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 modifications of the local density of states. The effect is washed out by increasing the pairing strength towards the weak-to-moderate coupling limit or by introduction of a weak smearing in the density of states, showing the evolution from a clean crystal to a weakly disordered metal.
We report the evolution of the Zeeman-mediated superconducting phase diagram (PD) in ultra-thin crystalline Al films. Parallel critical field measurements, down to 50 mK, were made across the superconducting tricritical point of films ranging in thickness from 7 ML to 30 ML. The resulting phase boundaries were compared with the quasi-classical theory of a Zeeman-mediated transition between a homogeneous BCS condensate and a spin polarized Fermi liquid. Films thicker than $\sim$20 ML showed good agreement with theory, but thinner films exhibited an anomalous PD that cannot be reconciled within …
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…
Topological crystalline insulators in IV-VI compounds host novel topological surface states consisting of multi-valley massless Dirac fermions at low energy. Here we show that strain generically acts as an effective gauge field on these Dirac fermions and creates pseudo-Landau orbitals without breaking time-reversal symmetry. We predict the realization of this phenomenon in IV-VI semiconductor heterostructures, due to a naturally occurring misfit dislocation array at the interface that produces a periodically varying strain field. Remarkably, the zero-energy Landau orbitals form a flat band in…
We consider effects of an externally applied electrostatic field on superconductivity, self-consistently within a BCS mean field model, for a clean 3D metal thin film. The electrostatic change in superconducting condensation energy scales as $μ^{-1}$ close to subband edges as a function of the Fermi energy $μ$, and follows 3D scaling $μ^{-2}$ away from them. We discuss nonlinearities beyond gate effect, and contrast results to recent experiments.
Family of Unconventional Superconductivities in Crystalline Graphene
Massachusetts Institute of Technology（麻省理工学院）；University of Basel（巴塞尔大学）；Florida State University（佛罗里达州立大学）；University of Florida（佛罗里达大学）；National Institute for Materials Science（国立材料研究所）
Superconductivity mostly appears in high carrier density systems and sometimes exhibits common phase diagrams in which the critical temperature Tc continuously develops with carrier density. Superconductivity enhanced in lightly doped regime has seldom been reported, although it is an ideal direction towards the crossover between Bardeen-Cooper-Schrieffer (BCS) and Bose-Einstein condensate (BEC) limits, where the behavior of Cooper pairs changes dramatically. Here we report transport properties and superconducting gaps in single-crystalline lithium-intercalated layered nitrides (LixHfNCl and L…
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 estim…
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 …
Gate tunable two-dimensional (2D) superconductors offer significant advantages when studying superconducting phase transitions. Here, we address superconductivity in exfoliated 1T'-MoTe2 monolayers with an intrinsic band gap of ~7.3 meV using electrostatic doping. Despite large differences in the dispersion of the conduction and the valence bands, superconductivity can be achieved easily for both electrons and holes. The onset of superconductivity occurs near 7-8K for both charge carrier types. This temperature is much higher than in bulk samples. Also the in-plane upper critical field is stro…
We report Muon Spin Relaxation studies in weak transverse fields of the superconductivity in the metal cluster compound, Ga$\_{84}$[N(SiMe$\_{3}$)$\_{2}$]$\_{20}$-Li$\_{6}$Br$\_{2}$(thf)$\_{20}\cdot $2toluene. The temperature and field dependence of the muon spin relaxation rate and Knight shift clearly evidence type II bulk superconductivity below $T\_{\text{c}}\approx7.8$ K, with $B\_{\text{c1}}\approx 0.06$ T, $B\_{\text{c2}}\approx 0.26 $ T, $κ\sim 2$ and weak flux pinning. The data are well described by the s-wave BCS model with weak electron-phonon coupling in the clean limit. A qualitat…
We report the characterization of the misfit compound (Pb1-xSnxSe2)1.16(TiSe2)2, in which a [100] rocksalt bilayer of Pb1-xSnxSe, which is a topological crystalline insulator in bulk form, alternates with a double layer of the normally non-superconducting layered transition metal dichalcogenide TiSe2. The x dependence of Tc displays a weak dome-like shape with a maximum Tc of 4.5 K at x = 0.2; there is only a subtle change in Tc corresponding to the expected trivial to topological transition in the Pb1-xSnxSe bi-layer. We present a more detailed characterization of the superconductor at x = 0.…
Typically the superconducting phase weakens at several points with the increase in disorder before it is distroyed in the 2d-thin films. This may lead to an inhomogeneous superconducting state without a continuous phase. Here we present scanning tunneling spectroscopy measurements at 0.1 K in the disordered polycrystalline film of TiN describing the nanoscale size features of the superconducting state. The imaging shows imcommensurate charge density modulations, originating at the crystalline bounadries, and intercepted on large scale by the beat patterns in the regions of overlap. Electronic …
In their original formulation of superconductivity, the London brothers predicted the exponential suppression of an $electrostatic$ field inside a superconductor over the so-called London penetration depth, $λ_L$. Despite a few experiments indicating hints of perturbation induced by electrostatic fields, no clue has been provided so far on the possibility to manipulate metallic superconductors via field-effect. Here we report field-effect control of the supercurrent in $all$-metallic transistors made of different Bardeen-Cooper-Schrieffer (BCS) superconducting thin films. At low temperature, o…
NdO$_{0.5}$F$_{0.5}$BiS$_{2}$ is a new layered superconductor. We have studied the low-lying electronic structure of a single crystalline NdO$_{0.5}$F$_{0.5}$BiS$_{2}$ superconductor, whose superconducting transition temperature is 4.87K, with angle-resolved photoemission spectroscopy. The Fermi surface consists of two small electron pockets around the X point and shows little warping along the $k_z$ direction. Our results demonstrate the multi-band and two-dimensional nature of the electronic structure. The good agreement between the photoemission data and the band calculations gives the reno…
Electrostatic charging changes the critical temperature of superconducting thin layers. To understand the basic mechanism, it is possible to use the Ginzburg-Landau theory with the boundary condition derived by de Gennes from the BCS theory. Here we show that a similar boundary condition can be obtained from the principle of minimum free energy. We compare the two boundary conditions and use the Budd-Vannimenus theorem as a test of approximations.
We present inelastic neutron scattering results of phonons in (Pb$_{0.5}$Sn$_{0.5}$)$_{1-x}$In$_x$Te powders, with $x=0$ and 0.3. The $x=0$ sample is a topological crystalline insulator, and the $x=0.3$ sample is a superconductor with a bulk superconducting transition temperature $T_c$ of 4.7 K. In both samples, we observe unexpected van Hove singularities in the phonon density of states at energies of 1--2.5 meV, suggestive of local modes. On cooling the superconducting sample through $T_c$, there is an enhancement of these features for energies below twice the superconducting-gap energy. We …
It is generally accepted that vortex core is charged, what illustrates that even in stationary superconductors electric field may be present. Vortex structure and other properties of superconductors are usually calculated in the framework of the Ginzburg-Landau theory, which does not cover electric field. We show that the generalization of the GL theory due to Bardeen allows one to derive a third GL equation for the electrostatic potential. Since the Bardeen theory applies to all temperatures, the presented theory enables one to calculate charge profiles of the vortex under quite general condi…
In this letter we describe the observation of a magnetic field dependent electronic gap, suggestive of local superconductivity, in the point-contact spectrum of micro-crystalline graphite. Magnetic field dependent point-contact spectroscopy was carried out at a temperature of $1.8\,\mathrm{K}$ using an etched aluminium tip. At zero field a gap structure in the differential conductance is observed, showing a gap of $Δ= 4.2\,\mathrm{meV}$. On applying magnetic fields of up to $500\,\mathrm{mT}$, this gap gradually closes, following the theoretical prediction by Ginzburg and Landau for a fully fl…
Neither BCS theory nor London theory contain any charge asymmetry. However it is an experimental fact that a rotating superconductor always exhibits a magnetic field parallel, never antiparallel, to its angular velocity. This and several other experimental observations point to a special role of charge asymmetry in superconductivity, which is the foundation of the theory of hole superconductivity. The theory describes heavy dressed {\it positive} hole carriers in the normal state that undress by pairing and become light undressed {\it negative} electron carriers in the superconducting state. S…
Richardson equations can be mapped on the classical electrostatic problem in two dimensions. We have recently suggested a new analytical approach to these equations in the thermodynamical limit, which is based on the `probability' of the system of charges to be in a given configuration at the effective temperature equal to the interaction constant. In the present paper, we apply this approach to excited states of the Richardson pairing model. We focus on the equally-spaced situation and address arbitrary fillings of the energy layer, where interaction acts. The `partition function' for the cla…
The temperature dependence of the London penetration depth $Δλ(T)$ in the superconducting doped topological crystalline insulator Sn$_{1-x}$In$_x$Te was measured down to 450 mK for two different doping levels, x $\approx$ 0.45 (optimally doped) and x $\approx$ 0.10 (underdoped), bookending the range of cubic phase in the compound. The results indicate no deviation from fully gapped BCS-like behavior, eliminating several candidate unconventional gap structures. Critical field values below 1 K and other superconducting parameters are also presented. The introduction of disorder by repeated parti…
From the outset of superconductivity research it was assumed that no electrostatic fields could exist inside superconductors, and this assumption was incorporated into conventional London electrodynamics. Yet the London brothers themselves initially (in 1935) had proposed an electrodynamic theory of superconductors that allowed for static electric fields in their interior, which they unfortunately discarded a year later. I argue that the Meissner effect in superconductors necessitates the existence of an electrostatic field in their interior, originating in the expulsion of negative charge fro…
The dynamical equations of an electromagnetic field coupled with a conducting material are studied. The properties of the interaction are described by a classical field theory with tensorial material laws in space-time geometry. We show that the main features of superconducting response emerge in a natural way within the covariance, gauge invariance and variational formulation requirements. In particular, the Ginzburg-Landau theory follows straightforward from the London equations when fundamental symmetry properties are considered. Unconventional properties, such as the interaction of superco…
A recent analysis by Kadin has noted that the superconducting wavefunction within the BCS theory may be represented in real-space as a spherical electronic orbital (on the scale of the coherence length) coupled to a standing-wave lattice vibration. This lattice vibration, effectively a bound phonon, has wavevector 2kf and a near-resonant frequency (on the order of the Debye frequency) that maximizes the attractive electrostatic interaction energy with the electronic orbital. The present paper extends this picture to a coherent standing-wave pattern of electron and phonon waves that traverses t…
Quantum confinement of the perpendicular motion of electrons in single-crystalline metallic superconducting nanofilms splits the conduction band into a series of single-electron subbands. A distinctive feature of such a nanoscale multi-band superconductor is that the energetic position of each subband can vary significantly with changing nanofilm thickness, substrate material, protection cover and other details of the fabrication process. It can occur that the bottom of one of the available subbands is situated in the vicinity of the Fermi level. We demonstrate that the character of the superc…
All solid phases of bismuth under pressure, but one, have been experimentally found to superconduct. From Bi-I to Bi-V, avoiding Bi-IV, they become superconductors and perhaps Bi-IV may also become superconductive. To investigate the influence of the electronic properties N(E) and the vibrational properties F(ω) on their superconductivity we have ab initio calculated them for the corresponding experimental crystalline structures, and using a BCS approach have been able to determine their critical temperatures Tc obtaining results close to experiment: For Bi-I (The Wyckoff Phase) we predicted a…
An overview of the recent efforts in point-contact (PC) spectroscopy of the nickel borocarbide superconductors RNi2B2C in the normal and superconducting (SC) state is given. The results of measurements of the PC electron- boson(phonon) interaction spectral function are presented. Phonon maxima and crystalline-electric-field (CEF) excitations are observed in the PC spectra of compounds with R=Dy, Ho, Er and Tm, while for R=Y a dominant phonon maximum around 12 meV is characteristic. Additionally, non-phonon and non-CEF maxima are observed near 3 meV in R=Ho and near 6 meV in R=Dy. Directional P…
We present a broadband optical-conductivity study of superconducting single-crystalline EuFe2(As1-xPx)2 with three different substitutional levels. We analyze the normal-state electrodynamics by decomposing the conductivity spectra using a Drude-Lorentz model with two Drude terms representing two groups of carriers with different scattering rates. The analysis reveals that the scattering rate of at least one of the Drude components develops linearly with temperature for each doping level. This points towards strong electron-electron correlations and a non-Fermi-liquid behavior in the P-substit…
Point-contact (PC) investigations on the title compound in the normal and superconducting (SC) state (Tc=10,6 K) are presented. The temperature dependence of the SC gap of TmNi2B2C determined from Andreev-reflection (AR) spectra using the standard single-gap approximation (SGA) deviates from the BCS behavior in displaying a maximum at about Tc/2. A refined analysis within the two-gap approximation provides evidence for the presence of a second gap twice as large as the main gap (the first one), while the latter is close to that within the SGA. This way, TmNi2B2C expands the number of nickel bo…
