Recently it has been proposed that a unitary topological mirror symmetry can stabilize multiple zero energy Majorana fermion modes in one dimensional (1D) time reversal (TR) invariant topological superconductors. Here we establish an exact equivalence between 1D "topological mirror superconductivity" and chiral topological superconductivity in BDI class which can also stabilize multiple Majorana-Kramers pairs in 1D TR-invariant topological superconductors. The equivalence proves that topological mirror superconductivity can be understood as chiral superconductivity in the BDI symmetry class co-existing with time-reversal symmetry. Furthermore, we show that the mirror Berry phase coincides with the chiral winding invariant of the BDI symmetry class, which is independent of the presence of the time-reversal symmetry. Thus, the time-reversal invariant topological mirror superconducting state may be viewed as a special case of the BDI symmetry class in the well-known Altland-Zirnbauer periodic table of free fermionic phases. We illustrate the results with the examples of 1D spin-orbit coupled quantum wires in the presence of nodeless s_{\pm} superconductivity and the recently discussed experimental system of ferromagnetic atom (Fe) chains embedded on a lead (Pb) superconductor.
Mirror Symmetry Breaking and Lateral Stacking Shifts in Twisted Trilayer Graphene
我们利用密度泛函理论的{ \it ab initio}方法构建了扭曲三层石墨烯的连续介质模型，并将其应用于扭曲三层石墨烯的电子结构.我们的模型占摩尔变化的网站能量，外层和层内之间的跳跃。我们专注于ABA石墨烯三层中存在的镜像对称性与中间层扭曲的作用。当层间施加位移场时，镜像对称性被有意地丢失，而当顶层相对于底层横向移位时，镜像对称性被无意地丢失。我们使用两个能带结构的特点，是直接相关的运输测量，德鲁德重量和弱场霍尔电导率，并将它们通过霍尔密度来评估目前存在于所有实验设备上的电子性能的意外横向堆垛层移的影响，并评论的作用的可能的重要性意外横向堆垛层移的超导扭曲三层。
Layer-Asymmetry-Induced Topological Superconductivity in High-T$_c$ Bilayer Nickelates
Hong Kong University of Science and Technology（香港科技大学）；RIKEN Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS)（理化学研究所交叉理论与数学科学中心）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所理论物理重点实验室）；School of Physics, Beijing Institute of Technology（北京理工大学物理学院）
