increasi... | {
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390fa5059890d1d03dfafe21eae8fb8e6447b5ef | subsection | 28 | 34 | Internet of Things Proposed Software Architectures | IoT architecture is still under construction, it is not fixed and does not have a concrete shape yet. However, rapid development of IoT has triggered a wave of unreasonable expectations . For example, some industries have launched huge projects despite that the key technologies, including the basic architecture of IoT,... | {
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3bb994d77c6f14c4447cfbfd581922bcf3f79efa | subsection | 29 | 34 | Real-world IoT Deployment Platforms | Eclipse Hono, which originates from Eclipse IoT project , allows the provisioning of remote service interfaces for connecting different devices and interacts with them uniformly regardless of their type or communication protocol. The platform provides a number of protocol implementations, i.e., HTTP REST, MQTT, etc., C... | {
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af7ef2d0fdc06533a24a35aaad0d304fe5ad4c83 | subsection | 30 | 34 | Future Directions for the Internet of Things | After connecting people anytime and everywhere, the next important step is to integrate heterogeneous things among themselves and with the Internet . This integration will allow the creation of value-added interoperable services and applications, enabled by their interconnections, in a way that they can be integrated w... | {
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1e2c65e50fa097772594580e87731221bce392eb | subsection | 31 | 34 | Conclusion | This paper presented a review on the integration and interoperability issues in IoT and some proposed solutions. Since its inception, IoT services and applications have been developed to be adapted in a vertical service model, i.e., in which every layer has been designed by a company or organization. Interoperability a... | {
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} | 1808.07355 | Is Fragmentation a Threat to the Success of the Internet of Things? | [
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338adfc20022c24e8be45db1af41a4630775c0dd | subsection | 32 | 34 | Conclusion | He is one of the organizers of the RELENG workshop series (http://releng.polymtl.ca) and has been guest editor for special issues in the IEEE Software magazine and JSEP.Yann-Gaël Guéhéneuc
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f8d021ba500ba2998ed88d34a119babcae294d50 | subsection | 33 | 34 | Conclusion | She holds a D.Sc. in Operations Research from Georges Washington University in USA, a B.Sc. and a M.Sc. in Industrial Engineering from Cairo University in Egypt. Her research interests include Condition Based Maintenance, distributed decision making for product quality and Industry 4.0. She is a senior member of the Am... | {
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3782519e3c4669157a72212d9e1f1782b33b761d | abstract | 0 | 15 | Abstract | The scatter of the spatially resolved star formation main sequence (SFMS) is
investigated in order to reveal signatures about the processes of galaxy
formation and evolution. We have assembled a sample of 355 nearby galaxies with
spatially resolved H{\alpha} and mid-infrared fluxes from the Survey for
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3112d31b58bbfc8df51673d2e9586943d9cfba81 | subsection | 1 | 15 | Introduction | Studies of the star formation main sequence (SFMS) of galaxies, the relation between star formation rates (SFRs) and stellar mass ( M_{*}), for galaxies throughout our universe have revealed that galaxy formation is an orderly process, and universal laws must govern their evolution throughout cosmological time and acro... | {
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498b8f50a0bab9e8b6b03aef5001ea29ffa1389f | subsection | 2 | 15 | Introduction | Such preliminary spatially resolved studies have demonstrated trends of comparable amplitude between the global and local SFMS properties such as their slope, zero-points, and scatter, whilst highlighting that variations in the SFMS on local scale do exist.
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a53831ac29ea0874806487963503479237d06a21 | subsection | 3 | 15 | Introduction | The substantial variation in a and b have largely been attributed to the evolution in SFRs over cosmic time; a definitive understanding of the SFMS scatter is however still lacking (even though the path that a galaxy follows in the SFMS is clearly a reflection of its mass accretion history and its ability to turn gas i... | {
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4c2825f7697274333b0ed10ae4abb0ee664765d9 | subsection | 4 | 15 | Data | Our study takes advantage of large, spatially resolved, complementary data sets for two extensive surveys of galaxies: the Survey for Ionization in Neutral Gas Galaxies (SINGG) and Wide-field Infrared Survey Explorer (WISE).The SINGG targets were selected from the HI Parkes All Sky Survey (HIPASS), which maps HI 21cm l... | {
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147efe864a0eae741139724db0c19f8f761346bf | subsection | 5 | 15 | Data | Ultimately, our profiles will be rebinned to a spatial scale of 500 pc. With 355 galaxies, this produces a statistically robust local main sequence with nearly 6,000 data points.A tremendous advantage also afforded by these data sets is their large radial extent, reaching out to almost 10 effective radii in some galaxi... | {
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eb4f8dbcbf5d4890f99ba4ebee94178fb8c774c8 | subsection | 6 | 15 | Star Formation Rates | There exists a multitude of transformations to infer SFRs in galaxies. These are typically based on UV spectrum slopes, H\alpha and far-infrared (IR) fluxes, and more (see , , for a review). These derivations can generally be traced back to motivation by the star formation (or K-S) law, which describes the SFR dependen... | {
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2e10e8f5ffc246fa56924e668c3c833d7f87207e | subsection | 7 | 15 | Star Formation Rates | The W4 transformation, which lies beyond the bulk of PAH emission, is therefore favored here. compared the corresponding W4 SFRs to those derived from optical tracers (ie. H\alpha ) in star-forming galaxies and found comparable agreement. Caution is offered for survey galaxy selections motivated by the W4 band emission... | {
"cite_spans": []
} | 10.3847/1538-4357/aadee1 | 1809.09111 | Unique Tracks Drive the Scatter of the Spatially-Resolved Star Formation
Main Sequence | [
"Christine Hall",
"Stephane Courteau",
"Thomas Jarrett",
"Michelle Cluver",
"Gerhardt Meurer",
"Claude Carignan",
"Fiona Audcent-Ross"
] | [
"astro-ph.GA"
] | 2,018 | en | Physics | [
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db3c82f971f2314c1d455ebaa3dc1990a70592d4 | subsection | 8 | 15 | Star Formation Rates | REF ) and C17C17 (W4, eq. REF ) produce the most consistent SFRs, while the former transformation has the highest overall agreement among all SFR transformations. This could be due to the fact that H\alpha and W4 are also in the K98K98 and C17C17, though despite the dominant contribution of H\alpha in C07C07, there is ... | {
"cite_spans": []
} | 10.3847/1538-4357/aadee1 | 1809.09111 | Unique Tracks Drive the Scatter of the Spatially-Resolved Star Formation
Main Sequence | [
"Christine Hall",
"Stephane Courteau",
"Thomas Jarrett",
"Michelle Cluver",
"Gerhardt Meurer",
"Claude Carignan",
"Fiona Audcent-Ross"
] | [
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743652ad0ff79903d094c7fa0a1a2422a5449642 | subsection | 9 | 15 | Stellar Masses | Stellar masses can be derived through multiple methods; these include color to mass-to-light ratio relations (CMLRs), multiband SED fitting, or straight band flux to stellar mass transformations. Each method takes advantage of specific wavelengths, and this study capitalizes on the availability of the WISE 3.4\mu m and... | {
"cite_spans": []
} | 10.3847/1538-4357/aadee1 | 1809.09111 | Unique Tracks Drive the Scatter of the Spatially-Resolved Star Formation
Main Sequence | [
"Christine Hall",
"Stephane Courteau",
"Thomas Jarrett",
"Michelle Cluver",
"Gerhardt Meurer",
"Claude Carignan",
"Fiona Audcent-Ross"
] | [
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55b5c5049645577c6883975292246f7042b53158 | subsection | 10 | 15 | Stellar Masses | Therefore strict color limits of -0.02\le W1-W2 \le 0.17 have been enforced. The proposed relation is:\log (\mbox{\,$M_{*}$}/L_{W1})_{\mathrm {C14}} = -0.17 - 2.54\times (W1-W2).where M_{*} is recovered from the resulting M_{*}/L_{W1} by multiplying by the corresponding luminosity: L_{W1} (L_{\odot }) = 10^{-0.4(M_{W... | {
"cite_spans": []
} | 10.3847/1538-4357/aadee1 | 1809.09111 | Unique Tracks Drive the Scatter of the Spatially-Resolved Star Formation
Main Sequence | [
"Christine Hall",
"Stephane Courteau",
"Thomas Jarrett",
"Michelle Cluver",
"Gerhardt Meurer",
"Claude Carignan",
"Fiona Audcent-Ross"
] | [
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bf2c6166021dd9f901856e5a2e4875c2fbb398a1 | subsection | 11 | 15 | Stellar Masses | A disadvantage of this calibration is the low-metallicity of to the LMC; thus the conversion mostly applies to similarly low-metallicity regions.(hereafter M14M14) produced an alternate conversion using spatial maps of 2300 galaxies from the Spitzer Survey of Stellar Structure in Nearby Galaxies (S^{4}G). These maps pr... | {
"cite_spans": []
} | 10.3847/1538-4357/aadee1 | 1809.09111 | Unique Tracks Drive the Scatter of the Spatially-Resolved Star Formation
Main Sequence | [
"Christine Hall",
"Stephane Courteau",
"Thomas Jarrett",
"Michelle Cluver",
"Gerhardt Meurer",
"Claude Carignan",
"Fiona Audcent-Ross"
] | [
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4289a9ffb66d1192ad6f2b1adb0587c694cf0dac | subsection | 12 | 15 | Stellar Masses | REF is clearly a good match to the applicable color range and consistent within the uncertainty associated with stellar mass approximations.The upper panel of Fig. REF demonstrates the consistency of various M_{*}/L methods, despite the varying MIR color ranges and M_{*}/L_{W1} trends (Fig. REF ) amongst common transfo... | {
"cite_spans": []
} | 10.3847/1538-4357/aadee1 | 1809.09111 | Unique Tracks Drive the Scatter of the Spatially-Resolved Star Formation
Main Sequence | [
"Christine Hall",
"Stephane Courteau",
"Thomas Jarrett",
"Michelle Cluver",
"Gerhardt Meurer",
"Claude Carignan",
"Fiona Audcent-Ross"
] | [
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225c39bdb704e43c665ef83616b302dee8b452dc | subsection | 13 | 15 | Stellar Masses | This study traces considerably more low mass systems than CALIFA or MaNGA, which are limited to log(M_{*,tot}/\mbox{\,$M_\odot $})>9; the upper limits in stellar mass are consistent , .
Additionally, the constant M_{*}/L_{W1} is not limited by color range. For this reason, we adopt a constant M_{*}/L_{W1}=0.5 for our ... | {
"cite_spans": []
} | 10.3847/1538-4357/aadee1 | 1809.09111 | Unique Tracks Drive the Scatter of the Spatially-Resolved Star Formation
Main Sequence | [
"Christine Hall",
"Stephane Courteau",
"Thomas Jarrett",
"Michelle Cluver",
"Gerhardt Meurer",
"Claude Carignan",
"Fiona Audcent-Ross"
] | [
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da24e4279be53b886351740e136c1b8952a3eb96 | subsection | 14 | 15 | Spatial Resolution of the SFMS | The star formation law (\Sigma _{\mathrm {SFR}}\propto \Sigma _{gas}^{N}) has received considerable attention (, , , ).
However, only recently has it become possible to study scales down to 30 pc and address on what physical scales the star formation law holds and possibly even breaks down (, , , , ).Measurements for t... | {
"cite_spans": []
} | 10.3847/1538-4357/aadee1 | 1809.09111 | Unique Tracks Drive the Scatter of the Spatially-Resolved Star Formation
Main Sequence | [
"Christine Hall",
"Stephane Courteau",
"Thomas Jarrett",
"Michelle Cluver",
"Gerhardt Meurer",
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ea99e31e9094802f46e63cf1d15abeffa14f59f9 | abstract | 0 | 93 | Abstract | Graphite under high magnetic field exhibits consecutive metal-insulator (MI)
transitions as well as re-entrant insulator-metal (IM) transition in the
quasi-quantum limit at low temperature. In this paper, we identify the low-$T$
insulating phases as excitonic insulators with spin nematic orderings. We first
point out t... | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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808967f58fa53352331984f2da0cb581b91dd64c | subsection | 1 | 93 | introduction | Graphite under high magnetic field exhibits a metal-insulator transition at low temperature
(H\ge H_{c,1}\simeq 30 \!\ {\rm T}) , . The transition has been often
considered as a prototype of one-dimensional
Peierls density-wave instability associated with the 2k_F logarithmic singularity in the
Lindhard response
functi... | {
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{
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"raw": "S. Tanuma, R. Inaba, A. Furukawa, O. Takahashi, Y. Iye and Y. Onuki, in Physics in High Magnetic Fields, edited by S. Chikazumi, and N. Miura, (Springer, Berlin, 1981), p. 316.",
"source_ref_i... | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
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6773daf910d6fdb096a88a8f6647731cf7bd1abf | subsection | 2 | 93 | introduction | T=0 metal-insulatortransition at H=H_{c,1} and insulator-metal transition at H=H_{c,2} are the quantumphase transition with the dynamical exponent z=1.]Theoretically, stabilities of the Peierls density wave phases against random single-particle
backward scatters depend crucially on a commensurability condition
of an el... | {
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{
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... | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
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9770f0059c534c1dad9d83a9f099b59d0e8bfd82 | subsection | 3 | 93 | direct metal-insulator transition | Under the magnetic field H (\parallel z), kinetic energy part of the three-dimensional semimetal
takes a form of decoupled one-dimensional quantum chains (or quantum wires). Namely, the kinetic
energy within the xy plane is quenched by the Landau quantization, while the kinetic energy
along the field direction remains ... | {
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{
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... | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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80ad95dc024a461b6b8ec957a0956a81cbb95404 | subsection | 4 | 93 | re-entrant insulator-metal transition | The second issue is the re-entrant insulator-metal transition observed at
the higher field region in the graphite experiment , , , , , , , ,
that can hardly be explained by the conventional Peierls DW scenarios. Namely, the
RPA density correlation function at finite temperature suggests that the transition temperature
... | {
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"doi": "... | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
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"Ryuichi Shindou"
] | [
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ac8cc7a7294642833936ce72702b60f355fc0718 | subsection | 5 | 93 | field-dependence of in-plane resistance | The third issue to be addressed in this paper is an unusual field-dependence of the
electric transport in the directions transverse to the magnetic field , , , , , , , .
Generally, the bulk electric transport perpendicular to the field is quenched in the clean limit at low
temperature (T\ll h\omega _0; h\omega _0 is th... | {
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"doi": "... | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
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] | 2,018 | en | Physics | [
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abc74a4ab24a481f67a1d3fbe57f9b28a37c5a76 | subsection | 6 | 93 | structure of the paper | The structure of the paper is as follows. In the next section with a help of appendix A,
we argue that the graphite under the relevant field regime ( 20\!\ {\rm T}< H) is in
the charge neutrality region, where electron and hole densities compensate each other.
Based on this observation, we enumerate in Sec. III possibl... | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
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ed4716de5aeb8711e4d357f4a39a03e9391ad0c9 | subsection | 7 | 93 | charge neutrality regime in graphite under high magnetic field | Low-temperature transport properties of graphite are dominated by four \pi -orbital bands around
zone boundaries of the first Brillouin zone , , .
Graphite is a three-dimensional AB stacking of graphene
layers. A unit cell has two graphene layers and it has four inequivalent carbon
sites. Call them as A, A^{\prime }, B... | {
"cite_spans": [
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... | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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d526e1bca63aa9313b8792205a4c7f25d485b6c6 | subsection | 8 | 93 | charge neutrality regime in graphite under high magnetic field | Namely,E_{0,\sigma }(k_z,y_j)/E_{1,\sigma }(k_z,y_j) goes higher/lower in energy, when y_j goes fromthe bulk region to the edge regions (see Appendix A).] | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
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fe6a810b547e6d22b45c6c0252bad5b204ef8783 | subsection | 9 | 93 | four pockets model ( | Based on this observation, we consider an electron model with two electron pockets
(n=0 LL with \uparrow spin and that with \downarrow spins)
and two hole pockets (n=-1 LL with \uparrow spin and that with \downarrow spins) with
the charge neutrality condition (N_e=N_h);H_{\rm kin}&=\sum _{k_z,j}
\sum _{n=0,-1}\sum _{\s... | {
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"end": 735,
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"raw": "D. Yoshioka, and H. Fukuyama, J. Phys. Soc. Japan, 50, 275, (1981).",
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"start": 429
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{
"arxiv_id": "",
"... | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
-0.05153306573629379,
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... |
04b22dc887dfd3986a63bbea2d290d6147feb685 | subsection | 10 | 93 | four pockets model ( | For simplicity, we label (n,\sigma )=(0,\uparrow ),(0,\downarrow ), (-1,\uparrow ) and
(-1,\downarrow ) as a=1,2,3 and 4 respectively throughout this paper, e.g.
k_{F,a} \equiv k_{F,n,\sigma }, c_{a,j}(k_z) \equiv c_{(n,\sigma ),j}(k_z),
and \psi _{a,\pm ,j}(z) \equiv \psi _{(n,\sigma ),\pm ,j}(z).
\psi _{a,\pm ,j}(z) ... | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
0.014258738607168198,
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... |
53ce32017feb142b10814b4bf486550972528b5b | subsection | 11 | 93 | four pockets model ( | The creation
field can be expanded in term of single-particle bases of the n=0 and n=-1 LLs in the Landau
gauge;\left(\begin{array}{c}
\psi _{\sigma }({r},A) \\
\psi _{\sigma }({r},A^{\prime }) \\
\psi _{\sigma }({r},B) \\
\psi _{\sigma }({r},B^{\prime }) \\
\end{array}\right) = \sum _{j} \frac{ e^{ik_j x}}{\sqrt{L_x}}... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 1482,
"openalex_id": "",
"raw": "J. C. Slonczewski, and P. R. Weiss, Phys. Rev. 99, 636 (A) (1955).",
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"start": 1082
},
{
"arxiv_id": "",
... | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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... |
c1f7f7e2dc26f47fe6b75723a37ce747c581e354 | subsection | 12 | 93 | four pockets model ( | L_x is a linear dimension of the system size along the x-direction.
A substitution of Eqs. (REF ,REF ,)
into Eq. (REF ) and expansion in \psi _{(n,\sigma ),\tau ,j}(z) \equiv \psi _{a,j}(z)
lead to scatterings between different pockets (inter-pocket scattering)
and scatterings within the same pocket (intra-pocket scatt... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 832,
"openalex_id": "",
"raw": "A. A. Abrikosov, J. Low Temp. Phys. 2, 37 (1970); J. Low Temp. Phys. 3, 10 (1973).",
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"start": 579
},
{
"arxiv_i... | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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99917a5a49b91aedfc104c5d8f30f39bc0fc2989 | subsection | 13 | 93 | four pockets model ( | (REF ) take the following
explicit form with their Hermitian conjugates,&({\rm 1st} \ {\rm and} \ {\rm 4th} \ {\rm terms} \ {\rm in} \ {\rm Eq}.~(\ref {Hu})) \\
& \ \ = 2 \sum _{j,m,n} V^{(12)}_{m-n,j-n} \int dz \int dz^{\prime } \!\ e^{-\frac{(z-z^{\prime })^2}{2l^2_{0,z}}} \\
& \hspace{0.0pt} \bigg \lbrace e^{-ik_{F,... | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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... |
66575fe1c24a3bbbee77be533adb469109872c48 | subsection | 14 | 93 | four pockets model ( | They areH_{\rm b} = \sum _{j,m,n} \left\lbrace \begin{array}{l}
\psi ^{\dagger }_{4,\pm ,n}\psi ^{\dagger }_{1,\mp ,j+m-n} \psi _{1,\mp ,m}\psi _{4,\pm ,j}, \\
\psi ^{\dagger }_{3,\pm ,n}\psi ^{\dagger }_{2,\mp ,j+m-n} \psi _{2,\mp ,m}\psi _{3,\pm ,j}, \\
\psi ^{\dagger }_{4,\pm ,n}\psi ^{\dagger }_{2,\mp ,j+m-n} \psi ... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
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"raw": "A. A. Abrikosov, J. Low Temp. Phys. 2, 37 (1970); J. Low Temp. Phys. 3, 10 (1973).",
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"start": 921
},
{
"arxiv_... | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
-0.029418786987662315,
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... |
628b87713f662a893cda00c377c45ffe6231f481 | subsection | 15 | 93 | four pockets model ( | () with (0,\uparrow ) \equiv 1, (0,\downarrow )\equiv 2,(-1,\uparrow ) \equiv 3 and (-1,\downarrow ) \equiv 4.][Figure: Schematic pictures of one of the inter-pocket scatterings, H_{{\rm b},2}.They are the exchange processes (m=n) of the first two terms in Eq. () with(0,\uparrow ) \equiv 1, (0,\downarrow )\equiv 2,(-1,... | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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... |
c7a00bc0197a699fbbabaef9b1dd1eff3e53bfdb | subsection | 16 | 93 | effective boson theory | In this section, we construct effective field theories of possible insulating phases that
are stabilized by the umklapp scattering
terms in Eq. (REF ). To this end, we first assume that the low-T insulating
phases in the graphite experiment do not break the translational symmetries within the graphene
plane [the graphe... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 496,
"openalex_id": "",
"raw": "S. Tanuma, R. Inaba, A. Furukawa, O. Takahashi, Y. Iye and Y. Onuki, in Physics in High Magnetic Fields, edited by S. Chikazumi, and N. Miura, (Springer, Berlin, 1981), p. 316.",
"source_ref_i... | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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... |
7d0b1c54f7cafac0372c668e6746b08e9011a878 | subsection | 17 | 93 | effective boson theory | (REF ) are Klein factors ensuring
the anticommutation relation
among fermion fields on different chains (j), pockets (a) and chiralities (\tau =\pm );
\lbrace \eta _{a,j}, \eta _{b,m} \rbrace = \lbrace \eta _{\overline{a},j}, \eta _{\overline{b},m} \rbrace
= \delta _{a,b} \delta _{j,m}, and \lbrace \eta _{a,j}, \eta _... | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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0.0... |
23cf79402d3c9323a086a49057e9eb11b3630064 | subsection | 18 | 93 | effective boson theory | (REF ) are bosonized asH_{{\rm u},1}& = \sum _{j,m} M^{(1)}_{j-m} \int dz \!\ \Big \lbrace \sigma _{3\overline{1},j} \sigma _{4\overline{2},m}
\cos \big [Q^{13}_{+,j} + Q^{24}_{+,m}\big ] \\
& \hspace{42.67912pt} + \!\ \sigma _{\overline{3}1,j} \sigma _{\overline{4}2,m}
\cos \big [Q^{13}_{-,j}+Q^{24}_{-,m}\big ] \Big \... | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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... |
3045af5df23c3160a788ddba1419b1f8c2c37db6 | subsection | 19 | 93 | effective boson theory | \sigma _{a\overline{b},j} and \sigma _{\overline{a}b,m} are Ising variables
associated with the Klein factors
within the same chain, \sigma _{a\overline{b},j} \equiv i \eta _{a,j} \eta _{\overline{b},j}, and
\sigma _{\overline{a}b,m} \equiv i \eta _{\overline{a},m} \eta _{b,m}. The Ising variables take \pm 1.The Fock t... | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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-... |
d0876ac1f2aedd0081bbd3f2b56002c31bba8a9d | subsection | 20 | 93 | effective boson theory | (REF ), are bosonized asH_{{\rm b},13}& = \sum _{j,m} H^{(13)}_{j-m} \int dz \!\ \Big \lbrace \sigma _{3\overline{1},j} \sigma _{3\overline{1},m}
\cos \big [\Delta _{jm}Q^{13}_{+}\big ] \\
&\hspace{59.75095pt} + \sigma _{\overline{3}1,j}\sigma _{\overline{3}1,m}
\cos \big [\Delta _{jm}Q^{13}_{-}\big ]\Big \rbrace \\
& ... | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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-0.... |
06e996c3045ab8d4dd84a14c91508c531f5a67b5 | subsection | 21 | 93 | effective boson theory | The Hartree term (j=n) of the inter-pocket scatterings
in Eq. (REF ) could also renormalize the Luttinger parameters and Fermi
velocities. For simplicity, however, we consider the renormalizations of K_a and u_{a} only
by the intra-pocket scatterings H_{\rm f} as given in appendix B.
Figs. REF and REF schematically
sho... | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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... |
a92b6bf10e1bde5284b18ddca3ec45b852bd6eb3 | subsection | 22 | 93 | effective boson theory | We show that, at the one-loop level of the perturbative
RG equations, H_{{\rm b},13}, H_{{\rm u},1} and H_{{\rm u},3} are coupled with one another and stabilize
(what we call) a plain excitonic insulator phase. Meanwhile, H_{{\rm u},2} and H_{{\rm b},2}
stabilize spin nematic excitonic insulator phase, H_{{\rm u},4} an... | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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-... |
850f6e4da6476abe6baf3596f5d4befb11f8e11d | subsection | 23 | 93 | spin-nematic excitonic insulator (SNEI-I) phase | We begin with the spin-nematic excitonic insulator phase stabilized by
H_{{\rm b},2} and H_{{\rm u},2}. The renormalization group (RG) equations
for the inter-chain interaction functions in H_{{\rm b},2} and H_{{\rm u},2}
take following forms at the one-loop level;\frac{dM^{(2)}_{j-m}}{d{\rm ln}b} &= \frac{A_{23}+A_{14... | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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... |
642347cc3a0d3326ba33a23ec4f40f53a76e32e1 | subsection | 24 | 93 | spin-nematic excitonic insulator (SNEI-I) phase | We assume that C_{ab} has no dependence on temperature and magnetic field.
Eqs. (REF ,,) are functional RG equations under which inter-chain
interactions change their functional forms. To gain a simpler idea of these functional RG equations,
we take a sum of the inter-chain interactions over their chain indices. The su... | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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657ff67c4255b2b908d28a154c8da3b954f9ac7c | subsection | 25 | 93 | spin-nematic excitonic insulator (SNEI-I) phase | The critical strength
decreases not only on increasing the magnetic field through a dependence of the one-loop terms
on the magnetic length l, but also on decreasing the temperature through a dependence of
A_{ab} on the temperature. This suggests that the strong coupling phase generally
appears in low temperature side ... | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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... |
8d64de5879b456c45a0300f3dc186acfb52294e5 | subsection | 26 | 93 | spin-nematic excitonic insulator (SNEI-I) phase | In the strong coupling regime, H_{{\rm u},2} and H_{{\rm b},2} are maximally minimized by&\phi _{3,m} + \phi _{2,m} = \Phi _{-}, \ \ \phi _{4,m} + \phi _{1,m} = \left\lbrace \begin{array}{l}
2n\pi - \Phi _{-} \\
(2n+1) \pi - \Phi _{-} \\
\end{array}\right. \\
&\theta _{3,m} - \theta _{2,m} = \Theta _{-}, \ \ \theta _{4... | {
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"doi": "",
"end": 1740,
"openalex_id": "",
"raw": "K. Akiba, A. Miyake, H. Yaguchi, A. Matsuo, K. Kindo, and M. Tokunaga, J. Phys. Soc. Japan, 84, 054709 (2015).",
"source_ref_id": "ed37b05803a588d52499ba85a0afe950cbc28c3d",
"start": 16... | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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0... |
d8cbd164cf23227afe061983bc723491adf5e44b | subsection | 27 | 93 | spin-nematic excitonic insulator (SNEI-I) phase | In the strong coupling phase with large m_{(2)},
we may employ a Gaussian approximation for the cosine terms in H_{{\rm u},2}.
\sigma _{zz}(\omega ) is calculated within the linear response
theory as \sigma _{zz}(\omega ) = (e^2 u K)/(2\pi l^2) \delta (\omega -\omega _g),
where uK \equiv \sum _{a}u_a K_a. \omega ^2_g \... | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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... |
ebd517ceaeb9b9d9df3217c64b943dfa68002b2a | subsection | 28 | 93 | spin-nematic excitonic insulator (SNEI-I) phase | The 2nd rank spin tensor is defined asQ^{cd}_{\mu \nu }({r}) &\equiv \langle S_{c,\mu }({r}) S_{d,\nu }({r})
+ S_{c,\nu }({r}) S_{d,\mu }({r})\rangle \\
& \hspace{28.45274pt} - \delta _{\mu \nu }
\langle {S}_{c,\perp }({r})\cdot {S}_{d,\perp }({r}) \rangle ,with c=A,A^{\prime }, d= B,B^{\prime }, \mu ,\nu =x,y, {S}_{c,... | {
"cite_spans": [
{
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"doi": "",
"end": 1682,
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"raw": "Y. Takada, and H. Goto, J. Phys. Condens. Matter 10, 11315 (1998).",
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"start": 1607
}
]
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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... |
3291dafedf7d033f2ab3c30e3e8cc5b43f95b77e | subsection | 29 | 93 | spin-nematic excitonic insulator (SNEI-I) phase | (REF )]. Thus,
according to Eqs. (REF ,), m_{(2)} and \overline{h}_{(2)} are renormalized
into smaller values at an early stage of the RG flow for H\lesssim H_0, irrespective of
bare values of m_{(2)} and \overline{h}_{(2)}. Meanwhile,
A_{23} as well as v_{F,2} and v_{F,3}
remain rather constant around H=H_0. Thus, acc... | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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0.0... |
0f70b83c30828632772557f5ec021b70fdb6b82c | subsection | 30 | 93 | magnetic Mott insulator and plain excitonic insulator phases | To see this, let us next consider a nature and a RG phase diagram of the
magnetic Mott insulator phase stabilized by H_{{\rm u},4} and H_{{\rm b},4}. By exchanging
2 and 4 in Eqs. (REF ,,), we can readily obtain corresponding
one-loop RG equations for their coupling constants;\frac{dm_{(4)}}{d{\rm ln}b} &= \frac{A_{34}... | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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-... |
5076f60fe394ba4b21c8f7b0b8871c9732f4c9a4 | subsection | 31 | 93 | magnetic Mott insulator and plain excitonic insulator phases | In the strong coupling phase with m_{(4)} \rightarrow \pm \infty and h_{(4)},\overline{h}_{(4)}\rightarrow -\infty , H_{{\rm b},4} and H_{{\rm u},4}
are maximally minimized by&\phi _{3,j} + \phi _{4,j} = \Phi _{-}, \ \ \phi _{2,j} + \phi _{1,j} = \left\lbrace \begin{array}{l}
2n\pi - \Phi _{-} \\
(2n+1) \pi - \Phi _{-}... | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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0.0... |
97dea3aac069d134f77117dc10106bdf23f92876 | subsection | 32 | 93 | magnetic Mott insulator and plain excitonic insulator phases | Accordingly, unlike in the spin nematic excitonic insulator case
in the previous section, all of the three coupling constants, m_{(4)}, h_{(4)} and
\overline{h}_{(4)}, are renormalized to zero for those H sufficiently close to H_0 (H < H_0).
In other words, the transition temperature of the magnetic Mott insulator
alwa... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 620,
"openalex_id": "",
"raw": "H. Ochimizu, T. Kakamasu, S. Takeyama, S. Sasaki, and N. Miura, Phys. Rev. B 46, 1986 (1992).",
"source_ref_id": "608333822024424748ca877da7b41b28082c9bd9",
"start": 495
},
{
... | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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0.012183156795799732,
-... |
913bf6d799394c450ee256b87ad1f7a982609e58 | subsection | 33 | 93 | magnetic Mott insulator and plain excitonic insulator phases | (REF ,) respectively;H^{\prime }_{\rm imp} &=
\sum _{j} \int dz A_{j,+}(z) \sigma _{1\overline{2},j}\\
& \hspace{17.07182pt} \times \cos \big [\phi _{2,j} + \phi _{1,j}
-\theta _{2,j} + \theta _{1,j} + \lambda _{+,j}(z) \big ] \\
& \hspace{5.69046pt} + \sum _{j} \int dz A_{j,-}(z) \sigma _{\overline{1}2,j} \\
&\hspace{... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 690,
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"raw": "Y. Imry, and S. K. Ma, Phys. Rev. Lett. 35, 1399 (1976).",
"source_ref_id": "125a9f21abe2983d0610669c06602f7929a8f491",
"start": 445
},
{
"arxiv_id": "",
"doi": "",
... | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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e879d66497e802749b3bc8ba6a0595de38aeae95 | subsection | 34 | 93 | two pockets model ( | For H > H_0, both the electron pocket with (n,\sigma )=(0,\uparrow ) and hole pocket
with (n,\sigma )=(-1,\downarrow ) leave the Fermi level , .
The low-energy electronic system for H>H_0 comprises only
of the electron pocket with (n,\sigma )=(0,\downarrow ) and
the hole pocket with (n,\sigma )=(-1,\uparrow ). As befor... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 144,
"openalex_id": "",
"raw": "Y. Takada, and H. Goto, J. Phys. Condens. Matter 10, 11315 (1998).",
"source_ref_id": "dc03c66c7b7a22d255931c5c566c586dc4674ecb",
"start": 0
},
{
"arxiv_id": "",
"doi... | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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... |
55b4ec9b5e17ccda2d16d72b9a8cb16491589407 | subsection | 35 | 93 | two pockets model ( | (REF ,REF ,REF ),
and bosonize them into cosine terms;&H^{\prime }_{\rm u} + H^{\prime }_{\rm b} + H^{\prime }_{\rm d}
= H^{\prime }_{{\rm u},1} + H^{\prime }_{{\rm u},2} + H^{\prime }_{{\rm d},1} + H^{\prime }_{{\rm b},2} + \cdots ,
\\
& H^{\prime }_{{\rm u},1} = \sum _{j,m} N^{(1)}_{j-m} \!\ \int dz \sigma _{3\overli... | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
0.008056270889937878,
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-... |
0348cae365359e21d67753d64f282d7ccc6d5dbf | subsection | 36 | 93 | two pockets model ( | (REF ), while
H^{\prime }_{{\rm u},2}, H^{\prime }_{{\rm d},1} and H^{\prime }_{{\rm b},2} are from
the Fock processes (m=n) of Eq. (REF ), Eq. (REF ) and Eq. (REF ) respectively (Fig. REF ).
The Hartree processes of H^{\prime }_{\rm d} and H^{\prime }_{\rm b}
renormalize the Luttinger parameters and Fermi velocities i... | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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... |
b61dc6cc65e4121318ad76e50ca6561c22483ce8 | subsection | 37 | 93 | a superposed CDW phase | When H^{\prime }_{{\rm u},1} and H^{\prime }_{{\rm d},1} become relevant, the
cosine terms in Eqs. (REF ,) are maximally
minimized by a charge density wave (CDW) phase, where a displacement
field of the electron pocket and that of the hole pocket exhibit long-range orders individually;&2\phi _{2,j} = \Phi _{2}, \ \ 2\p... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 1531,
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"raw": "Y. Imry, and S. K. Ma, Phys. Rev. Lett. 35, 1399 (1976).",
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"start": 1084
},
{
"arxiv_id": "",
"doi": "",... | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
-0.02966359443962574,
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0.010032826103270054,... |
4b2856eb2a4e7dff055aee611f172cac2c0a9a75 | subsection | 38 | 93 | spin nematic excitonic insulator (SNEI-II) phase | When H^{\prime }_{{\rm u},2} and H^{\prime }_{{\rm b},2} become relevant, the
cosine terms in Eqs. (,)
are maximally minimized by the excitonic insulator phase with broken U(1) spin rotational symmetry.
To see a nature and an RG phase diagram of this strong coupling phase, let us first reduce the inter-chain
coupling f... | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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0.0... |
17e9b93efad4046dde5795f1b9b4c868fa83c2b5 | subsection | 39 | 93 | spin nematic excitonic insulator (SNEI-II) phase | Thereby,
the equations immediately
give out a RG flow diagram as in Fig. REF .
The strong and weak coupling phases at T=0 are defined by\left\lbrace \begin{array}{cl}
|n_{(2)}| - p_{(2)} > x_c & ({\rm strong} \!\ \!\ {\rm coupling} \!\ \!\ {\rm phase}), \\
|n_{(2)}| - p_{(2)} < x_c & ({\rm weak} \!\ \!\ {\rm coupling} ... | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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0.03205... |
722851cfc36c17f141c3ecf6c2833d03098b8cdf | subsection | 40 | 93 | spin nematic excitonic insulator (SNEI-II) phase | ().]The phase boundary condition, Eqs. (REF ,REF ), explains the metal-insulator
transition at a lower field regime.
For simplicity, we assume that the bare values of n_{(2)} and p_{(2)}=\overline{p}_{(2)}
as well as (C_{23})_{|T=0} have no H-dependence. For a low H regime, the magnetic length l is
large, so is the cri... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "10.4279/pip.110003",
"end": 881,
"openalex_id": "https://openalex.org/W2950950081",
"raw": "B. Fauque, D. LeBoeuf, B. Vignolle, M. Nardone, C. Proust, and K. Behnia, Phys. Rev. Lett. 110, 266601 (2013).",
"source_ref_id": "a1c056f54cb... | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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... |
5afabbf180c4ebdf2cd68540465b0b6667e17c57 | subsection | 41 | 93 | critical natures of the MI and re-entrant IM transitions | The re-entrant transition point at H=H_{c,2} is a zero-temperature
continuous phase transition with dynamical exponent z=1.
Toward this quantum critical point, a correlation length along the field
direction \xi _z diverges as\xi _z \propto |H-H_{c,2}|^{-1/\nu _2}.A critical exponent \nu _{2} is given only by the Luttin... | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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0.... |
710067d42a783e3b1e4206295ca96de6e158e384 | subsection | 42 | 93 | in-plane resistance in the four pockets model ( | Generally, in-plane current operators in the clean limit have finite matrix elements
only between neighboring Landau levels. When the temperature is much lower than
the cyclotron frequency \hbar \omega _0, the in-plane resistance increases on increasing
magnetic field H. Contrary to this expectation, the low-temperatur... | {
"cite_spans": [
{
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"doi": "",
"end": 420,
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"raw": "H. Yaguchi and J. Singleton, Phys. Rev. Lett. 81, 5193 (1998).",
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"start": 125
},
{
"arxiv_id": "",
"doi":... | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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485f6625d8090301ac996d31f851f4cc2644fc1d | subsection | 43 | 93 | Body | The H-dependence of the in-plane resistance in 30 \!\ {\rm T} < H <H_0 \simeq 53 \!\ {\rm T}
can be explained by charge transports along the surface chiral Fermi arc (SCFA) states.
To see this, notice first that the electron/hole pockets in the bulk are terminated with
SCFA states of the electron/hole type around the b... | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
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] | 2,018 | en | Physics | [
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473aa8b1b292b9e07dd2d5b2167f43039f91a408 | subsection | 44 | 93 | Body | For N_3=(L_z/(2c_0))(1-H/H_1),
and N_1=(L_z/(2c_0))(1-H/H_0), the H-dependence of the resistance due to
the surface charge transport is given byR_{\rm s} = \frac{h}{e^2} \frac{c_0}{L_z} \frac{H_0 H_1}{H(H_1-H_0)}.The resistance is on the order of 1 \Omega at H=30 T [L_z=50\!\ \mu {\rm m},
c_0=0.67\!\ {\rm nm}, H_0=50 T... | {
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"doi": "10.4279/pip.110003",
"end": 429,
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"source_ref_id": "a1c056f54cb... | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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16843c66923bd7edadbdbd541085642bae1597b2 | subsection | 45 | 93 | Body | (REF ,)];f_j(z) &\equiv \big (\theta _{3,j}(z) -\theta _{2,j}(z) \big ) -
\big (\theta _{4,j}(z) -\theta _{1,j}(z) \big ) - 2\Theta _{-}, \\
g_j(z) &\equiv \big (\phi _{3,j}(z) +\phi _{2,j}(z) \big ) - \big (\phi _{4,j}(z) + \phi _{1,j}(z) \big ) - 2\Phi _{-}.When they vary slowly in z/c_0 and y_j/l \equiv 2\pi l j/L_x... | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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-... |
9a8acfa162230b93bdf094dc0e86c170149d1f23 | subsection | 46 | 93 | Body | (REF ) are restricted within the bulk
region and edge region respectively; L_y/2 \le |y_m|.When bosonized, the density operator in the bulk region is given by a linear
combination of the phase variables,
2\pi \rho _{a,\tau ,n}(z) \equiv \partial _z\phi _{a,n}(z)- \tau \partial _z \theta _{a,n}(z). Such
phase variables ... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 501,
"openalex_id": "https://openalex.org/W2997872173",
"raw": "A. L. Fetter and J. D. Walecka, Quantum Theory of Many-Particle Systems (Dover Publications, Mineola, New York, 2003).",
"source_ref_id": "a29114951da16300493c9... | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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... |
65a8e37ea5a94d8fa9456afab539377be6f84818 | subsection | 47 | 93 | in-plane resistance in the two pockets model ( | The in-plane resistance of graphite under the high magnetic field
stays almost constant in the field inside the high-field-side out-of-plane insulating
phase (H_0 < H < H_{c,2}) , , , , . Above the
re-entrant insulator-metal (IM) transition field (H_{c,2} < H), the resistance shows the normal
behaviour; R_{xx} increase... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "10.4279/pip.110003",
"end": 187,
"openalex_id": "https://openalex.org/W2950950081",
"raw": "B. Fauque, D. LeBoeuf, B. Vignolle, M. Nardone, C. Proust, and K. Behnia, Phys. Rev. Lett. 110, 266601 (2013).",
"source_ref_id": "a1c056f54cb... | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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c2c3db17995bd49fe85058466329f31e5c44412c | subsection | 48 | 93 | topological SNEI phase | The strong coupling phase discussed in Sec. VI (SNEI-II phase) consists of
two topologically distinct phases, depending on the sign of the umklapp term
n_{(2)}. A mean-field one-dimensional electronic Hamiltonian of the strong coupling phase
can be schematically described by the 2 by 2 Pauli matrices asH^{\rm snei2}_{\... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 1841,
"openalex_id": "",
"raw": "A. J. Heeger, S. A. Kivelson, J. R. Schrieffer, and W. P. Su, Rev. Mod. Phys. 60, 781 (1988).",
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"start": 1512
},
{
... | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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... |
db96b2eaba5518e839d4c151f748074e0f9ec856 | subsection | 49 | 93 | topological SNEI phase | The side surface is
subtended by z (\parallel H) and either x or
y (Fig. REF (A)). To be concrete, impose the periodic boundary conditions along
z and x, put a confining potential along y direction. The mass term
M in Eq. (REF ) depends on the coordinate y. In the vacuum
regime, |y| > L_y/2, the electron/hole pocket go... | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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0... |
5555d81495302999ca75210b1eee1d86fa4499d4 | subsection | 50 | 93 | topological SNEI phase | The non-zero bulk winding number leads to an in-gap end state
called as SSH (Su-Schrieffer-Heeger) state within the bulk excitonic gap
(left figure of Fig. REF ). The end states are
localized at the two open boundaries along z direction,
top and bottom surfaces. Due to the Landau degeneracy
associated with the in-plane... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 1449,
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"raw": "J. T. Chalker and P. D. Coddington, Journal of Physics C: Solid State Physics, 21 2665 (1988).",
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"start": 1125
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{
... | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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0215447976f3436f5c944a9fb9ded64587155fab | subsection | 51 | 93 | summary | Graphite under high magnetic field exhibits mysterious metal-insulator (MI)
transitions as well as insulator-metal (IM) re-entrant transitions. We discuss
these enigmatic electronic phase transitions in terms of perturbative RG
analyses of effective boson theories. We argue that the two
insulating phases in graphite un... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 473,
"openalex_id": "",
"raw": "Z. Zhu, R. D. MacDonald, A. Shekhter, B. J. Ramshaw, K. A. Modic, F. F. Balakirev, and N. Harrison, Scientific Reports, 7, 1733 (2017).",
"source_ref_id": "1cfc0e8da7dc090db262cb71ccd12cd037cd... | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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f61062a8e15c52e37a8030e5225c0b8bef1b7578 | subsection | 52 | 93 | natures of the `normal' metal phase and criticalities of metal-insulator transitions | Our theory regards the `normal' metallic phase in the graphite
experiment as decoupled Luttinger liquid (LL) phase, where we assume
that inter-chain electron-electron interactions only renormalize the Luttinger
parameters and Fermi velocities as in Eqs. (REF ,,REF ,).
Nonetheless, it could be possible that a fixed poin... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 801,
"openalex_id": "",
"raw": "R. Shankar, Physica A 177, 530 (1991).",
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{
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"end": 801,
... | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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81bb50957bd4aa3dad53c1edafc4569f9039229f | subsection | 53 | 93 | excitonic BCS-BEC crossover and nature of a transition between SNEI-I and SNEI-II phases | Our theory does not include an effect of an excitonic condensation, as emphasized
in Ref. . When H approaches H_0 from above (H > H_0),
electron-hole bound states formed by electron in (n,\sigma )=(0,\uparrow ) LL and hole in
(n,\sigma )=(-1,\downarrow ) LL could undergo the Bose-Einstein condensation. Such condensatio... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 91,
"openalex_id": "",
"raw": "Z. Zhu, R. D. MacDonald, A. Shekhter, B. J. Ramshaw, K. A. Modic, F. F. Balakirev, and N. Harrison, Scientific Reports, 7, 1733 (2017).",
"source_ref_id": "1cfc0e8da7dc090db262cb71ccd12cd037cdd... | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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5754ef308862c13d3107c1c73764967e94f4d62f | subsection | 54 | 93 | charge neutrality condition | Transverse conductivity \sigma _{xy} gives a precise information of electron carrier density
n_e and hole carrier density n_h in any given metal and semimetal under high magnetic field
through the following formula;\sigma _{xy} H = ec (n_e - n_h).e (>0) and c are the electron charge, and the speed of light respectively... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 638,
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"raw": "S. Uji, and J. S. Brooks, and Y. Iye, Physica B 246-247, 299 (1998).",
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"start": 469
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... | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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b1d16b5c9249e8039646605e79cfef4e92124a04 | subsection | 55 | 93 | charge neutrality condition | Under this assumption,
the explicit y-dependence of {\cal V} can be rewritten into
the y_c-dependence by use of
y\equiv (-i)(l^2/2)(\kappa _{+}-\kappa _{-})+y_c and y_c \equiv k_x l^2;\hat{\cal H}_{T}(k_z;\hat{\kappa }_{\pm },\hat{y})
= \hat{\cal H}^{\prime }_{T}(k_z,y_c;\hat{\kappa }_{\pm }).Eigenstates of such \hat{\... | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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97d414db7eb49d7081d34def77ef5b9e448d623b | subsection | 56 | 93 | charge neutrality condition | In the presence of a Hall voltage V_H in the +y direction, \mu _{+}-\mu _{-}=-eV_H.In graphite under the high field, the two electron/hole pockets in the bulk region
(n=0/n=-1 LLs with \uparrow and \downarrow spins) end up with
two electron/hole surface chiral Fermi arc (SCFA) states in the boundary region.
Namely,
E_{... | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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da37f91a4c745484ee11f93acf5a7e9c982a0d04 | subsection | 57 | 93 | charge neutrality condition | From the previous
Hall conductivity measurement , we typically have&n_e - n_h = 5 \times 10^{15} \!\ [{\rm cm}^{-3}], \\
&c_0 = 6.7 \times 10^{-10} \!\ [{\rm m}], \ \ l = 45 \times 10^{-10} \!\ [{\rm m}],for H=30 T and&n_e - n_h = -10 \times 10^{15} \!\ [{\rm cm}^{-3}], \\
&c_0 = 6.7 \times 10^{-10} \!\ [{\rm m}], \ \ ... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 505,
"openalex_id": "",
"raw": "K. Akiba, A. Miyake, H. Yaguchi, A. Matsuo, K. Kindo, and M. Tokunaga, J. Phys. Soc. Japan, 84, 054709 (2015).",
"source_ref_id": "ed37b05803a588d52499ba85a0afe950cbc28c3d",
"start": 0
... | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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-... |
c6642805293ce301fa6e38a263df618ce2136b81 | subsection | 58 | 93 | renormalization of Luttinger parameters and Fermi velocities | In the main text, we use the Hartree-Fock approximation for the four pockets model
or two pockets model, to introduce effective boson Hamiltonians, such as
Eqs. (REF ,,REF ,) with
Eqs. (REF ,,,,REF ,,)
or with Eqs. (REF ,,,).
Thereby, the bare kinetic energy part takes a quadratic form in the phase
variables, Eq. (), w... | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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... |
febaf1bdab657c1fa3df89912c40611cc955d2dd | subsection | 59 | 93 | renormalization of Luttinger parameters and Fermi velocities | With the Hartree-Fock
approximation, H_{\rm f} is bosonized into the followings,& H_{\rm f} = \sum _{a}\sum _{j,m} \int \!\ dz \sqrt{2\pi } l_{0,z}
\big (V^{(1),a}_{j-m,0} - V^{(1),a}_{0,j-m} \big ) \\
& \hspace{28.45274pt} \times \big (\rho _{a,+,j} \rho _{a+,m} + \rho _{a,-,j} \rho _{a,-,m} \big ) \\
& \ \ \ + \sum _... | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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... |
5d92731555fd8f1847584c5950b951537343586a | subsection | 60 | 93 | renormalization of Luttinger parameters and Fermi velocities | V).The first two terms in Eq. (REF ) lead to the renormalizations of the Luttinger
parameters and Fermi velocities. To quantify them, we employ a
gradient expansion with respect to the chain index,\rho _{a,\tau ,m} &= \rho _{a,\tau ,j} + (y_m-y_j) \partial _{y_j} \rho _{a,\tau ,j} \\
& \ \ \ \ + \frac{1}{2} (y_m-y_j)^2... | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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0.03351440280675888,
-0.012850239872932434,
0.... |
b5fe1b4700acb2e7450eeb78ba4ff4b6dce170b9 | subsection | 61 | 93 | derivation of renormalization group (RG) equations | In the main text, we employ one-loop RG equations, Eqs. (REF ,,), and
clarify possible insulating phases as well as natures of
T=0 metal-insulator and insulator-metal transition points in graphite
under the high field. We solve the RG equations numerically
to obtain a finite temperature phase diagram as in Fig. REF .
T... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "10.1093/acprof:oso/9780198525004.001.0001",
"end": 425,
"openalex_id": "https://openalex.org/W1542921455",
"raw": "T. Giamarchi, Quantum Physics in One Dimension (Clarendon, Oxford 2003).",
"source_ref_id": "f1fb66bcca2e0d68052dc5978a... | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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0.0... |
92ce012e9930edf8c04154b5f835dd71e9fdb5a1 | subsection | 62 | 93 | derivation of renormalization group (RG) equations | We decompose
the field operators into a slow mode and a fast mode in the momentum space,\phi _{j,a}({r}) &= \phi ^{<}_{j,a}({r}) + \phi ^{>}_{j,a}({r}), \\
\phi ^{<}_{j,a}({r}) & = \frac{1}{\beta L_z} \sum _{i\omega _n} \sum _{|k_z|<\Lambda ^{\prime }}
e^{i{q}\cdot {r}} \phi _{j,a}({q}), \\
\phi ^{>}_{j,a}({r}) & = \fr... | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
0.005360044073313475,
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0.048496000468730927,
-0.04071344435214996,
-0.013451612554490566,
0.01846449449658394,
0.016... |
fcc54d182d5674b35ea800f41609c8bad62da627 | subsection | 63 | 93 | derivation of renormalization group (RG) equations | We do so up to the second order in S_{1};Z &= Z^{>}_{0} \int {\cal D}\phi ^{<} {\cal D}\theta ^{<} e^{-S^{<}_{0}} e^{- \langle S_{U} \rangle _{>}}
+ {\cal O}(S^3_{i}),where\langle S_{U} \rangle _{>} &= \langle S_{1} \rangle _{>} - \frac{1}{2} \big (\langle S^2_{1} \rangle _{>}
- \langle S_{1} \rangle ^2_{>}\big ),and\l... | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
-0.009745333343744278,
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0.043682292103767395,
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0.040507618337869644,
0.012156864628195763,
... |
85523a686f4ac412100e40104ae7a44155d601a5 | subsection | 64 | 93 | tree-level renormalization | \langle S_1\rangle _{>} in Eq. | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
-0.009277785196900368,
0.08697923272848129,
-0.025834359228610992,
-0.024125292897224426,
-0.03001546487212181,
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0.011299670673906803,
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-0.026627853512763977,
0.02542235143482685,
0.0049173785373568535,
0.0056498353369534016,
... |
0b2ad2379e1386c287758c54af783748f6a89f7a | subsection | 65 | 93 | tree-level renormalization | (REF ) gives the tree-level renormalization to the interchain
interactions;\Big \langle \int _{0}^{\beta } H_{{\rm u},2} d\tau \Big \rangle _{>}
&= \frac{1}{2} \int d^2{r} \sum _{j,m} \sum _{\epsilon =\pm }
\sum _{\eta =\pm } \\
&\hspace{-14.22636pt} M^{(2)}_{j-m} \sigma ^{\eta }_{j} \tau ^{\eta }_{m} e^{i\epsilon M^{\... | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
-0.023556072264909744,
0.01810949295759201,
-0.0342661514878273,
-0.06932564079761505,
-0.01583627052605152,
0.003674915060400963,
0.010572770610451698,
0.0029921855311840773,
0.0017297082813456655,
0.02268644981086254,
-0.037103865295648575,
0.036920785903930664,
-0.004729521926492453,
0.... |
e2201413d263554da055a10f8e7d50bc8d34cab6 | subsection | 66 | 93 | one-loop level renormalization | \langle S^2_{1}\rangle _{>,c} \equiv \langle S^2_{1} \rangle _{>} - \langle S_{1} \rangle ^2_{>}
in Eq. (REF ) gives the one-loop level renormalization
to the interchain interactions. The one-loop renormalization comprises of products between
different interactions;S_{1} & = S_M + S_H + S_{\overline{H}} + \cdots , \\
... | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
-0.027804557234048843,
0.057867661118507385,
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-0.017366401851177216,
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-0.006024066358804703,
0.027590909972786903,
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0.00402876129373908,
-0.04468262568116188,
0.01883140578866005,
-0.00432252511382103,
0.... |
a2e83e0fe339a836adfa53a750b96184dc251969 | subsection | 67 | 93 | one-loop level renormalization | (REF ) with i=m,n and j\ne m,n and/or those terms with i\ne m,n and j=m,n.The one-loop renormalization in Eq. (REF ) generates S_M, S_H and S_{\overline{H}}
as well as other types of cosine terms. Nonetheless, tree-level scaling dimensions of all the
other cosine terms thus generated are negatively much larger than tho... | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
-0.025103440508246422,
0.03311517462134361,
-0.04269873723387718,
-0.03299309313297272,
0.0035633151419460773,
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0.05182448774576187,
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-0.0006366468733176589,
-0.03976873308420181,
0.014451646246016026,
-0.017457954585552216,
... |
91fb51ffb2878ca767673c8f92b20c9282e11037 | subsection | 68 | 93 | one-loop level renormalization | (REF ) with I=J=M reduces to\langle S^2_M \rangle _{>,c}
& = \frac{1}{4} \int d^2{r} \int d^2{r}^{\prime }
\sum ^{j\ne n}_{j,n} \sum _{i=m} \sum _{\epsilon ,\eta } \tau ^{\eta }_{j} \tau ^{\eta }_{n} M^{(2)}_{i-j}
M^{(2)}_{i-n} \\
&\hspace{-28.45274pt} e^{i\epsilon (M^{\eta ,<}_{ij}({r})
- M^{\eta ,<}_{in}({r}^{\prime ... | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
-0.007312842179089785,
0.06951968371868134,
-0.024765243753790855,
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-0.027847547084093094,
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0.021728716790676117,
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0.022918913513422012,
-0.02334616333246231,
0.0... |
d2093e926ca744eb42cb0367ecc8f396d0568569 | subsection | 69 | 93 | one-loop level renormalization | For the first term with j\ne n, we replace
\cos [Q^{23,<}_{\eta ,i}({r}) - Q^{23,<}_{\eta ,i}({r}^{\prime })]
by its normal ordering with use of a formula
\cos \Phi = :\cos \Phi : \exp [-\langle \Phi ^2\rangle /2] , .
Within the normal order, we employ a Taylor expansion with respect to small
{r}^{\prime }-{r}. At the ... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "10.1093/acprof:oso/9780198525004.001.0001",
"end": 217,
"openalex_id": "https://openalex.org/W1542921455",
"raw": "T. Giamarchi, Quantum Physics in One Dimension (Clarendon, Oxford 2003).",
"source_ref_id": "f1fb66bcca2e0d68052dc5978a... | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
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0.03620263561606407,
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-0.007089428137987852,
-0.03112022392451763,... |
694fe3040b815779b083171fe6fcde1dd39888f0 | subsection | 70 | 93 | one-loop level renormalization | (REF ) in combination
with Eqs (REF ,REF ) dictates
that \overline{H}^{(2)}_{j-n} acquires the following one-loop renormalization,\frac{d \overline{H}^{(2)}_{j-n}}{d\ln b} = \cdots -\frac{C_{23}}{2} \sum _{i} M^{(2)}_{i-j} M^{(2)}_{i-n} + \cdots .Since M^{(2)}_{i-j} = M^{(2)}_{j-i}, this is nothing
but the first term o... | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
-0.05675118789076805,
0.05592738091945648,
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0.005587398540228605,
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0.030129998922348022,
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0.0013415477005764842,
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0.010213688015937805,
-0.0030663947109133005,
... |
d2942d9258cad8480342a0702c2070c58aa53f2d | subsection | 71 | 93 | evaluation of | C_{ab} is defined in Eq. (REF ). Let us first calculate the integrand in Eq. (REF );&\big \langle Q^{ab,>}_{\eta ,i}({r}) Q^{ab,>}_{\eta ,i}({r}^{\prime }) \big \rangle _{>}
= \\
& \frac{1}{(\beta L_z)^2} \sum _{\Lambda ^{\prime }<|k_z|<\Lambda }
\sum _{i\omega _n} e^{i{q}({r}-{r}^{\prime })}
\big \langle {Q^{ab,>}_{\e... | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
0.010790728032588959,
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0.021871445700526237,
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0... |
883cdab366783d1da840a3276796c2645fc52c44 | subsection | 72 | 93 | evaluation of | The
gaussian integrals over the fast/slow modes lead to&\langle \phi ^{*}_{c,i}({q}) \phi _{c,i}({q}) \rangle _{>/<} = \frac{\beta L_z \pi u_{c} K_c}{u^2_c k^2_z + \omega ^2_n}, \\
&\langle \theta ^{*}_{c,i}({q}) \theta _{c,i}({q}) \rangle _{>/<} = \frac{\beta L_z \pi u_{c} K^{-1}_c}{u^2_c k^2_z + \omega ^2_n},
\\
& \l... | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
-0.03336237370967865,
0.048685260117053986,
-0.05637722462415695,
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0.035346414893865585,
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0.017551111057400703,
-0.0034644368570297956,
... |
8bd2c55da3610dadd4cb372bc81391143a31ee46 | subsection | 73 | 93 | evaluation of | In the right hand side,
M_{c}({r}), F^{\prime }_{2,c}({r}), F_{1,c}({r}) and F_{2,c}({r})
are evaluated
at the zero temperature. Substituting these into Eq. (REF ), we obtain
C_{ab} at T=0 as,&C_{ab,T=0} = \sum _{c=a,b} \int ^{\infty }_{-\infty } d\tau \int ^{\infty }_{-\infty } dz
\bigg (\frac{\alpha ^2}{z^2+y^2_a}\bi... | {
"cite_spans": []
} | 10.1103/PhysRevB.98.205121 | 1802.10253 | Theory of metal-insulator transitions in graphite under high magnetic
field | [
"Zhiming Pan",
"Xiao-Tian Zhang",
"Ryuichi Shindou"
] | [
"cond-mat.mes-hall",
"cond-mat.dis-nn",
"cond-mat.str-el"
] | 2,018 | en | Physics | [
-0.01631159707903862,
0.009040805511176586,
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0.00285719963721931,
0.019180240109562874,
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0.010070770978927612,
0.037078745663166046,
0.027969276532530785,
0.04721055179834366,
-0.013412435539066792,
-0.014625505544245243,
0.008392308838665485,
-0.... |
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