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We investigate Josephson junctions with superconducting ferropnictides, both in the diffusive and ballistic limit. We focus on the proposed $s_\pm$-wave state, and find that the relative phase shift intrinsic to the $s_\pm$-wave state may provide 0-$\pi$ oscillations in the Josephson current. |
The effects of planar hole content, p, on the static magnetic susceptibility, chi(T), of Y1-xCaxBa2Cu3O7-delta polycrystalline samples were investigated over a wide range of Ca (x) and oxygen contents. Non-magnetic Ca2+, in the 3p6 state, induces a Curie-like contribution to chi(T) that increases systematically and no... |
Studies on the new MgB2 superconductor, with a critical temperature Tc ~ 39 K, have evidenced its potential for applications although intense magnetic relaxation effects limit the critical current density, Jc, at high magnetic fields. This means that effective pinning centers must be added into the material microstruc... |
We present a systematic classification and analysis of possible pairing instabilities in graphene-based moiré superlattices. Motivated by recent experiments on twisted double-bilayer graphene showing signs of triplet superconductivity, we analyze both singlet and triplet pairing separately, and describe how these two ... |
The quasi-two-dimensional organic superconductor beta-(BEDT-TTF)_2SF_5CH_2CF_2SO_3 (T_c approx 4.4 K)shows very strong Shubnikov-de Haas (SdH) oscillations which are superimposed on a highly anomalous steady background magnetoresistance, R_b. Comparison with de Haas- van Alphen oscillations allow a reliable estimate o... |
We study the possible superconducting pairing symmetry mediated by spin and charge fluctuations on the honeycomb lattice using the extended Hubbard model and the random-phase-approximation method. From $2\%$ to $20\%$ doping levels, a spin-singlet $d_{x^{2}-y^{2}}+id_{xy}$-wave is shown to be the leading superconducti... |
The superconducting energy gap in $\rm DyNi_2B_2C$ has been investigated using a point-contact technique based on the Andreev reflection from a normal (N)-superconductor (S) boundary, where N is Ag. The observed differential resistance $dV/dI$ is well described by the Blonder-Tinkham-Klapwijk (BTK) theory based on the... |
We demonstrate a novel approach to thermometry at the nanoscale exploiting a superconducting weak link. Such a weak link probed with nanosecond current pulses serves as a temperature sensing element and, due to the fast inherent dynamics, is capable of delivering unprecedented temporal resolution. |
Thermally-activated flux flow (TAFF) resistivity above the irreversibility field is reported for two different c-axis textured MgB_2 superconducting films. Transport measurements at different perpendicular magnetic fields 0 < B < 9 T and temperatures from 5 to 40K reveal TAFF Ohmic resistivity described by the A... |
The ultimate spatial limit to establish a Josephson coupling between two superconducting electrodes is an atomic-scale junction. The Josephson effect in such ultrasmall junctions has been used to unveil new switching dynamics, study coupling close to superconducting bound states or reveal non-reciprocal effects. |
Superconducting thin-films are central to the operation of many kinds of quantum sensors and quantum computing devices: Kinetic Inductance Detectors (KIDs), Travelling-Wave Parametric Amplifiers (TWPAs), Qubits, and Spin-based Quantum Memory elements. In all cases, the nonlinearity resulting from the supercurrent is a... |
An intrinsic Josephson junction has been successfully fabricated without any micro-fabrication technique. Two Bi2212 whiskers were crossed with one another and joined by post-annealing. |
We argue that the Scanning Tunneling Microscope (STM) images of resonant states generated by doping Zn or Ni impurities into Cu-O planes of BSCCO are the result of quantum interference of the impurity signal coming from several distinct paths. The impurity image seen on the surface is greatly affected by interlayer tu... |
We consider an electronic phase separation process that generates regions of different charge densities, or local dopings, as the origin of the inhomogeneous charge density of high $T_c$ superconductors. We show that it gives rise to a phase boundary potential between such doping disordered regions or grains. |
Nb3Sn wires are now very close to their final optimization but despite its classical nature, detailed understanding of the role of Ta and Ti doping in the A15 is not fully understood. Long thought to be essentially equivalent in their influence on Hc2, they were interchangeably applied. |
The evolution of the Fermi surface across the quantum critical point (QCP), which is relevant for characterizing the quantum criticality and understanding its relation with unconventional superconductivity, is an intriguing subject in the study of strongly correlated electron systems. In this study, we report the ther... |
The relationship between unconventional superconductivity, antiferromagnetism and nematic order in iron-based superconductors (FeSCs) is still highly debated. In many FeSCs superconductivity is in proximity of a nematically and magnetically ordered state. |
Within the Ginzburg-Landau formalism, we predict two novel mechanisms of vortex-antivortex nucleation in a magnetically nanostructured superconductor. Although counterintuitive, nucleation of vortex-antivortex pairs can be activated in a superconducting (SC) film covered by arrays of submicron ferromagnets (FMs) when ... |
Topological crystalline superconductors have attracted rapidly rising attention due to the possibility of higher-order phases, which support Majorana modes on boundaries in $d-2$ or lower dimensions. However, although the classification and bulk topological invariants in such systems have been well studied, it is gene... |
A numerical simulation is carried out for static vortices in a long Josephson junction with an exponentially varying width. At specified values of the parameters the corresponding boundary-value problem admits more than one solution. |
The lanthanide (Ln) copper oxides of the general chemical formula Ln2CuO4 take two different crystal structures: K2NiF4(T) and Nd2CuO4(T'). La2CuO4 takes the T structure by high-temperature bulk processes. |
We report on the high-pressure growth, structural characterization, and investigation of the electronic properties of single-crystalline LaFeAsO co-substituted by Sm and P, in both its normal- and superconducting states. Here, the appearance of superconductivity is attributed to the inner chemical pressure induced by ... |
We present a quantitative analysis of the low-temperature, high parallel field pairing resonance in ultra-thin superconducting Al films with dimensionless conductance g>>1. In this regime we derive an analytical expression for the tunneling density-of-states spectrum from which a variety of normal-state spin par... |
We theoretically investigate the fusion rules of Majorana Kramers pairs in time-reversal-invariant topological superconductors. We find that the fusion of Majorana Kramers pairs is a process that Ising anyons fuse independently in the two distinct time-reversal sectors. |
The MgB2 superconductor has already demonstrated its applicative potential, in particular for DC applications such as MRI magnets, thanks to the low costs of the raw materials and to its simple production process. However further efforts have still to be made in order to broaden its employment also towards the AC appl... |
Proximity-effect and resistance magneto-fluctuations measurements in submicron Nd1.2Ba1.8Cu3Oz (NBCO) nano-loops are reported to investigate coherent charge transport in the non-superconducting state. We find an unexpected inhibition of cooper pair transport, and a destruction of the induced superconductivity, by lowe... |
Distinct from familiar $s$-, $p$-, or $d$-wave pairings, the monopole superconducting order represents a novel class of pairing order arising from nontrivial monopole charge of the Cooper pair. In the weak-coupling regime, this order can emerge when pairing occurs between Fermi surfaces with different Chern numbers in... |
While Nb3Sn theoretically offers better superconducting RF cavity performance (Q0 and Eacc) to Nb at any given temperature, peak RF magnetic fields consistently fall short of the 400 mT prediction. The relatively rough topography of vapor-diffused Nb3Sn is widely conjectured to be one of the factors that limit the att... |
High-pressure superconductivity in a rare-earth doped Ca0.86Pr0.14Fe2As2 single crystalline sample has been studied up to 12 GPa and temperatures down to 11 K using designer diamond anvil cell under a quasi-hydrostatic pressure medium. The electrical resistance measurements were complemented by high pressure and low t... |
We report experimental evidence for charged boson states in a solid without Cooper pairing, based on attaching two free carriers to an exciton in a semiconducting system. Theoretical calculations show that this type of complex is stable in bilayer systems next to a parallel metal layer. |
We examine the effect on the superconducting transition temperature (Tc) of chemical inhomogeneities in Bi2201 and Bi2212 single crystals. Cation disorder at the Sr crystallographic site is inherent in these materials and strongly affects the value of Tc. |
Specific heat has been measured down to 600 mK and up to 8 Tesla by the highly sensitive AC microcalorimetry on the MgCNi3 single crystals with Tc ~ 7 K. Exponential decay of the electronic specific heat at low temperatures proved that a superconducting energy gap is fully open on the whole Fermi surface, in agreement ... |
We have carried out a systematic study of the PbO-type compound FeSe_{1-x}Te_x (x = 0~1), where Te substitution effect on superconductivity is investigated. It is found that superconducting transition temperature reaches a maximum of Tc=15.2K at about 50% Te substitution. |
Lithium Sulfide, Li2S, is an anti-fluorite semiconductor with a band-gap of 3.865 eV. It also has exactly the same valence electron count, Ne, and atomic number, Z, as magnesium diboride, MgB2. |
Current and field profiles, and magnetization and ac losses are calculated for arrays of infinitely long superconducting tapes in the critical state in a perpendicularly applied magnetic field. The tapes are arranged both horizontally and in a matrix configuration, which is the geometry found in many actual high-T_c s... |
At present, hydrogen-based compounds constitute one of the most promising classes of materials for applications as a phonon-mediated high-temperature superconductors. Herein, the behavior of the superconducting phase in tellurium hydride (HTe) at high pressure ($p=300$ GPa) is analyzed in details, by using the isotrop... |
Plasmonic excitations behave fundamentally different in layered materials in comparison to bulk systems. They form gapless modes, which in turn couple at low energies to the electrons. |
Spintronics aims to utilize the spin degree of freedom for energy-efficient, non-volatile memory and logic devices. In this research update, we review state-of-the-art developments and new directions in charge- and spin-based memory/logic with a focus on spintronics and the fascinating potential for superconductivity ... |
Transition-metal oxides offer an opportunity to explore unconventional superconductors, where the superconductivity (SC) is often interrelated with novel phenomena such as spin/charge order, fluctuations, and Fermi surface instability (1-3). LiTi2O4 (LTO) is a unique compound in that it is the only known spinel oxide ... |
Condensed matter systems undergoing second order transition away from the critical fluctuation region are usually described sufficiently well by the mean field approximation. The critical fluctuation region, determined by the Ginzburg criterion, $\left \vert T/T_{c}-1\right \vert \ll Gi$, is narrow even in high $T_{c}... |
The non-linear microwave surface impedance of patterned YBCO thin films, was measured using a suspended line resonator in the presence of a perpendicular DC magnetic field of magnitude comparable to that of the microwave field. Signature of the virgin state was found to be absent even for relatively low microwave powe... |
We have studied the anisotropy of the London penetration depth, which was obtained from reversible magnetization measurements with the magnetic field both parallel and perpendicular to the c-axis. The anisotropy of the London penetration depth has a smaller magnitude than the anisotropy of the upper critical field and... |
This paper demonstrates the method of estimation of critical temperature Tc value of high-temperature superconductors from the dispersive part of AC susceptibility measurement using a pair of neural networks. |
We measure the effect of uniaxial pressure on the superconducting transition temperature Tc in CeIrIn5. We find a linear change in Tc with both a-axis and c-axis pressure, with slopes of 56 mK/kbar and -66 mK/kbar, respectively. |
A model is introduced describing the interplay between superconductivity and spin-ordering. It is characterized by on-site repulsive electron-electron interactions, causing antiferromagnetism, and nearest-neighbor attractive interactions, giving rise to d-wave superconductivity. |
The off-diagonal components of thermal conductance tensor, thermal Hall conductivities (THCs), have extensively been studied in recent condensed matter experiments to investigate fractionalized quantum spin liquids, and quantum Hall systems. Under zero magnetic field, THCs spontaneously become non-zero for time-revers... |
Polarized elastic neutron scattering measurements have been performed in the bilayer copper oxide system Bi2Sr2CaCu2O8+d, providing evidence for an intra unit cell (IUC) magnetic order inside the pseudo-gap state. That shows time reversal symmetry breaking in that state as already reported in Bi2Sr2CaCu2O8+d through d... |
We present a detailed comparison of numerical solutions of the quasiclassical Eilenberger equations with several approximation schemes for the density of states of s- and d-wave superconductors in the vortex state, which have been used recently. In particular, we critically examine the use of the Doppler shift method,... |
We report on transport and ac susceptibility studies below the peak effect in twinned YBa2Cu3O7 single crystals. We find that disorder generated at the peak effect can be partially inhibited by forcing vortices to move with an ac driving current. |
We report temperature dependent Andreev reflection measurements of Co/ Y$_{1}$Ba$_{2}$Cu$_{3}$O$_{7-\delta}$ (YBCO) heterostructure samples with junction areas of 1 $\mu$m diameter. Modelling of the 5-70 K conductivity data according to a modified Blonder-Tinkham-Klapwijk theory yields a spin polarization in Co film a... |
Capitalizing on the two-dimensional nature of superconductivity in field-effect doped C60, we show that it should be possible to increase the transition temperature Tc by applying uniaxial stress perpendicular to the gate electrode. This method not only holds the promise of substantially enhancing Tc (by about 30 K pe... |
We have investigated the effect of Zn substitution on the hole content, p, and the oxygen deficiency, d, for a series of high-quality crystalline c-axis oriented thin films and polycrystalline Y1-xCaxBa2(Cu1-yZny)3O7-delta compounds over a wide range of composition (x, y, and delta). p was determined from the room-tem... |
We examine recent high-precision experimental data on the magnetic field, ${\bf H}$, dependence of the penetration depth $\lambda(H)$ in $\rm{YBa_2Cu_3O_{7-\delta}}$ (YBCO) for several field directions in the $a-b$ plane. In a new theoretical analysis that incorporates the effects of orthorhombic symmetry, we show tha... |
We present a general study of the magnetic excitations within a weak-coupling five-orbital model relevant to itinerant iron pnictides. As a function of enhanced electronic correlations, the spin excitations in the symmetry broken spin-density wave phase evolve from broad low-energy modes in the limit of weak interacti... |
Why Bi2Sr2CaCu2Ox (Bi2212) allows high critical current density Jc in round wires rather than only in the anisotropic tape form demanded by all other high temperature superconductors is important for future magnet applications. Here we compare the local texture of state-of-the-art Bi2212 and Bi2223 ((Bi,Pb)2Sr2Ca2Cu3O... |
The Fermi surface in the state of cuprates is highly unusual because it appears to consist of disconnected segments called arcs. Their very existence challenges the traditional concept of a Fermi surface as closed contours of gapless excitations in momentum space. |
Recently, An electron-doped 12442-type iron-based superconductor BaTh$_2$Fe$_4$As$_4$(N$_{0.7}$O$_{0.3}$)$_2$ has been successfully synthesized with high-temperature solid-state reactions on basis of a structural design. The inter-block-layer charge transfer between the constituent units of "BaFe$_2$As$_2$" an... |
We consider a closed chain of even number of Majorana zero modes with nearest-neighbour couplings which are different site by site generically, thus no any crystal symmetry. Instead, we demonstrate the possibility of an emergent supersymmetry (SUSY), which is accompanied by gapless Fermionic excitations. |
Spin transport currents and the spin-transfer torques in voltage-biased superconducting-ferromagnetic nanopillars (SFNFS point contacts) are computed. We develop and implement an algorithm based on the Ricatti formulation of the quasiclassical theory of superconductivity to solve the time-dependent boundary conditions... |
Local magnetic field distribution B(r) in the mixed state of a boride superconductor, YB6, is studied by muon spin rotation (muSR). A comparative analysis using the modified London model and Ginzburg-Landau (GL) model indicates that the GL model exhibits better agreement with muSR data at higher fields, thereby demons... |
Spin fluctuations have been proposed as a key mechanism for mediating superconductivity, particularly in high-temperature superconducting cuprates, where conventional electron-phonon interactions alone cannot account for the observed critical temperatures. Traditionally, their role has been analyzed through tight-bind... |
We study mechanisms of vortex nucleation in Nb$_3$Sn Superconducting RF (SRF) cavities using a combination of experimental, theoretical, and computational methods. Scanning transmission electron microscopy (STEM) image and energy dispersive spectroscopy (EDS) of some Nb$_3$Sn cavities show Sn segregation at grain boun... |
Here we suggest a simple physical model of HTSC cuprates that provides qualitative explanation of the main features of these compounds, including the nature of Fermi arcs, pseudogap anomalies and the origin of free carriers. According to this model, the unusual properties of HTSC cuprates result from their unique elec... |
The topological structure of the order parameter in Zhang's SO(5) theory of superconductivity allows for an unusual type of dissipation mechanism via which current-carrying states can decay. The resistivity due to this mechanism, which involves orientation rather than amplitude order-parameter fluctuations, is cal... |
We combine neutron scattering (INS) and NMR/NQR nuclear spin lattice relaxation rate data to deduce the existence of a new contribution to the magnetic response (dynamic susceptibility) in cuprate superconductors. This contribution, which has yet to be observed with INS, is shown to embody the magnetic pseudogap effec... |
We study various inhomogeneity effects on superconductivity as due to quantum confinement, surfaces and impurities, using the self-consistent Bogoliubov-de Gennes formalism on the attractive Hubbard model. The results are also compared with those obtained from the Anderson prescription, a BCS formalism for incorporati... |
Julien et al. have commented on two of our publications claiming that we have made erroneous interpretations of the nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) data. Specifically, they believe that their model of an extended staggered moment about a Zn impurity is the only interpretation of... |
The effect of impurities on Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states in a layered superconductor with d-wave pairing symmetry is investigated using the tight-binding model and the Bogoliubov-de Gennes equations. At low temperature and a strong exchange field applied parallel to its conducting plane, a two-dimens... |
We analyze the use of layered superconductors as anisotropic metamaterials. Layered superconductors can have a negative refraction index in a wide frequency range for arbitrary incident angles. |
We predict that ferromagnetic resonance in insulating magnetic film with inplane magnetization radiates electric fields polarized along the magnetization with opposite amplitudes at two sides of the magnetic insulator, which can be modulated strongly by adjacent superconductors. With a single superconductor adjacent t... |
In this review we concentrate on the work of K. Alex Müller in connection with his activities on oxide perovskites and ferroelectrics which were central to his research career long before he successfully discovered the first high temperature superconductor (HTSC) together with J. G. Bednorz in 1986. Not accidentally, ... |
A general phenomenology for phase behaviour in the mixed phase of type-II superconductors with weak point pinning disorder is outlined. We propose that the ``Bragg glass'' phase generically transforms via two separate thermodynamic phase transitions into a disordered liquid on increasing the temperature. |
We consider a problem of superconductivity coexistence with the spin-density-wave order in disordered multiband metals. It is assumed that random variations of the disorder potential on short length scales render the interactions between electrons to develop spatial correlations. |
Topological insulators are a new class of materials, that exhibit robust gapless surface states protected by time-reversal symmetry. The interplay between such symmetry-protected topological surface states and symmetry-broken states (e.g. superconductivity) provides a platform for exploring novel quantum phenomena and... |
We measured the Josephson plasma resonance (JPR) in optimally doped Tl$_2$Ba$_2$CaCu$_2$O$_{8+\delta}$ thin films using terahertz time-domain spectroscopy in transmission. The temperature and magnetic field dependence of the JPR frequency shows that the c-axis correlations of pancake vortices remain intact at the tran... |
This is a system paper about a new GPLv2 open source C library GBLA implementing and improving the idea of Faugère and Lachartre (GB reduction). We further exploit underlying structures in matrices generated during Gröbner basis computations in algorithms like F4 or F5 taking advantage of block patterns by using a spe... |
Mixed trigonometric-polynomials (MTPs) are functions of the form $f(x,\sin{x}, \cos{x})$ with $f\in\mathbb{Q}[x_1,x_2,x_3]$. In this paper, an algorithm ``isolating" all the real roots of an MTP is provided and implemented. |
Symbolic integration is an important module of a typical Computer Algebra System. As for now, Mathematica, Matlab, Maple and Sage are all mainstream CAS. |
A complete reduction on a difference field is a linear operator that enables one to decompose an element of the field as the sum of a summable part and a remainder such that the given element is summable if and only if the remainder is equal to zero. In this paper, we present a complete reduction in a tower of $\Sigma... |
We present a package to perform partial fraction decompositions of multivariate rational functions. The algorithm allows to systematically avoid spurious denominator factors and is capable of producing unique results also when being applied to terms of a sum separately. |
We present an algorithm for computing a holonomic system for a definite integral of a holonomic function over a domain defined by polynomial inequalities. If the integrand satisfies a holonomic difference-differential system including parameters, then a holonomic difference-differential system for the integral can als... |
Let P and Q be two polynomials in K[x, y] with degree at most d, where K is a field. Denoting by R $\in$ K[x] the resultant of P and Q with respect to y, we present an algorithm to compute R mod x^k in O~(kd) arithmetic operations in K, where the O~ notation indicates that we omit polylogarithmic factors. |
We consider the computation of two normal forms for matrices over the univariate polynomials: the Popov form and the Hermite form. For matrices which are square and nonsingular, deterministic algorithms with satisfactory cost bounds are known. |
Cylindrical algebraic decomposition(CAD) is a key tool in computational algebraic geometry, particularly for quantifier elimination over real-closed fields. When using CAD, there is often a choice for the ordering placed on the variables. |
The purpose of this paper is twofold. An immediate practical use of the presented algorithm is its applicability to the parametric solution of underdetermined linear ordinary differential equations (ODEs) with coefficients that are arbitrary analytic functions in the independent variable. |
Polynomial multiplication is a key algorithm underlying computer algebra systems (CAS) and its efficient implementation is crucial for the performance of CAS. In this paper we design and implement algorithms for polynomial multiplication using approaches based the fast Fourier transform (FFT) and the truncated Fourier... |
We propose an algebraic geometric approach for studying rational solutions of first-order algebraic ordinary difference equations. For an autonomous first-order algebraic ordinary difference equations, we give an upper bound for the degrees of its rational solutions, and thus derive a complete algorithm for computing ... |
We perform a comparison of the performance and efficiency of four different function evaluation methods: black-box functions, binary trees, $n$-ary trees and string parsing. The test consists in evaluating 8 different functions of two variables $x,y$ over 5000 floating point values of the pair $(x,y)$. |
The paper compares computational aspects of four approaches to compute conservation laws of single differential equations (DEs) or systems of them, ODEs and PDEs. The only restriction, required by two of the four corresponding computer algebra programs, is that each DE has to be solvable for a leading derivative. |
The notion of differentiation index for DAE systems of arbitrary order with generic second members is discussed by means of the study of the behavior of the ranks of certain Jacobian associated sub-matrices. As a by-product, we obtain upper bounds for the regularity of the Hilbert-Kolchin function and the order of the... |
Insa and Pauer presented a basic theory of Groebner basis for differential operators with coefficients in a commutative ring in 1998, and a criterion was proposed to determine if a set of differential operators is a Groebner basis. In this paper, we will give a new criterion such that Insa and Pauer's criterion co... |
In this paper, we briefly discuss the dynamic and functional approach to computer symbolic tensor analysis. The ccgrg package for Wolfram Language/Mathematica is used to illustrate this approach. |
A Bohemian matrix family is a set of matrices all of whose entries are drawn from a fixed, usually discrete and hence bounded, subset of a field of characteristic zero. Originally these were integers -- hence the name, from the acronym BOunded HEight Matrix of Integers (BOHEMI) -- but other kinds of entries are also i... |
In classical invariant theory, the Gröbner base of the ideal of syzygies and the normal forms of polynomials of invariants are two core contents. To improve the performance of invariant theory in symbolic computing of classical geometry, advanced invariants are introduced via Clifford product. |
In this short note, we give a localized version of the basic triangle theorem, first published in 2011 (see [4]) in order to prove the independence of hyperlogarithms over various function fields. This version provides direct access to rings of scalars and avoids the recourse to fraction fields as that of meromorphic ... |
We show that a linear-time algorithm for computing Hong's bound for positive roots of a univariate polynomial, described by K. Mehlhorn and S. Ray in an article "Faster algorithms for computing Hong's bound on absolute positiveness", is incorrect. We present a corrected version. |
We describe a complete algorithm to compute millions of coefficients of classical modular forms in a few seconds. We also review operations on Euler products and illustrate our methods with a computation of triple product L-function of large conductor. |
A roadmap for an algebraic set $V$ defined by polynomials with coefficients in some real field, say $\mathbb{R}$, is an algebraic curve contained in $V$ whose intersection with all connected components of $V\cap\mathbb{R}^{n}$ is connected. These objects, introduced by Canny, can be used to answer connectivity queries... |
Cylindrical Algebraic Decomposition (CAD) has long been one of the most important algorithms within Symbolic Computation, as a tool to perform quantifier elimination in first order logic over the reals. More recently it is finding prominence in the Satisfiability Checking community as a tool to identify satisfying sol... |
Given the equations of the first and the second order surfaces in multidimensional space, our goal is to construct a univariate polynomial one of the zeros of which coincides with the square of the distance between these surfaces. To achieve this goal we employ Elimination Theory methods. |
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