Recent angle-resolved photoemission experiments have observed a proximity-induced superconducting gap in the helical surface states of a thin film of the 3D topological insulator Bi$_2$Se$_3$ grown on a superconducting NbSe$_2$ substrate. The superconducting coherence peaks in the electronic density of states are strongly suppressed when the topological insulator is doped with magnetic Mn impurities, which was interpreted as the complete destruction of helical superconductivity in the topological surface states. Motivated by these experiments, we explore a different possibility: gapless helical superconductivity, where a gapless electronic density of states coexists with a nonzero helical superconducting order parameter. We study a model of superconducting Dirac fermions coupled to random magnetic impurities within the Abrikosov-Gor'kov framework, and find finite regions of gapless helical superconductivity in the phase diagram of the system for both proximity-induced and intrinsic superconductivity. For the latter, we derive universal rates of supression of the superconducting transition temperature due to magnetic scattering and, for a Fermi level at the Dirac point, a universal rate of increase of the quantum critical attraction strength.
We explore Andreev states at the interface of graphene and a superconductor for a uniform pseudo-magnetic field. Near the zeroth-pseudo Landau level, we find a topological transition as a function of applied Zeeman field, at which a gapless helical mode appears. This 1D mode is protected from backscattering as long as intervalley- and spin-flip scattering are suppressed. We discuss a possible experimental platform to detect this gapless mode based on strained suspended membranes on a superconductor, in which dynamical strain causes charge pumping
Recent experimental investigations of arrays of magnetic atoms deposited on top of a superconductor have opened a new chapter in the search of topological superconductivity. We generalize the microscopic model derived by Pientka et al. [Phys. Rev. B \textbf{88}, 155420 (2013)] to accommodate the effects of finite supercurrent in the host material. Previously it was discovered that helical chains with nonplanar textures are plagued by a gapless phase. We show that by employing supercurrent it is possible to tune the chain from the gapless phase to the topological gapped phase. It is also possib…
Two-dimensional helical superconductivity and gapless superconducting edge modes in the 1T$^\prime$-WS$_2$/2H-WS$_2$ heterophase bilayer
University of California, Santa Barbara（加州大学圣塔芭芭拉分校）；Brookhaven National Laboratory（布鲁海文国家实验室）；Stony Brook University（石溪大学）；Flatiron Institute（平顿研究所）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；University of Nevada, Reno（内华达大学里诺分校）
We present the dispersion relations for quasiparticle excitations about the color-flavor locked ground state of QCD at high baryon density. In the presence of condensates which pair light and strange quarks there need not be an energy gap in the quasiparticle spectrum. This raises the possibility of gapless color superconductivity, with a Meissner effect but no minimum excitation energy. Analysis within a toy model suggests that gapless color superconductivity may occur only as a metastable phase.
We study a two-dimensional heterostructure comprised of a monolayer of the magnetic insulator chromium triiodide (CrI$_3$) on a superconducting lead (Pb) substrate. Through first-principles computation and a tight-binding model, we demonstrate that charge transfer from the Pb substrate dopes the CrI$_3$ into an effective half-metal, allowing for the onset of a gapless topological superconductivity phase via the proximity effect. This phase, in which there exists a superconducting gap only in part of the Fermi surface, is shown to occur generically in 2D half-metal-superconductor heterostructur…
We show that an in-plane magnetic field can drive two-dimensional spin-orbit-coupled systems under superconducting proximity effect into a gapless phase where parts of the normal state Fermi surface are gapped, and the ungapped parts are reconstructed into a small Fermi surface of Bogoliubov quasiparticles at zero energy. Charge distribution, spin texture, and density of states of such "partial Fermi surface" are discussed. Material platforms for its physical realization are proposed.
We show that a single-fermion quantum dot acquires odd-frequency Gor'kov anomalous averages in proximity to strongly correlated Majorana zero modes, described by the Sachdev-Ye-Kitaev (SYK) model. Despite the presence of finite anomalous pairing, the superconducting gap vanishes for the intermediate coupling strength between the quantum dot and Majoranas. The increase of the coupling leads to smooth suppression of the original quasiparticles. This effect might be used as a characterization tool for recently proposed tabletop realizations of the SYK model.
We study cross-flavor Cooper pairing in a relativistic system of two fermion species with mismatched Fermi surfaces. We find that there exist gapless phases which are characterized by either one or two gapless nodes in the energy spectra of their quasiparticles. An analysis of the current-current correlator reveals that, at strong coupling, both of these gapless phases can be free of magnetic instabilities and thus are stable. This is in contrast to the weak-coupling case where there are always two gapless nodes and the phase becomes magnetically unstable.
We study how non-helical spin textures at the boundary between a topological insulator (TI) and a superconductor (SC) affect the proximity-induced superconductivity of the TI interface state. We consider TIs coupled to both spin-singlet and spin-triplet SCs, and show that for the spin-triplet parent SCs the resulting order parameter induced onto the interface state sensitively depends on the symmetries which are broken at the TI-SC boundary. For chiral spin-triplet parent SCs, we find that nodal proximity-induced superconductivity emerges when there is broken twofold rotational symmetry which …
Non-centrosymmetric superconductors exhibit the magnetoelectric effect which manifests itself in the appearance of the magnetic spin polarization in response to a dissipationless electric current (supercurrent). While much attention has been dedicated to the thermodynamic version of this phenomenon (Edelstein effect), non-equilibrium transport magnetoelectric effects have not been explored yet. We propose the magnetoelectric Andreev effect (MAE) which consists in the generation of spin-polarized triplet Andreev conductance by an electric supercurrent. The MAE stems from the spin polarization o…
We reveal that in a magnetically polarized medium, a specific commensurate triplet pair density wave (TPDW) superconducting (SC) state, the staggered d-wave $Π$-triplet state, may coexist with homogeneous triplet SC states and even dominate eliminating them under generic conditions. When only this TPDW SC state is present, we have the remarkable phenomenon of gapless superconductivity. This may explain part of the difficulties in the realization of the engineered localized Majorana fermion modes for topological quantum computation. We point out qualitative characteristics of the tunneling dens…
Coexistence of superconducting and normal components in nanowires at currents below the critical (a "mixed" state) would have important consequences for the nature and range of potential applications of these systems. For clean samples, it represents a genuine interaction effect, not seen in the mean-field theory. Here we consider properties of such a state in the gravity dual of a strongly coupled superconductor constructed from D3 and D5 branes. We find numerically uniform gapless solutions containing both components but argue that they are unstable against phase separation, as their free en…
We establish quasi-two-dimensional thin films of iron-based superconductors (FeSCs) as a new high-temperature platform for hosting intrinsic time-reversal-invariant helical topological superconductivity (TSC). Based on the combination of Dirac surface state and bulk extended $s$-wave pairing, our theory should be directly applicable to a large class of experimentally established FeSCs, opening a new TSC paradigm. In particular, an applied electric field serves as a "topological switch" for helical Majorana edge modes in FeSC thin films, allowing for an experimentally feasible design of gate-co…
Using a single coil mutual inductance technique, we measure the low temperature dependence of the magnetic penetration depth in superconducting NbN films prepared with similar critical temperatures around 16 K but with different microstructures. Only (100) epitaxial and weakly granular (100) textured films display the characteristic exponential dependence of conventional BCS s-wave superconductors. More granular (111) textured films exhibit a linear dependence, indicating a gapless state in spite of the s-wave gap. This result is quantitatively explained by a model of thermal phase fluctuation…
We develop a unified framework to classify topological defects in insulators and superconductors described by spatially modulated Bloch and Bogoliubov de Gennes Hamiltonians. We consider Hamiltonians H(k,r) that vary slowly with adiabatic parameters r surrounding the defect and belong to any of the ten symmetry classes defined by time reversal symmetry and particle-hole symmetry. The topological classes for such defects are identified, and explicit formulas for the topological invariants are presented. We introduce a generalization of the bulk-boundary correspondence that relates the topologic…
We argue that the Fermi arc observed in angle resolved photoemission measurements in underdoped cuprates can be understood as a consequence of inelastic scattering in a d-wave superconductor. We analyze this phenomenon in the context of strong coupling Eliashberg theory, deriving a `single lifetime' model for describing the temperature evolution of the spectral gap as measured by single particle probes such as photoemission and tunneling.
We present a detailed study of the recently proposed gapless color superconductivity in neutral two-flavor quark matter in beta-equilibrium at zero as well as at finite temperature. We clarify the nature of the fermionic quasiparticles, and discuss the physical properties of this gapless phase of quark matter. The appearance of two "secondary" spin-1 condensates in the gapless ground state is pointed out. The gluon screening properties are also discussed. It is found that finite temperature properties of the gapless color superconductor are rather unusual. One of the most striking results is t…
Despite much effort for over the two decades, the paring symmetry of a Sr$_2$RuO$_4$ superconductor has been still unclear. In this Rapid Communication, motivated by the recent rapid progress in fabrication techniques for Sr$_2$RuO$_4$ thin-films, we propose a promising strategy for identifying the spin-triplet superconductivity in the thin-film geometry by employing an antisymmetric spin-orbit coupling potential and a Zeeman potential due to an external magnetic field. We demonstrate that a spin-triplet superconducting thin-film undergoes a phase transition from a helical state to a chiral st…
Large Hubbard U limit of the Kane-Mele model on a zigzag ribbon of honeycomb lattice near half-filling is studied via a renormalized mean-field theory. The ground state exhibits time-reversal symmetry (TRS) breaking d + i d'-wave superconductivity. At large spin-orbit coupling, the Z2 phase with non-trivial spin Chern number in the pure Kane-Mele model is persistent into the TRS broken state (called spin-Chern phase), and has two pairs of counter-propagating helical Majorana modes at the edges. As the spin-orbit coupling is reduced, the system undergoes a topological quantum phase transition f…
Recently the evidence of the helical magnetic structure modulated along $c$-axis with the period of four lattice parameters was obtained in easy $ab$ plane ferromagnetic superconductor EuRbFe$_4$As$_4$ [K. Iida et al., Phys. Rev. B 100, 014506 (2019)]. We argue that such structure may appear due to the presence of superconductivity. In spite of the very small value of the exchange field acting on the superconducting electrons in EuRbFe$_4$As$_4$, the exchange mechanism of interaction between superconductivity and ferromagnetism could dominate over the electromagnetic one and this circumstance …
In this letter we explore the Higgs instability in the gapless superfluid/superconducting phase. This is in addition to the (chromo)magnetic instability that is related to the fluctuations of the Nambu-Goldstone bosonic fields. While the latter may induce a single-plane-wave LOFF state, the Higgs instability favors spatial inhomogeneity and cannot be removed without a long range force. In the case of the g2SC state the Higgs instability can only be partially removed by the electric Coulomb energy. But this does not exclude the possibility that it can be completely removed in other exotic state…
The superconducting TMD 4Hb-TaS$_2$ consists of alternating layers of H and T structures, which in their bulk form are metallic and Mott-insulating, respectively. Recently, this compound has been proposed as a candidate chiral superconductor, due to an observed enhancement of the muon spin relaxation at $T_c$. 4Hb-TaS$_2$ also exhibits a puzzling $T$-linear specific heat at low temperatures, which is unlikely to be caused by disorder. Elucidating the origin of this behavior is an essential step in discerning the true nature of the superconducting ground state. Here, we propose a simple model t…
We investigate the superconductivity (SC) driven by correlation effects in electron-doped bilayer BiH near a type-II van Hove singularity (vHS). By functional renormalization group, we find triplet $p$-wave pairing prevails in the interaction parameter space, except for spin density wave (SDW) closer to the vHS or when the interaction is too strong. Because of the large atomic spin-orbital coupling (SOC), the $p$-wave pairing occurs between equal-spin electrons, and is chiral and two-fold degenerate. The chiral state supports in-gap edge states, even though the low energy bands in the SC state…
Strain-Induced Helical Superconductivity and the Zero-Field Diode Effect
Institute for Theory of Condensed Matter, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院凝聚态理论研究所）；Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院量子材料与技术研究所）
We study theoretically the two interacting one-dimensional helical modes at the edges of the quantum spin Hall systems. A new type of inter-edge correlated liquid (IECL) without the spin gap is found. This liquid shows the diverging density wave (DW) and superconductivity (SC) correlations much stronger than those of the spinfull electrons. Possible experimental observations are also discussed.
In a variety of rare-earth based compounds singlet superconductivity coexists with helical magnetism. Here we demonstrate that surfaces of these systems should generically host a finite density of zero-energy Majorana modes. In the limit of vanishing disorder, these modes lead to a divergent contribution to zero-energy density of states and to zero-temperature entropy proportional to the sample surface area. When confined to a wire geometry, a discrete number of Majorana modes can be isolated. The relatively large characteristic energy scales for superconductivity and magnetism, compared to ot…
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 report systematic measurements of ac-susceptibility, nuclear-quadrupole-resonance spectrum, and nuclear-spin-lattice-relaxation time ($T_1$) on the pressure ($P$)- induced heavy-fermion (HF) superconductor CeRhIn$_5$. The temperature ($T$) dependence of $1/T_1$ at $P$ = 1.6 GPa has revealed that antiferromagnetism (AFM) and superconductivity (SC) coexist microscopically, exhibiting the respective transition at $T_N = 2.8$ K and $T^{MF}_c$ = 0.9 K. It is demonstrated that SC does not yield any trace of gap opening in low-lying excitations below $T_c^{onset} = 2$ K, but $T_c^{MF} = 0.9$ K, fo…
A fundamental problem posed from the study of correlated electron compounds, of which heavy-fermion systems are prototypes, is the need to understand the physics of states near a quantum critical point (QCP). At a QCP, magnetic order is suppressed continuously to zero temperature and unconventional superconductivity often appears. Here, we report pressure ($P$) -dependent $^{115}$In nuclear quadrupole resonance (NQR) measurements on heavy-fermion antiferromagnet CeRh$_{0.5}$Ir$_{0.5}$In$_5$. These experiments reveal an antiferromagnetic (AF) QCP at $P_{\rm c}^{\rm AF}$ = 1.2 GPa where a dome o…
In recent years, Majorana physics has attracted considerable attention in both theoretical and experimental studies due to exotic new phenomena and its prospects for fault-tolerant topological quantum computation. To this end, one needs to engineer the interplay between superconductivity and electronic properties in a topological insulator, but experimental work remains scarce and ambiguous. Here we report experimental evidence for topological superconductivity induced in a HgTe quantum well, a two-dimensional topological insulator that exhibits the quantum spin Hall effect. The ac Josephson e…
We study the behavior of magnetic superconductors which involve a local attractive interaction between electrons, and a coupling between local moments and the electrons. We solve this `Hubbard-Kondo' model through a variational minimization at zero temperature and validate the results via a Monte Carlo based on static auxiliary field decomposition of the Hubbard interaction. Over a magnetic coupling window that widens with increasing attractive interaction the ground state supports simultaneous magnetic and superconducting order. The pairing amplitude remains s-wave like, without significant s…
Gapless superconductivity from extremely dilute magnetic disorder in 2H-NbSe2-xSx
Universidad Autónoma de Madrid（马德里自治大学）；Niels Bohr Institute, University of Copenhagen（哥本哈根大学尼尔斯·玻尔研究所）；University of Wisconsin–Milwaukee（威斯康星大学密尔沃基分校）；Universidad de Valencia（瓦伦西亚大学）；University of Twente（特温特大学）；Centro Atómico Bariloche, CNEA（巴里洛切原子能中心）；Donostia International Physics Center（圣塞巴斯蒂安国际物理中心）
We demonstrate how the non-trivial interplay between spin-orbit coupling and nodeless $s$-wave superconductivity can drive a fully gapped two-band topological insulator into a time-reversal invariant gapless topological superconductor supporting symmetry-protected Majorana flat bands. We characterize topological phase diagrams by a ${\mathbb Z}_2 \times{\mathbb Z}_2$ partial Berry-phase invariant, and show that, despite the trivial crystal geometry, no unique bulk-boundary correspondence exists. We trace this behavior to the anisotropic quasiparticle bulk gap closing, linear vs. quadratic, and…
We study the low temperature tunneling density of states of thin wires where superconductivity is destroyed through quantum phase-slip proliferation. Although this regime is believed to behave as an insulator, we show that for a large temperature range this phase is characterized by a conductivity falling off at most linearly with temperature, and has a gapless excitation spectrum. This novel conducting phase results from electron-electron interaction induced pair breaking. Also, it may help clarify the low temperature metallic features found in films and wires whose bulk realization is superc…
Magnetism and superconductivity often compete for preeminence as a material's ground state, and in the right circumstances the fluctuating remains of magnetic order can induce superconducting pairing. The intertwining of the two on the microscopic level, independent of lattice excitations, is especially pronounced in heavy fermion compounds, rare earth cuprates, and iron pnictides. Here we point out that for a helical arrangement of localized spins, a variable magnetic pitch length provides a unique tuning process from ferromagnetic to antiferromagnetic ground state in the long and short wavel…
A topological superconductor is characterized by having a pairing gap in the bulk and gapless self-hermitian Majorana modes at its boundary. In one dimension, these are zero-energy modes bound to the ends, while in two dimensions these are chiral gapless modes traveling along the edge. Majorana modes have attracted a lot of interest due to their exotic properties, which include non-abelian exchange statistics. Progress in realizing topological superconductivity has been made by combining spin-orbit coupling, conventional superconductivity, and magnetism. The existence of protected Majorana mod…
We show how the two-band nature of superconductivity in noncentrosymmetric compounds leads to a variety of novel nonuniform superconducting states induced by a magnetic field. At low fields, a two-band helical state is realized, with a distinctly non-BCS quasiparticle spectrum. At high fields, the superconducting state becomes unstable towards the formation of a lattice of topological phase solitons.
In the following paper we investigate the critical temperature $T_c$ behavior in the two-dimensional S/TI (S denotes superconductor and TI - topological insulator) junction with a proximity induced in-plane helical magnetization in the TI surface. The calculations of $T_c$ are performed using the general self-consistent approach based on the Usadel equations in Matsubara Green's functions technique. We show that the presence of the helical magnetization leads to the nonmonotonic behavior of the critical temperature as a function of the topological insulator layer thickness.
For strongly anisotropic time-reversal invariant (TRI) insulators in two and three dimensions, the band inversion can occur respectively at all TRI momenta of a high symmetry axis and plane. Although these classes of materials are topologically trivial as the strong and weak $Z_{2}$ indices are all trivial, they can host an even number of unprotected helical gapless edge states or surface Dirac cones on some boundaries. We show in this work that when the gapless boundary states are gapped by $s_{\pm}$-wave superconductivity, a boundary time-reversal invariant topological superconductor (BTRITS…
We investigate the competition between d-wave superconductivity and nematic order in high-$T_c$ superconductor, and examine the role played by gapless fermionic degrees of freedom. Apart from the competitive interaction with the superconducting order parameter, the nematic order parameter couples strongly to gapless nodal quasiparticles. The interplay of these two kinds of interactions is analyzed by means of renormalization group method. In case the fermionic degree of freedom are entirely neglected, the competitive interaction between two bosonic order parameters is strongly relevant, and ca…
It is demonstrated that the known for a long time transition between the gap and the gapless states in the Abrikosov-Gor'kov theory of a superconductor with paramagnetic impurities is of the Lifshitz type, i.e. of the $2\frac12$ order phase transition. We reveal the emergence of a cuspidal edge at the density of states surface $N(ω,Δ_0)$ ($Δ_0$ is the value of the superconducting order parameter in the absence of magnetic impurities) and the occurrence of the catastrophe phenomenon at the transition point. We study the stability of such a transition with respect to the spatial fluctuations of …
