拓扑超导体被理论预言为一类新的时间反演不变的超导体，其在体中是完全带隙的，但具有保护的无带隙表面Andreev束缚态。在这项工作中，我们提供了一个简单的标准，直接识别这种拓扑相位\textit{odd-parity}超导体。接下来，我们提出了一个双轨道$U-V$配对模型的新发现的超导体Cu $_x$ Bi $_2$ Se $_3$ %。由于其独特的三维狄拉克能带结构，我们发现，轨道间的奇宇称三重态配对是有利的相图的重要部分，因此产生了拓扑超导相。最后，我们提出了尖锐的实验测试这样的配对对称性。
英文摘要：
Topological superconductors have been theoretically predicted as a new class of time-reversal-invariant superconductors which are fully gapped in the bulk but have protected gapless surface Andreev bound states. In this work, we provide a simple criterion that directly identifies this topological phase in \textit{odd-parity} superconductors. We next propose a two-orbital $U-V$ pairing model for the newly discovered superconductor Cu$_x$Bi$_2$Se$_3$%. Due to its peculiar three-dimensional Dirac band structure, we find that an inter-orbital triplet pairing with odd-parity is favored in a significant part of the phase diagram, and therefore gives rise to a topological superconductor phase. Finally we propose sharp experimental tests of such a pairing symmetry.
Superconductivity, an emergence of a macroscopic quantum state, gives rise to unique electromagnetic responses leading to perfect shielding of magnetic field and zero electrical resistance. In this paper, we propose that superconductors with the space-inversion symmetry breaking host giant nonreciprocal optical phenomena, such as photocurrent generation and second harmonic generation. The nonreciprocal optical responses show divergent behaviors in the low-frequency regime and originate from two-fold indicators unique to parity-breaking superconductors, namely, the nonreciprocal superfluid dens…
A microscopic calculation and symmetry argument reveal superconductivity in the vicinity of parity-violating magnetic order. An augmented cluster magnetic multipole order in a crystal lacking local space inversion parity may break global inversion symmetry, and then, it is classified into an odd-parity multipole order. We investigate unconventional superconductivity induced by an odd-parity magnetic multipole fluctuation in a two-dimensional two-sublattice Hubbard model motivated by Sr$_2$IrO$_4$. We find that even-parity superconductivity is more significantly suppressed by a spin-orbit coupl…
The parity breaking gives rise to rich superconducting properties through the admixture of even and odd-parity Cooper pairs. A new light has been shed on parity-breaking superconductors by recent observations of nonreciprocal responses such as the nonlinear optical responses and the superconducting diode effect. In this Letter, we demonstrate that the nonreciprocal responses are characterized by a unidirectional correction to the superfluid density, which we call nonreciprocal superfluid density. This correction leads to the nonreciprocal Meissner effect, namely, asymmetric screening of magnet…
Nematic and chiral superconductivity induced by odd-parity fluctuations
最近的实验表明，Cu、Nb或Sr插入Bi $_2$ Se $_3$中，超导性是由旋转对称性破缺引起的。基于这一观察，我们提出了一个模型研究奇宇称涨落引起的手征和手征超导性。研究表明，$D_{3d}$晶体点群的二分量$E_u$表象中的奇宇称涨落在偶宇称$s$波和奇宇称$E_u$配对通道中都能产生吸引相互作用，而在其他奇宇称配对通道中则能产生排斥相互作用.库仑排斥可以相对于$E_u$配对抑制$s$-波配对，因此后者可以具有更高的临界温度. $E_u$配对有两个不同的阶段：手性阶段和手性阶段，这两个阶段都可以在我们的模型中实现。当$s$波和$E_u$对具有相似的不稳定温度时，我们发现了一个中间相，在这个中间相中两种类型的对共存。
We study unconventional superconductivity in a two-dimensional locally noncentrosymmetric triangular lattice. The model is relevant to bilayer transition metal dichalcogenides with 2H$_b$ stacking structure, for example. The superconducting instability is analyzed by solving the linearized Eliashberg equation within the random phase approximation. We show that ferromagnetic fluctuations are dominant owing to the existence of disconnected Fermi pockets near van Hove singularity, and hence odd-parity spin-triplet superconductivity is favored. In the absence of the spin-orbit coupling, we find th…
The spin transport inside an odd-frequency spin-triplet superconductor differs from that of a conventional superconductor due to its distinct symmetry properties. We study spin transport inside an emergent odd-frequency superconductor by replacing the spin-singlet gap matrix in the Usadel equation with a matrix representing spin-triplet pairing that is odd under inversion of energy. We show that the peculiar nature of the density of states allows for an even larger spin injection than in the normal-state. Moreover, when the odd-frequency pairing inherits its temperature dependence from a conve…
It is shown that the application of sufficiently strong magnetic field to the odd-frequency paired Pair Density Wave state described in Phys. Rev. B 94, 165114 (2016) leads to formation of a low temperature metallic state with zero Hall response. Applications of these ideas to the recent experiments on stripe-ordered La_{1.875}Ba_{0.125}CuO_4 are discussed.
The topological property of a gapped odd-parity superconductor is jointly determined by its pairing nodes and Fermi surfaces in normal state. We reveal that the contractibility of Fermi surfaces without crossing any time-reversal invariant momentum and the presence of nontrivial Berry phase on Fermi surfaces are two key conditions for the realization of higher-order topological odd-parity superconductors (HOTOPSCs). When the normal state is a normal metal, we reveal the necessity of removable Dirac pairing nodes and provide a general and simple principle to realize HOTOPSCs. Our findings can n…
The discovery of the multiple $H$-$T$ phase diagram of CeRh$_2$As$_2$ offers a new route to designing topological superconductors. Although weak-coupling theories explain the experimental phase diagram qualitatively, a quantitative discrepancy between them has discouraged conclusive interpretation. In this Letter, we thoroughly study the effect of Coulomb interaction and the phase diagrams of locally noncentrosymmetric superconductors. We reveal even-odd parity transition and the enhancement of the parity transition field in strongly correlated superconductors, and an issue of CeRh$_2$As$_2$ i…
The effects of spin independent hybridization potential and spin orbit coupling on two band superconductor with equal time s-wave inter band pairing order parameter is investigated theoretically. To study symmetry classes in two band superconductors the Gorkov equations are solved analytically. By defining spin singlet and spin triplet s wave order parameter due to two band degree of freedom the symmetry classes of Cooper pair are studied. For spin singlet case it is shown that spin independent hybridization generates Cooper pair belongs to even frequency spin singlet even momentum even band p…
Quantum dots are gate-defined within InSb nanowires, in proximity to NbTiN superconducting contacts. As the coupling between the dot and the superconductor is increased, the odd-parity occupations become non-discernible (erased) both above and below the induced superconducting gap. Above the gap, conductance in the odd Coulomb valleys increases until the valleys are lifted. Below the gap, Andreev bound states undergo quantum phase transitions to singlet ground states at odd occupancy. We observe that the apparent erasure of odd-parity regimes coincides at low-bias and at high-bias. This observ…
Odd-parity superconductors with two-component order parameters: nematic and chiral, full gap and Majorana node
最近的实验表明，掺杂拓扑绝缘体Cu $_x$ Bi $_2$ Se $_3$中的超导性具有奇宇称对对称性和旋转对称性破缺，基于这一实验，我们研究了三角晶系和六方晶系中具有双组分序参量的奇宇称超导体.在强自旋-轨道相互作用的存在下，我们发现了两个可能的超导相低于$T_c$，一个时间反演破缺（即，手性）相和各向异性（即，相位，并从动量空间中的能隙函数确定它们的相对能量。手征超导体通常具有完整的准粒子带隙，而具有三维（3D）费米表面的手征超导体具有提升自旋简并的点节点，导致体块中的巡回马约拉纳费米子和表面上的拓扑马约拉纳弧。
The fractional Josephson effect is known to be a characteristic phenomenon of topological Josephson junctions hosting Majorana zero modes (MZMs), where the Josephson current has a $4π$ (rather than a $2π$) periodicity in the phase difference between the two topological superconductors. We introduce a one-dimensional model of a topological superconductor/normal-metal/superconductor (SNS) junction with the normal-metal (N) region of finite length, which is intermediate regime between the short- and long-junction limits. Assuming weak tunneling at the SN interfaces, we investigate resonance and f…
Quantum transport in a normal metal/odd-frequency superconductor junction
最近的实验结果表明，在化合物CeCu $_2$ Si $_2$和CeRhIn $_5$中可能实现体奇频超导态。出于这一动机，我们提出了一个正常的金属/奇数频率超导体结的量子输运性质的研究，在寻找探针，以揭开奇频对称性。从Eliashberg方程，我们执行一个准经典近似占奇频超导体的Keldysh形式主义的运输形式主义。具体地说，我们考虑了隧穿电荷电导和隧穿热导。我们发现定性不同的行为在奇频率的情况下相比，传统的偶频率的情况下，在电流和热电流。这是一个有用的工具，以确定可能存在的体奇频超导态。
Recently, evidence has emerged for a field-induced even- to odd-parity superconducting phase transition in CeRh$_2$As$_2$ [S. Khim et al., Science 373 1012 (2021)]. Here we argue that the P4/nmm non-symmorphic crystal structure of CeRh$_2$As$_2$ plays a key role in enabling this transition by ensuring large spin-orbit interactions near the Brillouin zone boundaries, which naturally leads to the required near-degeneracy of the even- and odd-parity channels. We further comment on the relevance of our theory to FeSe, which crystallizes in the same structure.
我们研究了双组分超导体中的拓扑激发，特别关注Cu $_x$ Bi $_2$ Se $_3$作为候选材料。我们发现最低能量的拓扑激发是无核涡旋：两个空间分离的半量子涡旋的束缚态。这些物体是双螺旋Skyrmions，因为它们具有额外的拓扑电荷。在这个模型中，Skyrmion间的力是偶极的，即对Skyrmion的某些相对取向有吸引力，从而形成多Skyrmion束缚态。
We propose a route to achieve odd-parity spin-triplet superconductivity in metallic collinear antiferromagnets with inversion symmetry. Owing to the existence of hidden antiunitary symmetry, which we call the effective time-reversal symmetry (eTRS), the Fermi surfaces of ordinary antiferromagnetic metals are generally spin-degenerate, and spin-singlet pairing is favored. However, by introducing a local inversion symmetry breaking perturbation that also breaks the eTRS, we can lift the degeneracy to obtain spin-polarized Fermi surfaces. In the weak-coupling limit, the spin-polarized Fermi surfa…
Charge-transfer effect under odd-parity crystalline electric field (CEF) is analyzed theoretically. In quantum-critical metal $β$-YbAlB$_4$, seven-fold configuration of B atoms surrounding Yb atom breaks local inversion symmetry at the Yb site, giving rise to the odd-parity CEF. Analysis of the CEF on the basis of hybridization picture shows that admixture of 4f and 5d wave functions at Yb with pure imaginary coefficient occurs, which makes magnetic-toroidal (MT) and electric-dipole (ED) degrees of freedom active. By constructing the minimal model for periodic crystal $β$-YbAlB$_4$, we show th…
We present an overview of the contributions made by Konstantin B. Efetov and the authors to the field of triplet odd-frequency superconductivity in hybrid ferromagnet-superconductor structures and the repercussions they had on experimental and theoretical research. Konstantin B. Efetov passed away in August 2021. We hope the present short review gives a faithful testimony of an important part of his scientific legacy.
We study odd-parity nematic superconductivity in doped topological insulators in presence of surface magnetic impurities. The peculiar surface subgap spectrum, characterized by a Majorana flatband, nodal cones and the surface states of the parent topological insulator, gives rise to an overall ferromagnetic RKKY interactions between the surface impurities. An additional coupling between the impurities and a preemptive chiral order parameter promote a surface time-reversal symmetry breaking solution at the surface of the system. We discuss the relevant scenarios and suggest to engineer surface …
