Surfaces of $d$-wave superconductors may host a substantial density of zero-energy Andreev states. The zero-energy flat band appears due to a topological constraint, but comes with a cost in free energy. We have recently found that an adjustment of the surface states can drive a phase transition into a phase with finite superflow that breaks time-reversal symmetry and translational symmetry along the surface. The associated Doppler shifts of Andreev states to finite energies lower the free energy. Direct experimental verification of such a phase is still technically difficult and controversial, however. To aid further experimental efforts, we use the quasiclassical theory of superconductivity to investigate how the realization and the observability of such a phase are influenced by sample geometry and surface ruggedness. Phase diagrams are produced for relevant geometric parameters. In particular, critical sizes and shapes are identified, providing quantitative guidelines for sample fabrication in the experimental hunt for symmetry-breaking phases.
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 spontaneously breaks time reversal symmetry. We show that, in addition to the known $s+is$ state, there is additional phase, where the system's bulk is a conventional $s$-wave state, but superconducting surface states break time reversal symmetry. Furthermore, we show that $s+is$ superconductors can have spontaneous boundary currents and spontaneous magnetic fi…
Spontaneous currents in a superconductor with s+is symmetry
我们分析了强空穴掺杂Ba $_{1-x}$ K $_x$ Fe $_2$ As $_2$的候选超导态$s + is$态。这种状态破坏了时间反演对称性（TRS），但不会破坏任何其他离散对称性。我们解决了TRS单独断裂是否可以在杂质位点附近产生自发电流的问题，这可以在例如，muSR实验。我们认为，有没有自发电流，如果只有TRS被打破。然而，如果系统被置于外部应变和C4晶格旋转对称性被外部破缺，则会出现超电流。
Recently, a theoretical study [Li {\it et al.},~npj Quantum Materials 6, 36 (2021)] investigated a model of a disordered $d$-wave superconductor, and reported local time-reversal symmetry breaking current loops for sufficiently high disorder levels. Since the pure $d$-wave superconducting state does not break time-reversal symmetry, it is surprising that such persistent currents arise purely from nonmagnetic disorder. Here we perform a detailed theoretical investigation of such disorder-induced orbital currents, and show that the occurrence of the currents can be traced to local extended $s$-w…
Polarization of spontaneous magnetic field and magnetic fluctuations in $s+is$ anisotropic multiband superconductors
我们发现，具有破缺时间反转对称性的多带超导体可以产生自发电流和磁场，以响应对常数的局部变化。以铁磷属元素化物超导体Ba $_{1-x}$ K $_x$ Fe $_2$ As $_2$为例，证明了点群对称$s+is$态和C $_4$对称破缺$s+id$态一般产生相同大小的自发磁场.在$s+is$态中，这些场主要在ab晶面中极化，而在$s+id$态中，它们的ab晶面和c轴分量具有相同的量级。对于时间反演对称性破缺相变临界点附近序参量涨落所产生的随机磁场也是如此。我们的研究结果可以作为一个直接测试的$s+is/s+id$二分法和额外的离散对称破缺相变的帮助下，μ子自旋弛豫实验。
We investigate superconducting phase transition in superconductor(S)/ferromagnet(F) bilayer with Rasba spin-orbit interaction at S/F interface. This spin-orbit coupling produces spontaneous supercurrents flowing inside the atomic-thickness region near the interface, which are compensated by the screening Meissner currents [S. Mironov and A. Buzdin, Phys. Rev. Lett \textbf{118}, 077001 (2017)]. In the case of thin superconducting film the emergence of the spontaneous surface currents causes the increase of the superconducting critical temperature and we calculate the actual value of the critica…
We present a systematic investigation of muon-stopping states in superconductors that reportedly exhibit spontaneous magnetic fields below their transition temperatures due to time-reversal symmetry breaking. These materials include elemental rhenium, several intermetallic systems and Sr$_2$RuO$_4$. We demonstrate that the presence of the muon leads to only a limited and relatively localized perturbation to the local crystal structure, while any small changes to the electronic structure occur several electron volts below the Fermi energy leading to only minimal changes in the charge density on…
We consider magnetic field screening and spontaneous magnetic fields in $s+is$ and $s+id$ superconductors both analytically and numerically. We show that in general, the linearized model couples the moduli of order parameters to the magnetic modes. This causes magnetic field screening that does not follow the standard exponential law and hence cannot be characterized by a single length scale: the London penetration length. We also demonstrate that the resulting linear mixed modes, correctly predict spontaneous fields and their orientation. We show that these mixed modes cause external fields t…
We report the study of spontaneous magnetization (i.e., spin-polarization) for time-reversal symmetry (TRS)-breaking superconductors with unitary pairing potentials, in the absence of external magnetic fields or Zeeman fields. Spin-singlet ($Δ_s$) and spin-triplet ($Δ_t$) pairings can coexist in superconductors whose crystal structure lacks inversion symmetry. The TRS can be spontaneously broken once a relative phase of $\pmπ/2$ is developed, forming a TRS-breaking unitary pairing state ($Δ_s\pm iΔ_t$). We demonstrate that such unitary pairing could give rise to spontaneous spin-polarization w…
Discovery of a nonsymmorphic superconductor with spontaneous rotational symmetry breaking and nontrivial zero modes
Beijing National Center for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；National Center for Nanoscience and Technology, Chinese Academy of Sciences（中国科学院国家纳米科学中心）；School of Physics, Beijing Institute of Technology（北京理工大学物理学院）
