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arXiv 2401.06355cond-mat.supr-con
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二维准晶体中拓扑超导的自洽研究

Self-consistent study of topological superconductivity in two-dimensional quasicrystals

Masahiro Hori, Takanori Sugimoto, Takami Tohyama, K. Tanaka

AI总结:

通过自洽求解Bogoliubov-de Gennes方程,研究了Penrose和Ammann-Beenker准晶体中破坏时间反演对称性的二维拓扑超导,发现由Bott指数表征的拓扑相变及Majorana零模的存在。

摘要:

我们在Penrose和Ammann-Beenker准晶体中研究了具有Rashba自旋-轨道耦合和Zeeman场的二维$s$波拓扑超导。通过自洽求解Bogoliubov-de Gennes方程,不仅针对超导序参量,还针对自旋依赖的Hartree势,我们展示了在Penrose和Ammann-Beenker准晶体中均稳定出现破坏时间反演对称性的拓扑超导。准晶系统的拓扑性质由Bott指数$B$表征。研究发现,随着化学势或Zeeman场的变化,会发生$B$在0和$\pm 1$之间改变的拓扑相变。基于自洽解,我们证明了当$B=\pm 1$时,每个边缘或涡旋存在一个Majorana零模,这与周期性系统的体-边缘/缺陷对应关系一致。

英文摘要:

We study two-dimensional $s$-wave topological superconductivity with Rashba spin-orbit coupling and Zeeman field in Penrose and Ammann-Beenker quasicrystals. By solving the Bogoliubov-de Gennes equations self-consistently for not only the superconducting order parameter, but also the spin-dependent Hartree potential, we show the stable occurrence of topological superconductivity with broken time-reversal symmetry in both Penrose and Ammann-Beenker quasicrystals. The topological nature of the quasicrystalline system is signified by the Bott index $B$. Topological phase transitions are found to occur, where $B$ changes between 0 and $\pm 1$, as the chemical potential or Zeeman field is varied. In terms of self-consistent solutions, we demonstrate the existence of a Majorana zero mode per edge or vortex when $B=\pm 1$, consistently with the bulk-edge/defect correspondence for periodic systems.

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