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A major challenge to the chiral $p$-wave hypothesis for the pairing symmetry of the unconventional superconductor Sr$_2$RuO$_4$ is the null result of sensitive scanning magnetometry experiments designed to detect the expected spontaneous…
The spontaneous breaking of time-reversal symmetry is a hallmark of unconventional superconductivity, typically observed in type-II superconductors. Here, we report evidence of time-reversal symmetry breaking in the type-I superconductor…
A boundary between two d-wave superconductors or an s-wave and a d-wave superconductor generally breaks time-reversal symmetry and can generate spontaneous currents due to proximity effect. On the other hand, surfaces and interfaces in…
We investigate the properties of spontaneous currents generated at surfaces and interfaces of d-wave superconductors using the self-consistent quasiclassical Eilenberger equations. The influence of the roughness and reflectivity of the…
We analyze the presence of non-reciprocal critical currents, the so-called superconducting diode effect, in chiral superconductors within a generalized Ginzburg-Landau framework. After deriving its key symmetry conditions we illustrate the…
Multi-band superconductors in which frustrated inter-band couplings yield a time-reversal-symmetry breaking (TRSB) state are investigated. Stability condition for the TRSB state are derived based on the Bardeen-Cooper-Schrieffer (BCS)…
The two superconducting phases recently discovered in skutterudite PrOs4Sb12 are discussed by using the phenomenological Ginzburg-Landau theory in the cubic (tetrahedral) crystal symmetry T_h. Building on experimental imput coming from the…
Twin boundaries are generic crystalline defects in noncentrosymmetric crystal structures. We study theoretically twin boundaries in time-reversal symmetric noncentrosymmetric superconductors that admit parity-mixed Cooper pairing. Twin…
We present a study of the basic microscopic model of an $s$-wave superconductor with frustrated interband interaction. When frustration is strong, such an interaction gives raise to a $s+is$ state. This is a $s$-wave superconductor that…
We study the impurity effect in the time reversal symmetry (${\cal T}$) breaking superconductor based on the Bogoliubov-de Gennes (BdG) equations. In ${\cal T}$-violating superconductors, spontaneous currents are induced around the…
We study theoretically the spatial distribution of spontaneous magnetic fields near a (110) surface of cuprate high-$T_C$ superconductor YBCO by treating a bilayer $t-J$ model with the Bogoliubov-de Gennes method. Near a (110) surface where…
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…
We investigate the electronic structure of twin boundaries in orthorhombically distorted high-T$_c$ materials using the quasiclassical theory of superconductivity. At low temperatures we find a local instability to a time-reversal symmetry…
We explore edge currents in heterostructures formed of a high-$T_c$ cuprate and a conventional $s$-wave superconductors. The resulting $d\pm is$ superconductor spontaneously breaks time reversal symmetry and, remarkably, exhibits large edge…
We show that Rashba spin-orbit coupling at the interface between a superconductor and a ferromagnet should produce a spontaneous current in the atomic thickness region near the interface. This current is counter-balanced by the…
Time-reversal symmetry breaking (TRSB) with a Bardeen-Cooper-Schrieffer (BCS) -like superconductivity occurs in a small, but growing number of noncentrosymmetric (NCS) materials, although the mechanism is poorly understood. We present heat…
We introduce a model governing the copropagation of two components which represent circular polarizations of light in the optical fiber with relative strength g = 2 of the nonlinear repulsion between the components, and linear coupling…
At a (110) surface of a $d_{x^2-y-2}$-wave superconductor, superconducting order is strongly suppressed. In such a situation, ordered states that are forbidden in the bulk may arise. This problem is studied for high-$T_C$ cuprate…
Experimental evidences of spontaneous time-reversal (TR) symmetry breaking have been reported for the superconducting ground state in the transition metal dichalcogenide (TMD) superconductor 4H$_b$-TaS$_2$ or chiral molecule intercalated…
Time-reversal symmetry (TRS) may be broken in superconductors with three or more condensates interacting repulsively, yielding two degenerate states specified by chirality of gap functions. We consider a loop of such superconductor with two…