Large-scale simulations of vortex Majorana zero modes in topological crystalline insulators

Chun Yu Wan, Yujun Zhao, Yaoyi Li, Jinfeng Jia, Junwei Liu
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Abstract

Topological crystalline insulators are known to support multiple Majorana zero modes (MZMs) at a single vortex, their hybridization is forbidden by a magnetic mirror symmetry $M_T$. Due to the limited energy resolution of scanning tunneling microscopes and the very small energy spacing of trivial bound states, it remains challenging to directly probe and demonstrate the existence of multiple MZMs. In this work, we propose to demonstrate the existence of MZMs by studying the hybridization of multiple MZMs in a symmetry breaking field. The different responses of trivial bound states and MZMs can be inferred from their spatial distribution in the vortex. However, the theoretical simulations are very demanding since it requires an extremely large system in real space. By utilizing the kernel polynomial method, we can efficiently simulate large lattices with over $10^8$ orbitals to compute the local density of states which bridges the gap between theoretical studies based on minimal models and experimental measurements. We show that the spatial distribution of MZMs and trivial vortex bound states indeed differs drastically in tilted magnetic fields. The zero-bias peak elongates when the magnetic field preserves $M_T$, while it splits when $M_T$ is broken, giving rise to an anisotropic magnetic response. Since the bulk of SnTe are metallic, we also study the robustness of MZMs against the bulk states, and clarify when can the MZMs produce a pronounced anisotropic magnetic response.
拓扑晶体绝缘体中涡旋马约拉纳零模的大尺度模拟
众所周知,拓扑晶体绝缘体在单涡旋处支持多个马约拉零模(MZM),而非磁性镜像对称性$M_T$禁止它们杂化。由于扫描隧道显微镜的能量分辨率有限以及琐细束缚态的能量间距非常小,直接探测和证明多重 MZM 的存在仍然具有挑战性。 在这项工作中,我们建议通过研究对称破缺场中多重 MZM 的杂化来证明 MZM 的存在。琐碎束缚态和MZMs的不同反应可以从它们在涡旋中的空间分布推断出来。然而,理论模拟的要求非常高,因为它需要在真实空间中建立一个极其庞大的系统。通过利用核多项式方法,我们可以有效地模拟具有超过 10^8 美元轨道的大型晶格,从而计算出局部态密度,弥补了基于最小模型的理论研究与实验测量之间的差距。我们的研究表明,在倾斜磁场中,MZMs 和微涡束缚态的空间分布确实存在巨大差异。当磁场保持 $M_T$ 时,零偏置峰会拉长,而当 $M_T$ 被打破时,零偏置峰会分裂,从而产生各向异性的磁响应。由于锡碲的主体是金属,我们还研究了 MZM 对主体态的稳健性,并阐明了 MZM 何时会产生明显的各向异性磁响应。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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