The behavior of the topological index, characterizing the properties of superconducting phases of quasi-two-dimensional systems with nontrivial topology, is investigated depending on the temperature and parameters of the effective non-Hermitian Hamiltonian. For this purpose, a method of calculating the topological index, based on a self-consistent functional-integral theory, is proposed. The method makes it possible to take into account thermal fluctuations and study the behavior of the topological index as a function of temperature and Hamiltonian parameters. The chiral d+id superconducting phase of a quasi-two-dimensional model with effective attraction between the electrons located at the nearest sites of a triangular lattice is considered. It is shown that the characteristic features in the energy dependence of the self-energy part, which arise when thermal fluctuations are taken into account, have a structure that does not lead to a change in the topological properties of the system. It is found that thermal fluctuations, as well as an increase in effective attraction in this system, contribute to the expansion of the temperature region, in which the value of the topological index is close to the integer C1=-2.
We consider Aharonov - Bohm effect at normal metal-inhomogeneous LOFF superconducting state transition. It is shown that magnetic flux can increase the transition temperature and AB oscillations can have the double-peak structure at one period. Expressions for fuctuational heat capacity and persistent current are calculated for a thin ring and a cylinder. We also discuss the effect of fluctuations interaction in the nonuniform states in the vicinity of the superconducting transition.
Strong-coupling approach to temperature dependence of competing orders of superconductivity: Possible time-reversal symmetry breaking and nontrivial topology
Nontrivial Boundary-Mediated Superconducting Transport in a TRSB Topological Iron-Based Superconductor
Boston College（波士顿学院）；University of California, Irvine（加州大学尔湾分校）；Boston University（波士顿大学）；Hong Kong University of Science and Technology（香港科技大学）；National Institute of Standards and Technology（美国国家标准与技术研究院）；Theiss Research, Inc.（Theiss研究公司）；Cornell University（康奈尔大学）
The classification of topological states of matter in terms of unitary symmetries and dimensionality predicts the existence of nontrivial topological states even in zero-dimensional systems, i.e., a system with a discrete energy spectrum. Here, we show that a quantum dot coupled with two superconducting leads can realize a nontrivial zero-dimensional topological superconductor with broken time-reversal symmetry, which corresponds to the finite size limit of the one-dimensional topological superconductor. Topological phase transitions corresponds to a change of the fermion parity, and to the pr…
A nodeless $d$-wave state is likely in superconducting monolayer FeSe on SrTiO$_3$. The lack of nodes is surprising but has been shown to be a natural consequence of the observed small interband spin-orbit coupling. Here we examine the evolution from a nodeless state to the nodal state as this spin-orbit coupling is increased from a topological perspective. We show that this evolution depends strongly on the orbital content of the superconducting degrees of freedom. In particular, there are two $d$-wave solutions, which we call orbitally trivial and orbitally nontrivial. In both cases, the nod…
Precise gap structure in LiFeAs (Tc = 18 K) given by ARPES studies offers us significant information to understand the pairing mechanism in iron-based superconductors. The most remarkable characteristics in LiFeAs gap structure would be that "the largest gap emerges on the tiny hole-pockets around Z point". This result had been naturally explained in terms of the orbital-fluctuation scenario (T. Saito et al., Phys. Rev. B 90, 035104 (2014)), whereas an opposite result is obtained by the spin-fluctuation scenario. In this paper, we study the gap structure in LiFeAs by taking the spin-orbit inte…
Spectroscopic Evidence for Nontrivial Band Topology in Superconducting FeTe/MnTe Heterostructure
Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China（中国科学技术大学微尺度物质科学国家研究中心）；School of Emerging Technology, University of Science and Technology of China（中国科学技术大学前沿技术学院）；Hefei National Laboratory（合肥国家实验室）；Department of Physics, University of Science and Technology of China（中国科学技术大学物理系）
Discovery of a nonsymmorphic superconductor with spontaneous rotational symmetry breaking and nontrivial zero modes
Beijing National Center for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；National Center for Nanoscience and Technology, Chinese Academy of Sciences（中国科学院国家纳米科学中心）；School of Physics, Beijing Institute of Technology（北京理工大学物理学院）
We report the discovery of superconductivity in binary alloy Sn$_{1-x}$Sb$_{x}$ with $x$ in the range of 0.43 to 0.6, which possesses a modulated rhombohedral structure due to the incommensurate ordering of Sn and Sb layers along the $c$-axis. The specific heat measurements indicate a weakly coupled, fully gapped superconducting state in this homogeneity range with a maximum bulk $T_{\rm c}$ of 1.58 K at $x$ = 0.46, though the electronic specific heat and Hall coefficients remain nearly $x$-independent. The nonmonotonic dependence of the bulk $T_{\rm c}$ is discussed in relation to the effects…
Transition metal dichalcogenides offer unprecedented versatility to engineer 2D materials with tailored properties to explore novel structural and electronic phase transitions. In this work, we present the atomic-scale evolution of the electronic ground state of a monolayer of Nb$_{1-δ}$Mo$_δ$Se$_2$ across the entire alloy composition range (0 < $δ$ < 1) using low-temperature (300 mK) scanning tunneling microscopy and spectroscopy (STM/STS). In particular, we investigate the atomic and electronic structure of this 2D alloy throughout the metal to semiconductor transition (monolayer NbSe$_2$ to…
The interface between magnetic material and superconductors has long been predicted to host unconventional superconductivity, such as spin-triplet pairing and topological nontrivial pairing state, particularly when spin-orbital coupling (SOC) is incorporated. To identify these novel pairing states, fabricating homogenous heterostructures which contain such various properties are preferred, but often challenging. Here we synthesized a tri-layer type van-der Waals heterostructure of MnTe/Bi2Te3/Fe(Te, Se), which combined s-wave superconductivity, thickness dependent magnetism and strong SOC. Via…
The transition-metal-based kagome metals provide a versatile platform for correlated topological phases hosting various electronic instabilities. While superconductivity is rare in layered kagome compounds, its interplay with nontrivial topology could offer an engaging space to realize exotic excitations of quasiparticles. Here, we use scanning tunneling microscopy (STM) to study a newly discovered Z$_2$ topological kagome metal CsV$_3$Sb$_5$ with a superconducting ground state. We observe charge modulation associated with the opening of an energy gap near the Fermi level. When across single-u…
Three-dimensional line-nodal superconductors exhibit nontrivial topology, which is protected by the time-reversal symmetry. Here we investigate four types of short-range interaction between the gapless line-nodal fermionic quasiparticles by carrying renormalization group analysis. We find that such interactions can induce the dynamical breaking of time-reversal symmetry, which alters the topology and might lead to six possible distinct superconducting states, distinguished by the group representations. After computing the susceptibilities for all the possible phase-transition instabilities, we…
We study the behavior of spinless fermions in superconducting state, in which the phases of the superconducting order parameter depend on the direction of the link. We find that the energy of the superconductor depends on the phase differences of the superconducting order parameter. The solutions for the phases corresponding to the energy minimuma, lead to a topological superconducting state with the nontrivial Chern numbers. We focus our quantitative analysis on the properties of topological states of superconductors with different crystalline symmetry and show that the phase transition in th…
We study the superconducting proximity effect on the helical edge states of time-reversal-symmetric fractional topological insulators(FTI). The Cooper pairing of electrons results in many-particle condensation of the fractionalized excitations on the edge. We find in the strong-coupling phase, localized zero-energy modes emerge on interfaces between superconducting regions and magnetically insulating regions, which are responsible for topological degeneracy of the ground states. By mapping the low-energy effective Hamiltonian to quantum Potts model, we determine the operator algebra of the zer…
Robust quantum systems rely on having a protective environment with minimized relaxation channels. Superconducting gaps play an important role in the design of such environments. The interaction of localized single spins with a conventional superconductor generally leads to intrinsically extremely narrow Yu-Shiba-Rusinov (YSR) resonances protected inside the superconducting gap. However, this may not apply to superconductors with nontrivial, energy dependent order parameters. Exploiting the Fe-doped two-band superconductor NbSe$_2$, we show that due to the nontrivial relation between its compl…
We report the pressure dependence of the superconducting transition temperature, $T_c$, in TlNi$_2$Se$_{2-x}$S$_x$ detected via the AC susceptibility method. The pressure-temperature phase diagram constructed for TlNi$_{2}$Se$_{2}$, TlNi$_{2}$S$_{2}$ and TlNi$_{2}$SeS exhibits two unexpected features: (a) a sudden collapse of the superconducting state at moderate pressure for all three compositions and (b) a dome-shaped pressure dependence of $T_c$ for TlNi$_{2}$SeS. These results point to the nontrivial role of S substitution and its subtle interplay with applied pressure, as well as novel su…
Recently, superconductivity has been discovered in rock-salt structured binary lanthanum monoxide LaO through state-of-the-art oxide thin-film epitaxy. In this work, we reveal that the normal state of superconducting LaO is a $Z_2$ nontrivial topological metal, where the Dirac point protected by the crystal symmetry is located around the Fermi energy. By analysing the orbital characteristics, we show that the nature of the topological band structure of LaO originates from the intra-atomic transition from the outer shell La 5$d$ to the inner shell 4$f$ orbitals driven by the strong octahedral c…
We propose a simple model consisting of a magnetic domain wall proximity-coupled to an $s$-wave superconductor for realization of Majorana zero-energy modes. A spin-dependent gauge transformation translates the rotating magnetic profile through the domain wall to effective spin-orbit and Zeeman terms. The Hamiltonian breaks time reversal and chiral symmetries, while preserving particle-hole symmetry, placing itself into topological D class characterized by the $\mathbb{Z}_{2}$ topological invariant for quasi one-dimensional system. The low-energy sector of the model maps to the one isomorphic …
The behavior of thermal fluctuations of a superconducting order parameter with extended $ s $ and chiral $ d + id $ symmetry is investigated. The study is carried out on a triangular lattice within the framework of the quasi-two-dimensional single-band model with attraction between electrons at neighboring sites. The method of consistent consideration of the order parameter fluctuations and the charge carrier scattering by fluctuations of coupled electron pairs, based on the theory of functional integration is used. The distribution functions of the phase fluctuation probabilities depending on…
It is interesting to ask whether electron interaction can turn a topologically trivial superconductor into a nontrivial one without the presence of spin-obital coupling. In this paper we solve a correlated $s$-wave superconducting model exactly. The variation of the fermion number parity of the superconducting ground state as a function of the electron interaction is calculated and the topological phase diagram is obtained. Topological $s$-wave superconducting states are revealed in the doped Mott insulators, which is further confirmed by the numerical investigation of the topological boundary…
We study topological vortex phases in iron-based superconductors. Besides the previously known vortex end Majorana zero modes (MZMs) phase stemming from the existence of a three dimensional (3D) strong topological insulator state, we show that there is another topologically nontrivial phase as iron-based superconductors can be doped superconducting 3D weak topological insulators (WTIs). The vortex bound states in a superconducting 3D WTI exhibit two different types of quantum states, a robust nodal superconducting phase with pairs of bulk MZMs and a full-gap topologically nontrivial supercondu…
The interplay of BCS superconductivity and nontrivial band topology is expected to give rise to opportunities for creating topological superconductors, achieved through pairing spin-filtered boundary modes via superconducting proximity effects. The thus-engineered topological superconductivity can, for example, facilitate the search for Majorana fermion quasiparticles in condensed matter systems. Here we report a first-principles study of Mg$_2$Pb and predict that it should be a superconducting topological material. The band topology of Mg$_2$Pb is identical to that of the archetypal quantum s…
An unconventional pairing mechanism in the heavy-fermion material $\mathrm{URu_{2}Si_{2}}$ is studied. We propose a mixed singlet-triplet $d$-density wave to be the hidden-order state in $\mathrm{URu_{2}Si_{2}}$. The exotic order is topologically nontrivial and supports a charge $2e$ skyrmionic spin texture, which is assumed to fractionalize into merons and antimerons at the deconfined quantum critical point. The interaction between these fractional particles results in a (pseudo)spin-singlet chiral $d$-wave superconducting state, which breaks time reversal symmetry. Therefore, it is highly li…
The search for nontrivial superconductivity in novel quantum materials is currently a most attractive topic in condensed matter physics and material science. The experimental studies have progressed quickly over the past couple of years. In this article, we report systematic studies of superconductivity in Au2Pb single crystals. The bulk superconductivity (onset transition temperature, Tconset= 1.3 K) of Au2Pb is characterized by both transport and diamagnetic measurements, where the upper critical field Hc2 shows unusual quasi-linear temperature dependence. The superconducting gap is revealed…
Non-Abelian toplogical superconductors are characterized by the existence of {zero-energy} Majorana fermions bound in the quantized vortices. This is a consequence of the nontrivial bulk topology characterized by an {\em odd} Chern number. It is found that in topological semimetals with a single two-bands crossing point all the gapped superconductors are non-Abelian ones. Such a property is generalized to related but more generic systems which will be useful in the search of non-Abelian superconductors and Majorana fermions.
We show that finite angular momentum pairing chiral superconductors on the triangular lattice have point zeroes in the complex gap function. A topological quantum phase transition takes place through a nodal superconducting state at a specific carrier density $x_c$ where the normal state Fermi surface crosses the isolated zeros. For spin singlet pairing, we show that the second nearest neighbor $d+id$-wave pairing can be the dominant pairing channel. The gapless critical state at $x_c\simeq0.25$ has six Dirac points and is topologically nontrivial with a $T^3$ spin relaxation rate below $T_c$.…
Superconductivity in crystals without inversion symmetry has received extensive attention due to its unconventional pairing and possible nontrivial topological properties. Using first-principles calculations, we systemically study the electronic structure of noncentrosymmetric superconductors $A_2$Cr$_3$As$_3$ ($A$=Na, K, Rb and Cs). Topologically protected triply degenerate points connected by one-dimensional arcs appear along the $C_{3}$ axis, coexisting with strong ferromagnetic (FM) fluctuations in the non-superconducting state. Within random phase approximation, our calculations show that…
We have investigated the ternary noncentrosymmetric superconductors TaXSi (X=Re, Ru) by magnetization, resistivity, and specific heat measurements. The samples crystallize in orthorhombic TiFeSi structure having superconducting transition Tc = 5.32 K and 3.91 K, for TaReSi and TaRuSi respectively. Specific heat measurements indicated an s-wave nature of both materials with a moderately coupled nature. However, a low value of specific heat jump and the concave nature of the upper critical field suggests a nontrivial superconducting gap.
A large number of half-Heusler compounds have been recently proposed as three-dimensional (3D) topological insulators (TIs) with tunable physical properties.However, no transport measurements associated with the topological surface states have been observed in these half-Heusler candidates due to the dominating contribution from bulk electrical conductance. Here we show that, by reducing the mobility of bulk carriers, a two-dimensional (2D) weak antilocalization (WAL) effect, one of the hallmarks of topological surface states, was experimentally revealed from the tilted magnetic field dependen…
We present a unified description of a junction between $s$-wave (BCS) superconductors and a junction between $p$-wave superconductors in a topologically nontrivial phase, which relies on a scattering state expansion. We compute Josephson current and thermal noise in the two kinds of junction and exhibit some characteristic features for a junction of two topological superconductors hosting Majorana zero-energy modes.
The authors of the Letter PRL 89, 017004 (2002) predict nontrivial flux lattice structures in UPt3 in vicinity of the superconducting transition between the A and B phases for low magnetic fields, an important conclusion for motivating future experiments. We show that the approach and the conclusions of this Letter are wrong. The transitions between the different superconducting phases in the mixed state are pointed out to be rather crossovers than real second-order phase transitions within the most popular theoretical models of a two-component superconducting order parameter for UPt3.
The interplay of nontrivial topology and superconductivity in condensed matter physics gives rise to exotic phenomena. However, materials are extremely rare where it is possible to explore the full details of the superconducting pairing. Here, we investigate the momentum dependence of the superconducting gap distribution in a novel Dirac material PdTe. Using high resolution, low temperature photoemission spectroscopy, we establish it as a spin-orbit coupled Dirac semimetal with the topological Fermi arc crossing the Fermi level on the (010) surface. This spin-textured surface state exhibits a …
For superconducting nanowire with the pairing of extended s-type symmetry, Rashba spin-orbit interaction in a magnetic field, the influence of strong intersite charge correlations on single-particle Majorana excitations is analyzed. This problem is investigated on the basis of the density matrix renormalization group numerical method. It is shown that with an increase in the repulsion intensity of electrons located at the neighboring sites, two subbands emerge in the lower Hubbard band of the open system. Based on calculations of the Majorana polarization and degeneracy of the entanglement spe…
As one of the most fundamental physical phenomena, the anomalous Hall effect (AHE) typically occurs in ferromagnetic materials but is not expected in the conventional superconductors. Here, we have observed a giant AHE in kagome superconductor CsV3Sb5 with transition temperature (Tc) of 2.7 K. The anomalous Hall conductivity reaches up to 2.1*10^4 Ω-1 cm-1 which is larger than those observed in most of the ferromagnetic metals. Strikingly, the emergence of AHE exactly follows the higher-temperature charge-density-wave (CDW) transition with TCDW ~ 94 K, indicating a strong correlation between t…
High-temperature superconductivity and a wide variety of exotic superconducting states discovered in FeSe-based materials have been at the frontier of research on condensed matter physics over the past decade. Unique properties originating from the multiband electronic structure, strongly orbital-dependent phenomena, extremely small Fermi energy, electronic nematicity, and topological aspects give rise to many distinct and fascinating superconducting states. Here, we provide an overview of our current understanding of the superconductivity of {\it bulk} FeSe-based materials, focusing on FeSe a…
We study Josephson junctions made of semiconducting nanowires with Rashba spin-orbit coupling, where superconducting correlations are induced by the proximity effect. In the presence of a suitably directed magnetic field, the system displays the anomalous Josephson effect: a nonzero supercurrent in the absence of a phase bias between two superconductors. We show that this anomalous current can be increased significantly by tuning the nanowire into the helical regime. In particular, in a short junction, a large anomalous current is a signature for topologically nontrivial superconductivity in t…
The diversity of emergent phenomena in quantum materials often arises from the interplay between different physical energy scales or broken symmetries. Cooperative interactions among them are rare; however, when they do occur, they often stabilize fundamentally new ground states or phase behaviors. For instance, a pair density wave can form when the superconducting order parameter borrows spatial periodical variation from charge order; a topological superconductor can arise when topologically nontrivial electronic states proximitize with or participate in the formation of the superconducting c…
Over the past fifteen years, tremendous efforts have been devoted to realizing topological superconductivity in realistic materials and systems, predominately propelled by their promising application potentials in fault-tolerant quantum information processing. In this article, we attempt to give an overview on some of the main developments in this field, focusing in particular on two-dimensional crystalline superconductors that possess either intrinsic p-wave pairing or nontrivial band topology. We first classify the three different conceptual schemes to achieve topological superconductor (TSC…
Topological nonsymmorphic crystalline superconductivity (TNCS) is an intriguing phase of matter, offering a platform to study the interplay between topology, superconductivity, and nonsymmorphic crystalline symmetries. Interestingly, some of TNCS are classified into $Z_4$ topological phases, which have unique surface states referred to as a Möbius strip or an hourglass, and have not been achieved in symmorphic superconductors. However, material realization of $Z_4$ TNCS has never been known, to the best of our knowledge. Here we propose that the paramagnetic superconducting phase of UCoGe unde…
High-pressure synthesis techniques have allowed for the growth of samples on the indium-rich side of (Pb,In)Te, which have increased superconducting transition temperatures compared to lead-rich compounds. In this study we present measurements of the temperature dependence of the London penetration depth $Δλ(T)$ in the compound In$_{0.8}$Pb$_{0.2}$Te, which shows a bulk $T_{c,onset}$ of $\sim4.75$ K. The results indicate fully gapped BCS-like behavior, ruling out odd-parity, topologically nontrivial $A_{2u}$ pairing; however, odd-parity $A_{1u}$ pairing is still possible. Critical field values…
Semiconductor-superconductor hybrid systems are promising candidates for the realization Majorana fermions and topological order, i.e. topologically protected degeneracies, in solid state devices. We show that the topological order is mirrored in the excitation spectra and can be observed in nonlinear Coulomb blockade transport through a ring-shaped nanowire. Especially, the excitation spectrum is almost independent of magnetic flux in the topologically trivial phase but acquires a characteristic $h/e$ magnetic flux periodicity in the nontrivial phase. The transition between the trivial and no…
Orthorhombic (space group: Pnma) Nb2P5 is a high-pressure phase that is quenchable to ambient pressure, which could viewed as the zigzag infinite P chain-inserted NbP2. We report herein the high-pressure crystal growth of Nb2P5 and the discovery of its superconducting transition at Tc ~ 2.6 K. The electrical resistivity, magnetization, and specific heat capacity measurements on the high-quality crystal unveiled a conventional type-II weakly coupled s-wave nature of the superconductivity, with the upper critical field Hc2(0) ~ 0.5 T, the electron-phonon coupling strength λep ~ 0.5 - 0.8, and th…
We review some recent advances in studies of phase-coherent thermoelectric effects in superconducting hybrid structures such as, e.g., Andreev interferometers. We elucidate a number of mechanisms of electron-hole symmetry breaking in such systems causing dramatic enhancement of thermoelectric effects. We demonstrate that the flux-dependent thermopower exhibits periodic dependence on the applied magnetic flux $Φ_x$ which in some limits may reduce to either odd or even functions of $Φ_x$ in accordance with experimental observations. We also show that dc Josephson current in Andreev interferomete…
Superconductivity frequently appears by doping compounds that show a collective phase transition. So far, however, this has not been observed in topological materials. Here we report the discovery of superconductivity induced by Ga doping in orthorhombic Re$_{3}$Ge$_{7}$, which undergoes a second-order metal-insulator-like transition at $\sim$58 K and is predicted to have a nontrivial band topology. It is found that the substitution of Ga for Ge leads to hole doping in Re$_{3}$Ge$_{7-x}$Ga$_{x}$. As a consequence, the phase transition is gradually suppressed and disappears above $x$ = 0.2. At …
We consider two possible mechanisms for single-vortex fluctuative entry/exit through the surface barrier in ultrathin superconducting disk-shaped nanoislands made of Pb and consisting of just few monoatomic layers, which can be fabricated using modern techniques. We estimate tunnelling probabilities and establish criteria for the crossover between these two mechanisms depending on magnetic field and system sizes. For the case of vortex entry, quantum tunnelling dominates on the major part of the temperature/flux phase diagram. For the case of vortex exit, thermal activation turns out to be mor…
Interference of proximity induced superconducting correlations in mesoscopic metallic rings is sensitive to the magnetic flux $Φ$ inside these rings. This is the reason for magnetoconductance oscillations in such systems. We detected experimentally and explained theoretically a novel effect: the phase of these oscillations can switch between 0 and $π$ depending on the resistance of intermetallic interfaces and temperature. The effect is due to a nontrivial interplay between the proximity induced enhancement of the local conductivity and the proximity induced suppression of the density of state…
The proximity induced pair potential in a topological insulator-superconductor hybrid features an interesting superposition of a conventional spin-singlet component from the superconductor and a spin-triplet one induced by the surface state of the topological insulator. This singlet-triplet superposition can be altered by the presence of a magnetic field. We study the interplay between topological order and superconducting correlations performing a symmetry analysis of the induced pair potential, using Green functions techniques to theoretically describe ballistic junctions between superconduc…
