We report on the superconducting properties of In doped SnTe which has recently been explored as a topological crystalline superconductor. Single crystals of Sn0.5In0.5Te have been synthesized by modified Bridgman method. Resistivity measurement performed in the range 1.6K to 300K shows metallic normal state with onset of superconducting transition at Tc = 4.5K. Bulk superconductivity has also been confirmed by DC magnetization, AC susceptibility and rf penetration depth measurements. The zero temperature upper critical field, lower critical field, coherence length, penetration depth are estimated to be 1.6T, 10Oe, 143.5 Å and 832nm respectively. Temperature dependence of low temperature penetration depth indicates S-wave fully gapped characteristics with BCS gap meV. Hall and Seebeck coefficient measurements confirm dominance of hole conduction with possible phonon-drag effects around ~45K. Resistive transition studied under the applied magnetic field shows thermally activated flux flow behavior.
Line nodes in the superconducting gap are known to be a source of Majorana flat bands (MFBs) in time-reversal-invariant superconductors (SCs). Here, we extend this relation to all symmetry-protected line nodes where an additional constraint arising from a symmetry of the crystal destabilizes or hides the existence of MFBs. By establishing a one-to-one correspondence between group theoretical and topological classifications, we are able to classify the possible line-node-induced MFBs, including cases with (magnetic) non-symmorphic space groups. Our theoretical analysis reveals a new type of MFB…
We prove a topological criterion for the existence of zero-energy Majorana bound-state on a disclination, a rotation symmetry breaking point defect, in 4-fold symmetric topological crystalline superconductors (TCS). We first establish a complete topological classification of TCS using the Chern invariant and three integral rotation invariants. By analytically and numerically studying disclinations, we algebraically deduce a Z_2-index that identifies the parity of the number of Majorana zero-modes at a disclination. Surprisingly, we also find weakly-protected Majorana fermions bound at the corn…
Superconductors derived from topological insulators and topological crystalline insulators by doping have long been considered to be candidates as topological superconductors. Pb$_{0.5}$Sn$_{0.5}$Te is a topological crystalline insulator with mirror symmetry protected surface states on (001), (011) and (111) oriented surfaces. The superconductor (Pb$_{0.5}$Sn$_{0.5}$)$_{0.7}$In$_{0.3}$Te is induced by In doping in Pb$_{0.5}$Sn$_{0.5}$Te, and is thought to be a topological superconductor. Here we report the first scanning tunneling spectroscopy measurement of the superconducting state as well a…
We present a unified framework to construct and classify topological crystalline superconductors (TCSCs). The building blocks are one-dimensional topological superconductors (TSCs) protected solely by onsite symmetries, which are arranged and glued by crystalline symmetries in real space. We call this real-space scheme "wire construction", and we show its procedure can be formulated mathematically. For illustration, we treat TCSCs of Altland-Zirnbauer (AZ) class[1] DIII protected by wallpaper group as well as layer group symmetries, with the resulting states by wire construction being TCSCs in…
Majorana Kramers pairs emerged on surfaces of time-reversal-invariant topological crystalline superconductors show the Ising anisotropy to an applied magnetic field. We clarify that crystalline symmetry uniquely determines the direction of the Majorana Ising spin for given irreducible representations of pair potential, deriving constraints to topological invariants. Besides, necessary conditions for nontrivial topological invariants protected by the n-fold rotational symmetry are shown.
Topological superconductors possess a nodeless superconducting gap in the bulk and gapless zero energy modes, known as "Majorana zero modes", at the boundary of a finite system. In this work, we introduce a new class of topological superconductors, which are protected by nonsymmorphic crystalline symmetry and thus dubbed "topological nonsymmorphic crystalline superconductors". We construct an explicit Bogoliubov-de Gennes type of model for this superconducting phase in the D class and show how Majorana zero modes in this model are protected by glide symmetry. Furthermore, we generalize the cla…
Crystal point group symmetry is shown to protect Majorana fermions (MFs) in spinfull superconductors (SCs). We elucidate the condition necessary to obtain MFs protected by the point group symmetry. We argue that superconductivity in Sr2RuO4 hosts a topological phase transition to a topological crystalline SC, which accompanies a d-vector rotation under a magnetic field along the c-axis. Taking all three bands and spin-orbit interactions into account, symmetry-protected MFs in the topological crystalline SC are identified. Detection of such MFs provides evidence of the d-vector rotation in Sr2R…
It has been observed that the effect of magnetic impurities in a superconductor is drastically different depending on whether the host superconductor is in a crystalline or an amorphous state. Based on the recent theory of Kim and Overhauser, it is shown that as the system is getting disordered, the initial slope of the $T_{c}$ depression is decreasing by a factor $\sqrt{\ell/ξ_{0}}$, when the mean free path $\ell$ becomes smaller than the BCS coherence length $ξ_{0}$, which is in agreement with experimental findings. In addition, for a superconductor in a pure crystalline state the supercondu…
In iron-based superconductors, band inversion of $d$- and $p$-orbitals yields Dirac semimetallic states. We theoretically investigate their topological properties in normal and superconducting phases, based on the tight-binding model involving full symmetry of the materials. We demonstrate that a Cooper pair between electrons with $d$- and $p$-orbitals relevant to the band structure yields odd-parity superconductivity. Moreover, we present the typical surface states by solving the Bogoliubov-de Gennes equation and characterize them by topological invariants defined with crystal symmetry. It is…
Topological crystalline superconductivity in the locally non-centrosymmetric multilayer superconductors (SCs) is proposed. We study the odd-parity pair-density wave (PDW) state induced by the spin-singlet pairing interaction through the spin-orbit coupling. It is shown that the PDW state is a topological crystalline SC protected by a mirror symmetry, although it is topologically trivial according to the classification based on the standard topological periodic table. The topological property of the mirror subsectors is intuitively explained by adiabatically changing the BdG Hamiltonian. A subs…
We propose to study the lattice-symmetry protection of Majorana zero bound modes in topological crystalline superconductors (SCs). With an induced $s$-wave superconductivity in the $(001)$-surface of the topological crystalline insulator Pb$_{1-x}$Sn$_x$Te, which has a C$_4$ rotational symmetry, we show a new class of 2D topological SC with four Majorana modes obtained in each vortex core, while only two of them are protected by the cyclic symmetry. Furthermore, applying an in-plane external field can break the four-fold symmetry and lifts the Majorana modes to finite energy states in general.…
Single crystal neutron diffraction study has been performed on new superconductor A2Fe4Se5, where A = Cs, K, (Tl,Rb) and (Tl,K), and the same Fe vacancy ordered crystal structure and the same block checkerboard antiferromagne tic order recently discovered in the K2Fe4Se5 superconductor are observed. Thus, all known alkali metal and/or Tl intercalated iron selenide superconductors share common crystalline and magnetic structure. Investigation on electronic process in these new superconductors, for which a different electronic structure from those in previous Fe-based high-Tc superconductors is …
There exists a connection between the creation of toroidal moments (TM) and the breaking of the one-cell relativistic crystalline symmetry (RCS) associated to any given crystal into which non-trivial magnetoelectric coupling effects (ME) exist. Indeed, in this kind of crystals, any interaction between a charge carrier and an elementary magnetic cell can breaks the RCS of this previous given cell by varying, in the simplest case, the continuous defining parameters of the initial RCS. This breaking can be associated to a change of the initial Galilean proper frame of any given carrier to an "eff…
The electromagnetic properties of a Fermi liquid superconductor with singular Landau parameter $F_{1s}\to-1$, corresponding to a state with marginal spin-charge separation (MSCS) is analyzed in this paper. We show that the MSCS state describes a strongly phase-disordered superconductor which is a diamagnetic metal with Drude-like optical conductivity. The phase diagram and electromagnetic properties of the MSCS state is found to be in qualitative agreement with what is observed in the pseudo-gap phase of (underdoped) High-$T_c$ cuprates. We predicted that vortices with {\em un-quantized} magne…
$\require{mediawiki-texvc}$The locally non-centrosymmetric superconductor SrPtAs is proposed to host a topological chiral $d$-wave state, but experimental reports have been limited to polycrystalline samples. Here we report the synthesis of single crystalline SrPtAs grown from Pb flux. SrPtAs crystallizes in the hexagonal space group $P6_{3}$/$mmc$ with lattice parameters $a$ = 4.2445(4) $Å$ and $c$ = 8.9513(18) $Å$. Magnetic susceptibility and electrical resistivity measurements reveal a superconducting transition at T$_c$ $\sim$2.2 K, in agreement with previous reports on polycrystalline sam…
We classify discrete-rotation symmetric topological crystalline superconductors (TCS) in two dimensions and provide the criteria for a zero energy Majorana bound state (MBS) to be present at composite defects made from magnetic flux, dislocations, and disclinations. In addition to the Chern number that encodes chirality, discrete rotation symmetry further divides TCS into distinct stable topological classes according to the rotation eigenspectrum of Bogoliubov-de Gennes quasi-particles. Conical crystalline defects are shown to be able to accommodate robust MBS when a certain combination of the…
Effects of order parameter collective modes on electromagnetic response are studied for a clean spin-triplet superconductor with $k_x\pm ik_y$ orbital symmetry, which has been proposed as a candidate pairing symmetry for Sr$_2$RuO$_4$. It is shown that the $k_x \pm ik_y$ superconductor has characteristic massive collective modes analogous to the clapping mode in the A-phase of superfluid $^3$He. We discuss the contribution from the collective modes to ultrasound attenuation and electromagnetic absorption. We show that in the electromagnetic absorption spectrum the clapping mode gives rise to a…
Superconductor-insulator transition is one of the remarkable phenomena driven by quantum fluctuation in two-dimensional (2D) systems. Such a quantum phase transition (QPT) was investigated predominantly on highly disordered thin films with amorphous or granular structures using scaling law with constant exponents. Here, we provide a totally different view of QPT in highly crystalline 2D superconductors. According to the magneto-transport measurements in 2D superconducting ZrNCl and MoS2, we found that the quantum metallic state commonly observed at low magnetic fields is converted via the quan…
We present results of a microwave surface impedance study of the heavy fermion superconductor UBe13. We clearly observe an absorption peak whose frequency- and temperature-dependence scales with the BCS gap function. Resonant absorption into a collective mode, with energy approximately proportional to the superconducting gap, is proposed as a possible explantation.
In this review, we discuss recent progress in the explorations of topological materials beyond topological insulators; specifically, we focus on topological crystalline insulators and bulk topological superconductors. The basic concepts, model Hamiltonians, and novel electronic properties of these new topological materials are explained. The key role of symmetries that underlie their topological properties is elucidated. Key issues in their materials realizations are also discussed.
Inhomogeneous superconductors and inhomogeneous superfluids appear in a variety of contexts including quark matter at extreme densities, fermionic systems of cold atoms, type-II cuprates, and organic superconductors. In the present review the focus is on properties of quark matter at high baryonic density, which may exist in the interior of compact stars. The conditions realized in these stellar objects tend to disfavor standard symmetric BCS pairing and may favor an inhomogeneous color superconducting phase. The properties of inhomogeneous color superconductors are discussed in detail and in …
We report detailed investigations of the properties of a superconductor obtained by substituting In at the Sn site in the topological crystalline insulator (TCI), SnTe. Transport, magnetization and heat capacity measurements have been performed on crystals of Sn0.6In0.4Te, which is shown to be a bulk superconductor with Tc(onset) at ~4.70(5) K and Tc(zero) at ~3.50(5) K. The upper and lower critical fields are estimated to be μ0Hc2(0) = 1.42(3) T and μ0Hc1(0) = 0.90(3) mT respectively, while κ = 56.4(8) indicates this material is a strongly type II superconductor.
We investigate the topological aspect of the spin-triplet $f$-wave superconductor UPt$_3$ through microscopic calculations of edge- and vortex-bound states based on the quasiclassical Eilenberger and Bogoliubov-de Gennes theories. It is shown that a gapless and linear dispersion exists at the edge of the $ab$-plane. This forms a Majorana valley, protected by the mirror chiral symmetry. We also demonstrate that, with increasing magnetic field, vortex-bound quasiparticles undergo a topological phase transition from topologically trivial states in the double-core vortex to zero-energy states in t…
We have successfully grown high quality single crystals of SrFe$_2$As$_2$ and A$_{0.6}$K$_{0.4}$Fe$_2$As$_2$(A=Sr, Ba) using flux method. The resistivity, specific heat and Hall coefficient have been measured. For parent compound SrFe$_2$As$_2$, an anisotropic resistivity with $ρ_c$ / $ρ_{ab}$ as large as 130 is obtained at low temperatures. A sharp drop in both in-plane and out-plane resistivity due to the SDW instability is observed below 200 K. The angular dependence of in-plane magnetoresistance shows 2-fold symmetry with field rotating within ab plane below SDW transition temperature. Thi…
Crystalline topological phases have recently attracted a lot of experimental and theoretical attention. Key advances include the complete elementary band representation analyses of crystalline matter by symmetry indicators and the discovery of higher-order hinge and corner states. However, current classification schemes of such phases are either implicit or limited in scope. We present a new scheme for the explicit classification of crystalline topological insulators and superconductors. These phases are protected by crystallographic point group symmetries and are characterized by bulk topolog…
Two-dimensional (2D) materials are not expected to be metals at low temperature due to electron localization. Consistent with this, pioneering studies on thin films reported only superconducting and insulating ground states, with a direct transition between the two as a function of disorder or magnetic field. However, more recent works have revealed the presence of an intermediate metallic state occupying a substantial region of the phase diagram whose nature is intensely debated. Here, we observe such a state in the disorder-free limit of a crystalline 2D superconductor, produced by mechanica…
Disorder driven superconductor to insulator transition via intermediate metallic regime is reported in nano-crystalline thin films of molybdenum. The nano-structured thin films have been deposited at room temperature using DC magnetron sputtering at different argon pressures. The grain size has been tuned using deposition pressure as the sole control parameter. A variation of particle sizes, room temperature resistivity and superconducting transition has been studied as a function of deposition pressure. The nano-crystalline molybdenum thin films are found to have large carrier concentration b…
We revisit the importance of collective-mode fluctuations and gauge invariance in the electromagnetic response of superconducting systems. In particular, we show that order-parameter fluctuations, gapless or not, have no contribution to the Meissner effect in both $s$- and $p$-wave superconductors. More generally, we extend this result to uniform and nonuniform superfluids with no external wavevector scale. To facilitate this analysis, we formulate a path-integral-based matrix methodology for computing the electromagnetic response of fermionic fluids in the presence of concomitantly fluctuatin…
Using a systematic relation between topological gapless phases in three dimensions and topological gapped phases in two dimensions, we identify four types of higher-order topological semimetals or nodal superconductors (HOTS), hosting (i) flat zero-energy "Fermi arcs" at crystal hinges, (ii) flat zero-energy hinge arcs coexisting with surface Dirac cones, (iii) chiral or helical hinge modes, or (iv) flat zero-energy hinge arcs connecting nodes only at finite momentum. Bulk-boundary correspondence relates the hinge states to the bulk topology protecting the nodal point or loop. We classify all …
The details of the superconducting to quantum metal transition (SQMT) at T=0 are an open problem that invokes much interest in the nature of this exotic and unexpected ground state1-3. However, the SQMT was not yet investigated in a crystalline 2D superconductor with coexisting and fluctuating quantum orders. Here, we report the observation of a SQMT in 2D ion-gel gated 1T-TiSe24, driven by magnetic field. A field-induced crossover between Bose quantum metal and vortex quantum creeping with increasing field is observed. We discuss the interplay between superconducting and CDW fluctuations (dis…
Recent technological advances in controlling materials have developed methods to produce idealized two-dimensional (2D) electron systems such as heterogeneous interfaces, molecular-beam-epitaxy (MBE) grown atomic layers, exfoliated thin flakes and field-effect devices. These 2D electron systems are highly-crystalline with less disorder in common, some of which indeed show sheet resistance more than one order of magnitude lower even in atomic layers or single layers than that of conventional amorphous/granular thin films. Here, we present a review on the recent developments of highly-crystallin…
In this work we consider whether nonsymmorphic symmetries such as a glide plane can protect the existence of topological crystalline insulators and superconductors in three dimensions. In analogy to time-reversal symmetric insulators, we show that the presence of a glide gives rise to a quantized magnetoelectric polarizability, which we compute explicitly through the Chern-Simons 3-form of the bulk wave functions for a glide symmetric model. Our approach provides a measurable property for this insulator and naturally explains the connection with mirror symmetry protected insulators and the rec…
The interrelation between the condensation energy and the optical sum rules has been investigated. It has been shown that the so called 'partial' sum rule violation is related mainly to a temperature dependence of the relaxation rate rather than to the appearance of superconductivity itself. Moreover, we demonstrate that the experimental data on the temperature dependence of the optical sum rule can be explained rather well by an account of strong electron-phonon interaction.
We consider the Hall conductivity due to the motion of a vortex in a lattice-model of a clean superconductor, using a combination of general arguments, unrestricted Hartree-Fock calculations, and exact diagonalization. In the weak coupling limit, $k_F ξ\gg 1$, the sign of the Hall response of the superconducting state is the same as that of the normal (non-superconducting) state. For intermediate and strong coupling, however, ($k_F ξ\sim 1$) we find that the sign of the Hall response in the superconducting state can be opposite to that of the normal state. In addition, we find that the sign re…
The Ginzburg-Landau (GL) free energy of crystalline color superconductors is important for understanding the nature of the phase transition to the normal quark matter and predicting the preferred crystal structure. So far the GL free energy at zero temperature has only been evaluated up to the sixth order in the condensate. To give quantitative reliable predictions we need to evaluate the higher-order terms. In this work, we present a new derivation of the GL free energy by using the discrete Bloch representation of the fermion field. This derivation introduces a simple matrix formalism withou…
Starting from the generalised London equations, which include a gravitomagnetic term, the gravitational and the electromagnetic properties of superconductors are derived. A phenomenological synthesis of those properties is proposed.
We investigate the macroscopic effects of charge density waves (CDW) and superconductivity in layered superconducting systems with broken lattice inversion symmetry (allowing for piezoelectricity) such as two dimensional (2D) transition metal dichalcogenides (TMD). We work with the low temperature time dependent Ginzburg-Landau theory and study the coupling of lattice distortions and low energy CDW collective modes to the superconducting order parameter in the presence of electromagnetic fields. We show that superconductivity and piezoelectricity can coexist in these singular metals. Furthermo…
Within the framework of the kinetic energy driven superconducting mechanism, the doping dependence of the electromagnetic response in the electron-doped cuprate superconductors is studied. It is shown that although there is an electron-hole asymmetry in the phase diagram, the electromagnetic response in the electron-doped cuprate superconductors is similar to that observed in the hole-doped cuprate superconductors. The superfluid density depends linearly on temperature, except for the strong deviation from the linear characteristics at the extremely low temperatures.
Topological superconductors are exotic phases of matter featuring robust surface states that could be leveraged for topological quantum computation. A useful guiding principle for the search of topological superconductors is to relate the topological invariants with the behavior of the pairing order parameter on the normal-state Fermi surfaces. The existing formulas, however, become inadequate for the prediction of the recently proposed classes of topological crystalline superconductors. In this work, we advance the theory of symmetry indicators for topological (crystalline) superconductors to…
Topological classification in our previous paper [K. Shiozaki and M. Sato, Phys. Rev. B ${\bf 90}$, 165114 (2014)] is extended to nonsymmorphic crystalline insulators and superconductors. Using the twisted equivariant $K$-theory, we complete the classification of topological crystalline insulators and superconductors in the presence of additional order-two nonsymmorphic space group symmetries. The order-two nonsymmorphic space groups include half lattice translation with $Z_2$ flip, glide, two-fold screw, and their magnetic space groups. We find that the topological periodic table shows modulo…
Within the framework of the kinetic energy driven superconductivity, the electromagnetic response in cuprate superconductors is studied in the linear response approach. The kernel of the response function is evaluated and employed to calculate the local magnetic field profile, the magnetic field penetration depth, and the superfluid density, based on the specular reflection model for a purely transverse vector potential. It is shown that the low temperature magnetic field profile follows an exponential decay at the surface, while the magnetic field penetration depth depends linearly on tempera…
We complete a classification of topological phases and their topological defects in crystalline insulators and superconductors. We consider topological phases and defects described by non-interacting Bloch and Bogoliubov de Gennes Hamiltonians that support additional order-two spatial symmetry, besides any of ten classes of symmetries defined by time-reversal symmetry and particle-hole symmetry. The additional order-two spatial symmetry we consider is general and it includes $Z_2$ global symmetry, mirror reflection, two-fold rotation, inversion, and their magnetic point group symmetries. We fi…
Recent theoretical and experimental studies demonstrated that an electromagnetic metamaterial approach is capable of drastically increasing the critical temperature Tc of composite metamaterial superconductors. This progress was achieved by engineering the frequency-dependent dielectric response function of the metamaterial. Here we further extend this approach by introducing the concept of hybrid acousto-electromagnetic hyperbolic metamaterial superconductors, which are projected to exhibit strongly enhanced superconducting properties due to artificially engineered broadband divergency of the…
Resting on the gauge theory of topological quantum melting in 2+1 dimensions, we predict that a superconductor characterized by crystalline correlations on a length scale large compared to the lattice carries a new collective mode: the massive shear photon. This mode is visible in the electrodynamic response and the ramification of our theory is that electron energy loss spectroscopy can be employed to prove or disprove the existence of dynamical stripes in cuprate superconductors.
Motivated by the recent controversy surrounding the Kerr effect measurements in strontium ruthenate \cite{xia:167002}, we examine the electromagnetic response of a clean chiral p-wave superconductor. When the contributions of the collective modes are accounted for, the Hall response in a clean chiral superconductor is smaller by several orders of magnitude than previous theoretical predictions and is too small to explain the experiment. We also uncover some unusual features of the collective modes of a chiral superconductor, namely, that they are not purely longitudinal and couple to external …
Motivated by recent experiments reporting the suppression of the critical current in superconducting Dayem bridges by the application of strong electrostatic fields, in this work we study the impact on the superconducting gap of charge redistribution in response to an applied electric field in thin crystalline metals. By numerically solving the BCS gap equation and the Poisson equation in a fully self-consistent way, we find that by reducing the pairing strength we observe an increased sensitivity of the gap on the applied field, showing sudden rises and falls that are compatible with surface …
After a brief introduction to crystalline organic superconductors and metals, we shall describe two recently-observed exotic phases that occur only in high magnetic fields. The first involves measurements of the non-linear electrical resistance of single crystals of the charge-density-wave (CDW) system (Per)$_2$Au(mnt)$_2$ in static magnetic fields of up to 45 T and temperatures as low as 25 mK. The presence of a fully gapped CDW state with typical CDW electrodynamics at fields higher that the Pauli paramagnetic limit of 34 T suggests the existence of a modulated CDW phase analogous to the Ful…
Quantum Griffiths singularity (QGS) reveals the profound influence of quenched disorder on the quantum phase transitions, characterized by the divergence of the dynamical critical exponent at the boundary of the vortex glass-like phase, named as quantum Griffiths phase. However, in the absence of vortices, whether the QGS can exist under parallel magnetic field remains a puzzle. Here we study the magnetic field induced superconductor-metal transition in ultrathin crystalline PdTe2 films grown by molecular beam epitaxy. Remarkably, the QGS emerges under both perpendicular and parallel magnetic …
The interaction between radiation and superconductors is explored in this paper. In particular, the calculation of a plane standing wave scattered by an infinite cylindrical superconductor is performed by solving the Helmholtz equation in cylindrical coordinates. Numerical results computed up to $\mathcal{O}(77)$ of Bessel functions are presented for different wavelengths showing the appearance of a diffraction pattern.
We derive the current response to the linearly polarized electromagnetic field with finite frequency and wave vector incident normally on the specular surface of a clean nonconventional superconductor with orbital spontaneous magnetization parallel to the crystal axis and perpendicular to the crystal surface. The result includes the usual part known from the theory of conventional superconductivity and as well the magneto-optical term typical for the superconductors with spontaneous time reversal breaking. As an application of the basic current-field relation we consider the Kerr effect for th…
The coupling between superconductivity and othorhombic distortion is studied in vapor-grown FeSe single crystals using high-resolution thermal-expansion measurements. In contrast to the Ba122-based (Ba122) superconductors, we find that superconductivity does not reduce the orthorhombicity below Tc. Instead we find that superconductivity couples strongly to the in-plane area, which explains the large hydrostatic pressure effects. We discuss our results in light of the spinnematic scenario and argue that FeSe has many features quite different from the typical Fe-based superconductors.
We present a comprehensive study of the binary intermetallic superconductor, BaSn5. High-quality single crystalline BaSn5 was grown out of Sn flux. Detailed thermodynamic and transport measurements were performed to study BaSn5's normal and superconducting state properties. This material appears to be a strongly coupled, multiband superconductor. Hc2(T)is almost isotropic. De Haas-van Alphen oscillations were observed and two effective masses were estimated from the FFT spectra. Hydrostatic pressure causes a decrease in the superconducting transition temperature at the rate of ~ -0.053 K/kbar.
We calculate the response of a vortex core in a layered superconductor to {\em ac} electromagnetic fields with frequencies $ω\lsim 2Δ/\hbar$. In this frequency range the response is dominated by order parameter collective modes which are coupled to the vortex-core bound states of Caroli, de Gennes and Matricon. Our calculations show that a vortex core has a more complex and richer dynamics than predicted by previous theories. The {\em ac} field drives an oscillating, nearly homogeneous supercurrent in the direction of the electric field, superimposed with a dissipative current flow which has a…
