We show that under certain conditions multiband superconductors with broken time-reversal symmetry have a new vortex viscosity-generating mechanism which is different from that in conventional superconductors. It appears due to the existence of mixed superfluid phase-density mode inside vortex core. This new contribution is dominant near the time reversal symmetry breaking phase transition. The results could be relevant for three band superconductor $Ba_{1-x}K_{x}Fe_2As_2$.
The striped cuprate La$_{2-x}$Ba$_x$CuO$_4$ ($x=\frac18)$ undergoes several transitions below the charge-ordering temperature $T_{co}$ = 54 K. From Nernst experiments, we find that, below $T_{co}$, there exists a large, anomalous Nernst signal $e_{N,even}(H,T)$ that is symmetric in field $H$, and remains finite as $H\to 0$. The time-reversal violating signal suggests that, below $T_{co}$, vortices of one sign are spontaneously created to relieve interlayer phase frustration.
Broken time reversal symmetry (BTRS) in d wave superconductors is studied and is shown to yield current carrying surface states. The corresponding spontaneous magnetization is temperature independent near the critical temperature Tc for weak BTRS, in accord with recent data. For strong BTRS and thin films we expect a temperature dependent spontaneous magnetization with a paramagnetic anomaly near Tc. The Hall conductance is found to vanish at zero wavevector q and finite frequency w, however at finite q,w it has an unusual structure.
Broken time reversal symmetry (BTRS) in d+id' as well as in d+is superconductors is studied and is shown to yield current carrying surface states. We evaluate the temperature and thickness dependence of the resulting spontaneous magnetization and show a marked difference between weak and strong BTRS. We also derive the Hall conductance which vanishes at zero wavevector q and finite frequency w, however at finite q,w it has an unusual structure. The chirality of the surface states leads to quantum Hall effects for spin and heat transport in d+id' superconductors.
We discuss the phase diagram and phase transitions in $U(1)\times \groupZ{2}$ three-band superconductors with broken time reversal symmetry. We find that beyond mean field approximation and for sufficiently strong frustration of interband interactions there appears an unusual metallic state precursory to a superconducting phase transition. In that state, the system is not superconducting. Nonetheless, it features a spontaneously broken $\groupZ{2}$ time reversal symmetry. By contrast, for weak frustration of interband coupling the energy of a domain wall between different $\groupZ{2}$ states i…
We demonstrate that films of unconventional (d-wave) superconductor at temperatures $T\lesssim 0.43 T_c$ can exhibit unusual superconducting phases. The new ground states beside the broken gauge and the point group symmetries can spontaneously break (i) continuous translational symmetry and form periodic order parameter structures in the plane of the film, or (ii) time-reversal symmetry and develop supercurrent flowing along the film. These states are result of the strong transverse inhomogeniety present in films with thickness of several coherence lengths. We show a natural similarity between…
Conventional superconductors are strong diamagnets that through the Meissner effect expel magnetic fields. It would therefore be surprising if a superconducting ground state would support spontaneous magnetics fields. Such time-reversal symmetry broken states have been proposed for the high-temperature superconductors, but their identification remains experimentally controversial. Here we show a route to a low-temperature superconducting state with broken time-reversal symmetry that may accommodate currently conflicting experiments. This state is characterised by an unusual vortex pattern in t…
The flux flow regime of high-T$_{\rm c}$ samples of different normal state resistivities is studied in the temperature range where the sign of the Hall effect is reversed. The scaling of the vortex viscosity with normal state resistivity is consistent with the Bardeen-Stephen theory. Estimates of the influence of possible mechanisms suggested for the sign reversal of the Hall effect are also given.
Type II Lifshitz invariant and optically active Higgs mode in time-reversal symmetry broken superconductors
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）；Department of Physics, University of Tokyo（东京大学物理学系）；RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所新兴物质科学中心）；Trans-Scale Quantum Science Institute, University of Tokyo（东京大学跨尺度量子科学研究所）
We investigate nonlocal vortex motion in weakly pinning a-NbGe nanostructures, which is driven by a transport current I and remotely detected as a nonlocal voltage Vnl. At high I, the measured Vnl exhibits dramatic sign reversals that at low and high temperatures T occur for opposite polarities of I. The sign of Vnl becomes independent of that of the drive current at large abs(I). These unusual effects can be nearly quantitatively explained by a novel enhancement of magnetization, arising from a nonequilibrium distribution of quasiparticles at high T, and a Nernst-like effect resulting from lo…
A theory of dispersionless Andreev bound states on surfaces of time-reversal invariant unconventional superconductors is presented. The generalized criterion for the dispersionless Andreev bound state is derived from the bulk-edge correspondence, and the chiral spin structure of the dispersionless Andreev bound states is argued from which the Andreev bound state is stabilized. Then we summarize the criterion in a form of index theorems. The index theorems are proved in a general framework to certify the bulk-edge correspondence. As concrete examples, we discuss (i) dxy-wave superconductor (ii)…
Within a Ginzburg-Landau formalism we establish analytically the necessary and sufficient conditions to realize a doubly degenerate superconducting ground state with broken time-reversal symmetry (BTRS) in a multi-band superconductor. Using these results we analyze the ground state of a three-band superconductor in the cylindrical geometry in an external magnetic field. We show that depending on the interband coupling constants, a magnetic flux can induce current density jumps in such superconducting geometries that are related to adiabatic or non-adiabatic transitions from BTRS to time-revers…
We have investigated the temperature and magnetic field dependence of the Hall coefficient of two well-characterized superconducting MgB$_2$ films (T$_{c0}$=38.0 K) in both the normal and superconducting states. Our results show that the normal-state Hall coefficient R$_H$ is positive and increases with decreasing temperature, independent of the applied magnetic field. Below T$_c$(H), R$_H$ decreases rapidly with temperature and changes sign before it reaches zero. The position and magnitude at which R$_H$ shows a minimum depends on the applied field. Quantitative analysis of our data indicate…
Josephson current between two superconductors provides a phase sensitive tool for probing their pairing symmetries. Here we fabricate and study experimentally high-quality Josephson junctions between a conventional s-wave superconductor Nb and a multi-band iron-pnictide Ba$_{1-x}$Na$_x$Fe$_2$As$_2$. Junctions exhibit a large enough critical current density to preclude the d-wave symmetry of the order parameter in the pnictide. However, the $I_cR_n$ product is very small $\simeq 3~μ$V, which is not consistent with the sign-preserving $s_{++}$ symmetry either. We argue that the small $I_cR_n$ va…
Time reversal and spatial inversion are two key symmetries for conventional Bardeen-Cooper-Schrieffer (BCS) superconductivity. Breaking inversion symmetry can lead to mixed-parity Cooper pairing and unconventional superconducting properties. Two-dimensional (2D) NbSe$_2$ has emerged as a new non-centrosymmetric superconductor with the unique out-of-plane or Ising spin-orbit coupling (SOC). Here, we report the observation of an unusual continuous paramagnetic-limited superconductor-normal metal transition in 2D NbSe$_2$. Using tunneling spectroscopy under high in-plane magnetic fields, we obser…
Recently, superconductivity with spontaneous time-reversal or parity symmetry breaking is attracting much attention owing to its exotic properties, such as nontrivial topology and nonreciprocal transport. Particularly fascinating phenomena are expected when the time-reversal and parity symmetry are simultaneously broken. This work shows that time-reversal symmetry-breaking mixed-parity superconducting states generally exhibit an unusual asymmetric Bogoliubov spectrum due to nonunitary interband pairing. For generic two-band models, we derive the necessary conditions for the asymmetric Bogoliub…
We investigate an unusual symmetry of Fe-based superconductors (FeSCs) and find novel superconducting pairing structures. FeSCs have a minimal translational unit cell composed of two Fe atoms due to the staggered positions of anions with respect to the Fe plane. We study the physical consequences of the additional glide symmetry that further reduces the unit cell to have only one Fe atoms. In the regular momentum space, it not only leads to a particular orbital parity separated spectral function but also dictates orbital parity distinct pairing structures. Furthermore, it produces accompanying…
We show in this letter that P- and T-odd terms of the electromagnetic potentials (P; parity, T; time reversal) are induced and lead an unusual phenomenon in P- and T-violating superconductors discovered recently. The Ginzburg-Landau action includes this term in the gauge invariant manner. The coefficient of the term is nearly topological invariant with a small correction and equals to the fine structure constant approximately. Unusual ``Hall effect'' {\it without external} magnetic field could be observed by SQUID.
We report measurements of the microwave complex resistivity at 48 GHz in SmBaCuO thin films. Measurements are performed with a moderate magnetic field, $μ_{0}H<$ 0.8T, applied along the c-axis. We find that the complex resistivity presents clear sublinear field dependences, and that the imaginary part is remarkably sensitive to the moderate magnetic field. Interpretation considering an unusually strong pinning leads to very anomalous field dependences of the single-vortex viscosity and of the pinning constant. By contrast, allowing for a significant effect of the magnetic field on the depletio…
The kagome metal CsV$_{3}$Sb$_{5}$ features an unusual competition between the charge-density-wave (CDW) order and superconductivity. Evidence for time-reversal symmetry breaking (TRSB) inside the CDW phase has been accumulating. Hence, the superconductivity in CsV$_{3}$Sb$_{5}$ emerges from a TRSB normal state, potentially resulting in an exotic superconducting state. To reveal the pairing symmetry, we first investigate the effect of nonmagnetic impurity. Our results show that the superconducting critical temperature is insensitive to disorder, pointing to conventional $s$-wave superconductiv…
The ordinary magnetoresistance (MR) of doped semiconductors is positive and quadratic in a low magnetic field, B, as it should be in the framework of the Boltzmann kinetic theory or in the conventional hopping regime. We observe an unusual highly-anisotropic in-plane MR in graphite, which is neither quadratic nor always positive. In a certain current direction MR is negative and linear in B in fields below a few tens of mT with a crossover to a positive MR at higher fields, while in a perpendicular current direction we observe a giant super-linear and positive MR. These extraordinary MRs are r…
Among unconventional superconductors, Sr$_2$RuO$_4$ has become a benchmark for experimentation and theoretical analysis because its normal-state electronic structure is known with exceptional precision, and because of experimental evidence that its superconductivity has, very unusually, a spontaneous angular momentum, i.e. a chiral state. This hypothesis of chirality is however difficult to reconcile with recent evidence on the spin part of the order parameter. Measurements under uniaxial stress offer an ideal way to test for chirality, because under uniaxial stress the superconducting and chi…
We discuss the novel superconducting characteristics and unusual normal-state properties of iron (Fe)-based pnictide superconductors REFeAsO$_{1-y}$ (RE=La,Pr,Nd) and Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$($T_{c}=$ 38 K) by means of $^{57}$Fe-NMR and $^{75}$As-NQR/NMR. In the superconducting state of LaFeAsO$_{0.7}$ ($T_{c}=$ 28 K), the spin component of the $^{57}$Fe-Knight shift decreases to almost zero at low temperatures, which provide firm evidence of the superconducting state formed by spin-singlet Cooper pairing. The nuclear spin-lattice relaxation rates $(1/T_{1})$ in LaFeAsO$_{0.7}$ and Ba$_…
We show that a heavy fermion superconductor UPt_3 is a topological Weyl superconductor with tunable Weyl nodes. Adopting a generic order parameter in the E_2u representation allowed by nonsymmorphic crystal symmetry, we clarify unusual gap structure and associated topological properties. The pair creation, pair annihilation, and coalescence of Weyl nodes are demonstrated in the time-reversal symmetry broken B-phase. At most 98 point nodes compatible with Blount's theorem give rise to line node-like behaviors in low-energy excitations, consistent with experimental results. We also show an arc n…
