The optical response of superconductors with odd-frequency Berezinskii pairing is studied. By using a simple model with a parabolic dispersion law and a non-magnetic disorder, the spectral function, the electron density of states, and the optical conductivity are calculated for a few gap ansatzes. The spectral function and the electron density of states clearly reveal the gap for the Berezinskii pairing for the sufficiently strong frequency dependence of the order parameters. It is found that, similarly to the conventional BCS pairing, the odd-frequency gaps induce peaks in the real part of the conductivity, which, however, are sharper than in the BCS case. The magnitude and position of these peaks are determined by the frequency profile of the gap. The imaginary part of the optical conductivity for the Berezinskii pairing demonstrates sharp cusps that are absent in the case of the BCS superconductors. The corresponding results suggest that the Berezinskii pairing might allow for the optical transparency windows related to the onsets of the attenuation peaks in the real part of the conductivity. Thus, the study of the optical response not only provides an alternative way to probe the odd-frequency gaps but can reveal also additional features of the dynamic superconducting pairing.
Comment on "Spectroscopic Evidence for Multiple Order Parameters in the Heavy Fermion Superconductor CeCoIn5"
这是对Rourke等人最近发表的题为“Spectroscopic Evidence for Multiple序参量Parameters in the Heavy Fermion Superconductor CeCoIn 5”（cond-mat/0409562 v1 22 Sep 2004）的论文的评论。我们认为，洛克等人观察到的功能。这是因为它们的接触不在弹道极限内。
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…
We show that dilute magnetic impurities in a conventional superconductor give origin to an odd-frequency component of superconductivity, manifesting itself in Yu-Shiba-Rusinov bands forming within the bulk superconducting gap. Our results are obtained in a general model solved within the dynamical mean field theory. By exploiting a disorder analysis and the limit to a single impurity, we are able to provide general expressions that can be used to extract explicitly the odd-frequency superconducting function from scanning tunneling measurements.
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…
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…
Observation of vortices and hidden pseudogap from scanning tunneling spectroscopic studies of electron-doped cuprate superconductor $Sr_{0.9}La_{0.1}CuO_2$
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。
We theoretically study the effects of spin-orbit interactions on symmetry of a Cooper pair in a spin-singlet d-wave superconductor in two-dimension. The pairing symmetry is analyzed in terms of the anomalous Green's function which is obtained by solving the Gor'kov equation analytically. A spin-orbit interaction induces a spin-triplet p-wave pairing correlation in a uniform superconductor. An odd-frequency spin-triplet s-wave pairing correlation appears at a surface of such superconductor as a result of breaking inversion symmetry locally. We also discuss a close relationship among the odd-fre…
We study the unconventional superconducting correlations caused by a single isolated magnetic impurity in a conventional s-wave superconductor. Due to the local breaking of time-reversal symmetry, the impurity induces unconventional superconductivity which is even in both space and spin variables but odd under time inversion. We derive an exact proportionality relation between the even-frequency component of the local electron density of states and the imaginary part of the odd-frequency local pairing function. By applying this relation to scanning tunneling microscopy spectra taken on top of …
The Meissner effect is one of the defining properties of superconductivity, with a conventional superconductor completely repelling an external magnetic field. In contrast to this diamagnetic behavior, odd-frequency superconducting pairing has often been seen to produce a paramagnetic Meissner effect, which instead makes the superconductor unstable due to the attraction of magnetic field. In this work we study how both even- and odd-frequency superconducting pairing contributes to the Meissner effect in a generic two-orbital superconductor with a tunable odd-frequency pairing component. By div…
Transport and spectroscopic properties of superconductor - ferromagnet - superconductor junctions of $La_{1.9}Sr_{0.1}CuO_4$ - $La_{0.67}Ca_{0.33}MnO_3$ - $La_{1.9}Sr_{0.1}CuO_4$
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.
Odd-Parity Topological Superconductors: Theory and Application to Cu$_x$Bi$_2$Se$_3$
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。
Visualization of vortex sheets and half quantum vortices in the chiral odd-parity superconductor UPt$_{3}$
Université Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；CNRS（法国国家科学研究中心）；Institut Néel（奈尔研究所）；Aix Marseille Univ（艾克斯-马赛大学）；Université de Toulon（土伦大学）；IM2NP（物质与纳米结构物理化学研究所）；CEA（法国原子能和替代能源委员会）；IRIG（研究和技术集成部）；PHELIQS（低温、激光和量子科学实验室）；The University of Edinburgh（爱丁堡大学）；Centre for Science at Extreme Conditions（极端条件科学中心）；Tohoku University（东北大学）；Institute for Materials Research（材料研究所）
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。
Odd-frequency Cooper pairs are gathering attention for the convenience of investigating the edge state of topological superconductors including Majorana fermions. Although a spinless p-wave superconductor has only one Majorana fermion in a topological phase, the system with magnetic fields can reach the topological phases with multiple Majorana fermions. To distinguish these multiple Majorana fermion phases, we correlate the energy spectrum with the odd-frequency pair amplitude as increasing the system size. The system size dependence tells us three pieces of information: the parity of the num…
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。
