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Majorana vortex phases have been extensively studied in topological materials with conventional superconducting pairing. Inspired by recent experimental progress in realizing time-reversal invariant higher-order topological insulators (THOTIs) and inducing superconducting proximity effects, we investigate Majorana vor... |
Explorations of the order-disorder transformation in vortex matter in single crystals of tetragonal structured (c/a $\sim$3) borocarbide superconductors, $YNi_2B_2C$ and $LuNi_2B_2C$, reveal that vortex arrays experience different effective pinning in different crystallographic directions. We surmise that correlation ... |
We present a detailed study of vortex core spectroscopy in slightly overdoped Bi2Sr2CaCu2O8 using a low temperature scanning tunneling microscope. Inside the vortex core we observe a four-fold symmetric modulation of the local density of states with an energy-independent period of (4.3\pm 0.3)a0. |
We present an extensive irradiation study involving five state-of-the-art Nb3Sn wires which were subjected to sequential neutron irradiation up to a fast neutron fluence of 1.6 * 10^22 m^-2 (E > 0.1 MeV). The volume pinning force of short wire samples was assessed in the temperature range from 4.2 to 15 K in applie... |
Recent developments in theory, synthesis, and experimental probes of quantum systems have revealed many suitable candidate materials to host chiral superconductivity. Chiral superconductors are a subset of unconventional superconductors which break time-reversal symmetry. |
We study experimentally and theoretically, the reorganization of superconducting vortices driven by oscillatory forces near the plastic depinning transition. We show that the system can be taken to configurations that are tagged by the shaking parameters but keep no trace of the initial conditions. |
Some topological insulators become superconducting when doped with Cu and Pd. Superconductivity in a non-superconductor may be induced by proximity effect: i.e. Contacting a non-superconductor with a superconductor. |
Superconductivity has continued to be a fascinating phenomenon ever since its discovery in 1911. The magnitude of the transition temperature, Tc, provides valuable insight into the underlying physics. |
A 63Cu and 139La NMR/NQR study of superconducting (Tc=7 K) La1.94Sr0.06CuO4 single crystal is reported. Coexistence of spin-glass and superconducting phases is found below ~5 K from 139La NMR relaxation. |
It was suggested by Rasolt and Tešanović that the Landau level quantization in isotropic superconductors could enhance superconductivity in a very strong magnetic field, above the upper critical field ($H_{c2}$). We derive a generalized Harper equation for superconducting systems, and show that a similar reentrant beh... |
A novel scanning probe technique is presented: Scanning microSQUID Force microscopy (SSFM). The instrument features independent topographic and magnetic imaging. |
It is shown that the magnetic energy of a quantum current, contrary to the classical case, is essentially negative. Since this result allows to escape a famous theorem by Bloch, it can be expected that, under appropriate conditions, the ground state of a quantum conductor may be characterized by a spontaneous current.... |
We present a quantitative analysis of an escape rate for switching from the superconducting state to a resistive one in series arrays of globally coupled Josephson junctions. A global coupling is provided by an external shunting impedance. |
Recently the influence of antisymmetric spin-orbit coupling has been studied in novel topological superconductors such as half-Heuslers and artificial hetero-structures. We investigate the effect of Rashba and/or Dresselhaus spin-orbit couplings on the band structure and topological properties of a two-dimensional non... |
To understand the chemical reaction at the interface of materials, we performed a transmission electron microscopy (TEM) observation in four types of Fe(Te,Se) superconducting thin films prepared on different types of substrates: CaF2 substrate, CaF2 substrate with a CaF2 buffer layer, CaF2 substrate with a FeSe buffer... |
I consider superconducting condensates which become incompressible in the infinite gap limit. Classical 2D incompressible fluids possess the dynamical symmetry of area-preserving diffeomorphisms. |
We use high-resolution inelastic neutron scattering to study the low-temperature magnetic excitations of electron-doped superconducting Pr$_{0.88}$LaCe$_{0.12}$CuO$_{4-\delta}$ ($T_c=21\pm 1$ K) over a wide energy range (4 meV$\le\hbar\omega\le 330$ meV). The effect of electron-doping is to cause a wave vector ($Q$) b... |
Measurements of conductance spectra in a superconductor - topological insulator - normal metal thin film junctions of NbN-$\rm Bi_2Se_3$-Au are reported. Junctions with ex-situ and in-situ prepared $\rm NbN-Bi_2Se_3$ interfaces were studied. |
The key ingredients in any superconductor are the Cooper pairs, in which two electrons combine to form a composite boson. In all conventional superconductors the pairing strength alone sets the majority of the physical properties including the superconducting transition temperature T$_c$. |
High-temperature superconductors are reviewed in light of the fact that their binding energy is ionic. The conducting electrons are dominated by the much larger energy scales coming from ligand Coulomb integrals, including the out-of-plane ones, which are responsible for the Fermi arcs. |
We present an electronic circuit whose dynamical properties emulate those of a resistively and capacitively shunted Josephson junction (RCSJ). We show how it reproduces the switching properties of a shunted junction and its dependence on the quality factor. |
We consider the current density distribution function of a flux creep regime in type-II superconductors by mapping the flux creep process to the dynamics of a model with a self-organized criticality. We use an extremal Robin Hood type model which evolves to Been's type critical state to treat magnetic flux penetra... |
Superconductor with a spatially-modulated order parameter is known as Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconductor. Using the time-dependent Ginzburg-Landau (TDGL) formalism we have theoretically studied the temporal behaviour of the equal-time correlation function, or the structure factor, of a FFLO superco... |
Cuprates currently hold the record for the highest temperature superconductivity at ambient pressure, but the microscopic understanding of these materials remains elusive. Here we utilize nuclear magnetic resonance (NMR) data of planar oxygen and copper from essentially all hole-doped cuprates to provide a universal p... |
The quantum master equation is introduced for the density matrix representing Bogoliubov-BCS quasiparticles. A constraint to relate the loss and gain factors is taken into account to preserve the form of the density matrix. |
In this report, we describe the proximity effect which arises when a quasicrystal is placed in contact with a superconductor. We consider the simplest known model of a quasicrystal, the 1D Fibonacci chain, for which all states are known to be critical. |
Understanding the interplay between individual magnetic impurities and superconductivity is crucial for bottom-up construction of novel phases of matter. For decades, the description by Yu, Shiba and Rusinov (YSR) of single spins in a superconductor and its extension to include quantum effects has proven highly succes... |
Magnetic monopoles, that are particle-like field configurations with which one can associate a topological charge, widely exist in various three dimensional condensate systems. In this paper, by making use of \emph{Duan}'s topological current theory, we obtain the charge density of magnetic monopoles and their bif... |
To elucidate the superconductor to metal transition at the end of superconducting dome, the overdoped regime has stepped onto the center stage of cuprate research recently. Here, we use scanning tunneling microscopy to investigate the atomic-scale electronic structure of overdoped trilayer Bi-2223 and bilayer Bi-2212 ... |
We have performed high-resolution angle-resolved photoemission spectroscopy on heavily electron-doped non-superconducting (SC) BaFe$_{1.7}$Co$_{0.3}$As$_2$. We find that the two hole Fermi surface pockets at the zone center observed in the hole-doped superconducting Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$ are absent or very s... |
By integrating a set of model equations for Josephson ladder subjected to a uniform transverse bias current we have found almost all of the kinds of breathers described in recent experiments, and closely reproduced their voltage-current characteristics and switching behaviour. Our main result is that a chaotic transie... |
Since the announcement in 2011 of the Materials Genome Initiative by the Obama administration, much attention has been given to the subject of materials design to accelerate the discovery of new materials that could have technological implications. Although having its biggest impact for more applied materials like bat... |
We managed to synthesize non-linear YBa2Cu3Ox whiskers, i.e. half loops or kinked shapes, which are promising candidates for solid-state devices based on the intrinsic Josephson effect and with improved electrical connections. We report on a complete characterization of their structural properties via synchrotron nano... |
F-substituted NdOBiS2 superconducting single crystals were grown using CsCl/KCl flux. This is the first example of the single-crystal growth of a BiS2-based superconductor. |
From the sixties a deep and surprising connection has followed the development of superconductivity and quantum field theory. The Anderson-Higgs mechanism and the similarities between the Dirac and Bogoliubov-de Gennes equations are the most intriguing examples. |
A topological transition in high-temperature superconductors FeTe1-xSex, occurring at a critical range of Se concentration x, underlies their intrinsic topological superconductivity and emergence of Majorana states within vortices. Nonetheless, the influence of Se concentration and distribution on the electronic state... |
We consider the evolution of d-wave pairing, mediated by nearly critical spin fluctuations, with the coupling strength. We show that the onset temperature for pairing, T*, smoothly evolves between weak and strong coupling, passing through a broad maximum at intermediate coupling. |
Strongly interacting systems are characterized by heavily dressed entities with internal degrees of freedom, which, on a local level, can be described in terms of coherent quantum states. We examine the modification of these local coherent quantum states when such entities condense into a macroscopic coherent quantum ... |
Excellent fits of the tunneling density of states in disordered superconductors can be often achieved making use of the phenomenological Dynes formula. However, no consistent derivation of this formula has been available so far. |
We have performed magnetic susceptibility measurements in Mo$_{(1-x)}$Ge$_x$ amorphous thin films biased with an electrical current using anisotropic coils. We tested the symmetry of the vortex response changing the relative orientation between the bias current and the susceptibility coils. |
Superconductor-topological insulator-superconductor Josephson junctions have been fabricated in order to study the width dependence of the critical current, normal state resistance and flux periodicity of the critical current modulation in an external field. Previous literature reports suggest anomalous scaling in top... |
The magnetic-field-tuned quantum superconductor-insulator transitions of disordered amorphous indium oxide films are a paradigm in the study of quantum phase transitions, and exhibit power-law scaling behavior. For superconducting indium oxide films with low disorder, such as the ones reported on here, the high-field ... |
We examine the discontinuous first-order superfluid $^3$He A to B transition in the vicinity of the polycritical point (2.232 mK and 21.22 bar). We find path-dependent transitions: cooling at fixed pressure yields a well defined transition line in the temperature-pressure plane, but this line can be reliably crossed b... |
We show that in the presence of a pseudogap, the spectral function in the superconducting state of the underdoped cuprates exhibits additional Bogoliubov quasiparticle peaks at both positive and negative energy which are revealed by the particle-hole asymmetry of the pseudogapped energy bands. This provides direct inf... |
We show that dilute magnetic impurities in a conventional superconductor give origin to an odd-frequency component of superconductivity, manifesting itself in Yu-Shiba-Rusinov bands forming within the bulk superconducting gap. Our results are obtained in a general model solved within the dynamical mean field theory. |
We have performed flux noise and AC-susceptibility measurements on two 400 nm thick MgB$_2$ films. Both measurement techniques give information about the vortex dynamics in the sample, and hence the superconducting transition, and can be linked to each other through the fluctuation-dissipation-theorem. |
The in-plane thermal conductivity of iron-based superconductor Ca$_{10}$(Pt$_{4-\delta}$As$_8$)((Fe$_{1-x}$Pt$_{x}$)$_2$As$_2$)$_5$ single crystal (``10-4-8", $T_c$ = 22 K) was measured down to 80 mK. In zero field, the residual linear term $\kappa_0/T$ is negligible, suggesting nodeless superconducting gaps in th... |
The electronic structure of BaTi2As2O, a parent compound of the newly discovered titanium-based oxypnictide superconductors, is studied by angle-resolved photoemission spectroscopy. The electronic structure shows multi-orbital nature and possible three-dimensional character. |
We present self-consistent calculations of the multi-gap structure measured in some Fe-based superconductors. These materials are known to have structural disorder in real space and a multi-gap structure due to the $3d$ Fe-orbitals contributing to a complex Fermi surface topology with hole and electron pockets. |
The realization of Majorana corner modes generally requires unconventional superconducting pairing or $s$-wave pairing. However, the bulk nodes in unconventional superconductors and the low $T_c$ of $s$-wave superconductors are not conducive to the experimental observation of Majorana corner modes. |
Rare-earth infinite-layer nickelates represent an emerging class of unconventional superconductors, with materials synthesis largely limited to early lanthanide compounds. Here, we report the synthesis and characterization of phase-pure superconducting samarium-based infinite-layer nickelate thin films, including the ... |
A microscopic theory for the spin triplet Cooper pairing in non-centrosymmetric superconductors like CePt_3Si and CeTSi_3 (T=Rh, Ir) is presented. The lack of inversion symmetry leads to new anomalous spin fluctuations which stabilize the triplet part in addition to the singlet part originating from the centrosymmetri... |
We present time-of-flight inelastic neutron scattering measurements of $La_{1.965}Ba_{0.035}CuO_{4}$ (LBCO), a lightly doped member of the high temperature superconducting La-based cuprate family. By using time-of-flight neutron instrumentation coupled with single crystal sample rotation we obtain a four-dimensional d... |
At zero temperature, a Josephson junction coupled to an ohmic environment displays a quantum phase transition between superconducting and insulating phases, depending whether the resistance of the environment is below or above the resistance quantum. At finite temperature, this so-called Schmid transition turns into a... |
The discovery of 80 K superconductivity in bilayer La$_3$Ni$_2$O$_7$ at pressures greater than 14 GPa presents a unique opportunity to study a novel class of high-temperature superconductors. Therefore, other bilayer nickelate following the classical ($T^{4+}$) Ruddlesden-Popper (RP) series of Sr$_3$Ni$_2$O$_7$ would ... |
Transitions between states with continuous (called as classical state) and discrete (called as quantum state) spectrum of permitted momentum values is considered. The persistent current can exist along the ring circumference in the quantum state in contrast to the classical state. |
It is widely accepted that: (i) the angle-resolved photoemission spectroscopy (ARPES) data produce evidences for the opening of a d-wave pairing gap in cuprates compounds described at low energies and temperatures by a BCS theory, and |
Ising superconductivity, observed experimentally in NbSe$_{2}$ and similar materials, has generated tremendous interest. Recently, attention was called to the possible role that spin fluctuations (SF) play in this phenomenon, in addition to the dominant electron-phonon coupling (EPC); the possibility of a predominantl... |
We fabricated (Ba,Na)Fe2As2 superconducting wires using the powder-in-tube method and hot isostatic pressing. By improving powder synthesis processes compared with previous studies, highly pure raw materials for the wire fabrication were obtained. |
Resistivity and irreversible magnetisation data taken within the high-magnetic-field CDWx phase of the quasi-two-dimensional organic metal alpha-(BEDT-TTF)2KHg(SCN)4 are shown to be consistent with a field-induced inhomogeneous superconducting phase. In-plane skin-depth measurements show that the resistive transition ... |
Quantum processing units (QPUs) based on superconducting Josephson junctions promise significant advances in quantum computing. However, they face critical challenges. |
We take advantage of the connection between the free carrier optical conductivity and the glue function in the normal state, to reconstruct from the infrared optical conductivity the glue-spectrum of ten different high-Tc cuprates revealing a robust peak in the 50-60 meV range and a broad con- tinuum at higher energies... |
Researchers have studied the normal-superconducting phase transition in the high-$T_c$ cuprates in a magnetic field (the vortex-glass or Bose-glass transition) and in zero field. Often, transport measurements in "zero field" are taken in the Earth's ambient field or in the remnant field of a magnet. |
Conformal crystals are non-uniform structures created by a conformal transformation of regular two-dimensional lattices. We show that gradient-driven vortices interacting with a conformal pinning array exhibit substantially stronger pinning effects over a much larger range of field than found for random or periodic pi... |
We argue that recently observed superconductivity-induced blue shift of the plasma frequency $\delta \omega_{pl}$ in $Bi_2Sr_2CaCu_2O_{8+\delta}$ is related to the change in the integrated dynamical structure factor associated with the development of the spin resonance below $T_c$. We show that the magnitude of $\delt... |
The minimal theory of spin of gapless quasiparticles coupled to fluctuating vortex defects in the phase of the d-wave superconducting order parameter at T=0 is studied. With the proliferation of the vortex loops the theory reduces to the previuosly studied QED3, with its concomitant spin-density-wave (chiral) instabil... |
Impurities with the pronounced forward scattering (FS impurities) change analytical properties of the quasiparticle Green's function substantially compared to the isotropic scattering. By assuming that the superconducting pairing is due to the forward E-P scattering (FEP pairing) it is shown that the critical temp... |
We theoretically propose a mechanism to realize the superconducting diode effect (SDE): The current can generate a magnetic field, affecting the magnetic moment of magnetic impurity. When the connection region of the Josephson junction is coupled with the magnetic impurity, the supercurrents in positive and negative d... |
We study the phase transition of a star-shaped superconductor, which covers smoothly the range from zero to two dimensions with respect to the superconducting coherence length. Detailed measurements and numerical calculations show that the nucleation of superconductivity in this device is very inhomogeneous, resulting... |
After decades of fundamental research, unconventional superconductivity has recently been demonstrated in rare-earth infinite-layer nickelates. The current view depicts these systems as a new category of superconducting materials, as they appear to be correlated metals with distinct multiband features in their phase d... |
A systematic study of I-V characteristic curves for RuSr2GdCu2O8 [Ru-(1212)] is presented, with magnetic fields up to 3 T and 5 K<T<30 K, in the region of the superconducting transition. The activation energy E_{a}(H,T) for flux line depinning was determined by fitting the nonlinear region of the curves using th... |
Various properties of mesoscopic two-dimensional Josephson junction arrays are reviewed. Particular attention is paid to structure of the topological excitations, charges and vortices, which are shown to be dual to each other. |
We identified quasiparticle states at well-defined energies inside the superconducting gap of the electron system at the LaAlO$_3$-SrTiO$_3$ interface using tunneling spectroscopy. The states are found only in a number of samples and depend upon the thermal-cycling history of the samples. |
Motivated by the desire to investigate the fundamental relationship between impurity-induced states and the sign change of the superconducting order parameter, as well as to explore the impurity effects in Ruddlesden-Popper nickelate superconductors with interlayer pairing, we employ the $T$-matrix approach to study si... |
Topological superconductors are novel classes of quantum condensed phases, characterized by topologically nontrivial structures of Cooper pairing states. On the surfaces of samples and in vortex cores of topological superconductors, Majorana fermions, which are particles identified with their own anti-particles, appea... |
We present a formulation of the quasiclassical theory of junctions between itinerant antiferromagnets (AF) and s-wave (sSC) and d-wave superconductors (dSC). For the simplest two-sublattice antiferromagnet on a bipartite lattice, we derive Andreev-type equations and show that their solutions lead to a novel channel of... |
In this article, we report the occurrence of superconductivity in Sn0.4Sb0.6 single crystal at below 4K. Rietveld refined Powder XRD data confirms the phase purity of as grown crystal, crystallizing in rhombohedral R-3m space group with an elongated (2xc) unit cell in c-direction. |
The possible stable singular vortex (SV) and half-quantum vortex (HQV) of the superfluid $^3$He-A phase confined in restricted geometries are investigated. The associated low-energy excitations are calculated in connection with the possible existence of Majorana zero modes obeying non-Abelian statistics. |
We analyze properties of bifurcation quantum detectors based on weakly nonlinear superconducting resonance circuits, in particular, with application to quantum readout. The developed quantitative description demonstrates strong influence of higher harmonics on their characteristics. |
The temperature dependence of the real and imaginary parts of magnetic susceptibility of YBa2Cu3O7-{\delta} superconducting thin films were researched at the electron irradiation with the energy of 2{\cdot}10<4> eV in the magnetic field of -2.4{\cdot}10<4> A/m at the temperature T=77 K. It is retrieved that... |
We report on novel superconducting characteristics of the heavy fermion (HF) superconductor CePt3Si without inversion symmetry through 195Pt-NMR study on a single crystal with T_c= 0.46 K that is lower than T_c= 0.75 K for polycrystals. We show that the intrinsic superconducting characteristics inherent to CePt3Si can... |
The screening currents induced in a superconducting film by a magnetic annulus whose magnetization is perpendicular to the superconductor are calculated. We show that close to the superconductor transition temperature $T_c$ particular values of the magnetization and radii of the annulus make the creation of supercondu... |
We survey recent experimental results including quantum oscillations and complementary measurements probing the electronic structure of underdoped cuprates, and theoretical proposals to explain them. We discuss quantum oscillations measured at high magnetic fields in the underdoped cuprates that reveal a small Fermi s... |
Recent experiments on the spin-spin relaxation time in high-Tc cuprate superconductors are discussed on the basis of the BCS-RPA theory. |
We have studied the isothermal magnetization $M(H)$ of CeCo(In$_{1-x}$Cd$_x$)$_5$ with $x$ = 0.0075 and 0.01 down to 50 mK. Pronounced field-history dependent phenomena occur in the coexistence regime of the superconducting and antiferromagnetic phases. |
Superconducting devices are prone to reduced performance caused by impurities and defects along the edges of their wires, which can lead to local current crowding. In this study, we explored the use of helium ion irradiation to modify the lattice structure of the superconducting material to change its intrinsic proper... |
We investigate the realization of a topological superconductor in a generic bucked honeycomb system equipped with four types of mass-generating terms, where the superconductor gap is introduced by attaching the honeycomb system to an $s$-wave superconductor. Constructing the topological phase diagram, we show that Maj... |
The coexistence of magnetism and superconductivity in the isovalent-P-substituted BaFe$_2$(As$_{1-x}$P$_x$)$_2$ has been investigated microscopically by $^{31}$P-NMR measurements. We found that superconducting (SC) transition occurs in a magnetic region with static ordered moments and that the moments are reduced belo... |
While 203 K high temperature superconductivity in H3S has been interpreted by BCS theory in the dirty limit here we focus on the effects of hydrogen zero-point-motion and the multiband electronic structure relevant for multigap superconductivity near Lifshitz transitions. We describe how the topology of the Fermi surf... |
We report quantum oscillation measurements in SrFe2As2 - which is an antiferromagnetic parent of the iron-arsenide family of superconductors - known to become superconducting under doping and the application of pressure. The magnetic field and temperature dependences of the oscillations between 20 and 55 T in the liqu... |
Synchronization between the internal dynamics of the superconducting phase in a Josephson junction (JJ) and an external ac signal is a fundamental physical phenomenon, manifesting as constant-voltage Shapiro steps in the current-voltage characteristic. Mathematically, this phase-locking effect is captured by the Resis... |
Superconductivity has been observed in doped SrTiO$_3$ at charge-carrier densities below 10$^{18}$ cm$^{-3}$, where the density of states at the Fermi level of the itinerant electrons is several orders of magnitude lower than that of conventional metals. In terms of the Bardeen-Cooper-Schrieffer description, this impl... |
For a Ba_{0.63}K_{0.37}BiO_3 single crystal with T_c=31 K, H_{c1}=750 Oe at 5 K, and dimensions 3x3x1 mm^3, the temperature and field dependences of magnetic hysteresis loops have been measured within 5-25 K in magnetic fields up to 6 Tesla. The critical current density is J_c(0)=1.5 x 10^5 A/cm^2 at zero field and 1 ... |
Sr$_{2}$RuO$_{4}$ is one of the most promising candidates of a topological superconductor with broken time-reversal symmetry, because a number of experiments have revealed evidences for a spin-triplet chiral $p$-wave superconductivity. In order to clarify the time-reversal symmetry of Sr$_{2}$RuO$_{4}$, we introduce a... |
The ${}^{11}$B NMR spectra in polycrystalline MgB$_2$ were measured for several magnetic fields (1.97 T and 3.15 T) as a function of temperature from 5 K to 40 K. The composite spectra in the superconducting state can be understood in terms of anisotropy of the upper critical field, $\gamma_{H}$, which is determined to... |
In this study, we fabricate 5-30-nm-thick films of FeSe/STO using pulsed laser deposition (PLD). The grown films exhibit superconductivity with an onset $T_{\mathrm{c}}$ that is much higher than that of bulk FeSe under ambient pressure. |
For decades, the conventional view is that an s-wave BCS superfluid can not support uniform spin polarization due to a gap $\Delta$ in the quasiparticle excitation spectrum. We show that this is an artifact of the dismissal of quasiparticle interactions $V_{qp}^{}$ in the conventional approach at the outset. |
The electronic structure of nearly optimally-doped novel superconductor LaO$_{1-x}$F$_x$BiS$_2$ (${\it x}$ = 0.46) was investigated using angle-resolved photoemission spectroscopy (ARPES). We clearly observed band dispersions from 2 to 6 eV binding energy and near the Fermi level (${\it E}_{\rm F}$), which are well re... |
Superconductivity has been first observed in TlNi$_2$Se$_2$ at T$_C$=3.7 K and appears to involve heavy electrons with an effective mass $m^*$=14$\sim$20 $m_b$, as inferred from the normal state electronic specific heat and the upper critical field, H_${C2}$(T). Although the zero-field electronic specific heat data, $... |
For a spinless quantum particle in a one-dimensional box or an electromagnetic wave in a one-dimensional cavity, the respective Dirichlet and Neumann boundary conditions both lead to non-degenerate wave functions. However, in two spatial dimensions, the symmetry of the box or microstrip antenna is an important feature... |
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