arXiv 2603.087862026-03-09cond-mat.mes-hall

基于Pfaffian的拓扑不变量用于一维半导体-超导异质结构

Pfaffian-based topological invariants for one dimensional semiconductor-superconductor heterostructures

Clemson University（克莱姆森大学）；BITS Pilani-Pilani Campus（比拉理工学院皮拉尼校区）

Binayyak B. Roy, William B. Cason, Nimish Sharma, Sumanta Tewari

阅读 PDF

arXiv 页面 ↗HTML 原文 ↗

AI总结：

本文提出基于Pfaffian的拓扑不变量用于一维半导体-超导异质结构，证明其在有限和无序系统中的有效性，并等价于周期性无序不变量。

摘要：

我们回顾了一维半导体-超导（SM-SC）纳米线异质结构中的基于Pfaffian的$\mathbb{Z}_2$拓扑不变量，并澄清其在有限和无序系统中的有效性。对于干净的纳米线，哈密顿量在粒子-空穴对称动量$k=0,π$处的Pfaffian乘积在拓扑相变点定义的本征间隙闭合时改变符号，导致定义了$\mathbb{Z}_2$ Kitaev不变量，也称为Majorana数。我们证明这种动量空间不变量等价于基于扭曲边界条件的实空间构造，在此构造中，哈密顿量在周期性和反周期性边界条件下的Pfaffian乘积的符号定义了$\mathbb{Z}_2$指数。通过引入周期性重复无序的超晶格描述，我们证明了实空间Pfaffian不变量，定义为具有周期性和反周期性边界条件的哈密顿量的Pfaffian符号，在没有微观平移对称性的情况下仍然是一个良好的不变量。在此框架下，它也等价于最近定义的周期性无序不变量（PDI），这在存在chiral对称性的情况下构成一个整数值（$\mathbb{Z}$）的拓扑不变量。最后，我们证明了二次哈密顿量的Pfaffian符号等于其基态费米子 parity，建立了不变量的直接物理解释，即基态费米子 parity的符号乘积的周期性和反周期性边界条件下的符号。数值结果证实了Pfaffian符号的反转、磁通诱导能级交叉和基态parity切换在干净和无序纳米线中的对应关系。

英文摘要：

We review the Pfaffian-based $\mathbb{Z}_2$ topological invariants in one dimensional semiconductor-superconductor (SM-SC) nanowire heterostructures and clarify their validity in finite and disordered systems. For the clean nanowire, the product of the Pfaffians of the Hamiltonian at particle-hole symmetric momenta $k=0,π$ changes sign at the topological phase transition defined by the bulk gap closing, leading to the definition of $\mathbb{Z}_2$ Kitaev invariant also known as Majorana number. We show that this momentum-space invariant is equivalent to a real space construction based on twisted boundary conditions, in which the sign of the product of the Pfaffians of the Hamiltonian under periodic and anti-periodic boundary conditions defines the $\mathbb{Z}_2$ index. By introducing a superlattice description of periodically repeated disorder, we demonstrate that the real space Pfaffian invariant defined as the sign of the Pfaffians of the Hamiltonian with periodic and anti-periodic boundary conditions, remains a well defined invariant even in the absence of microscopic translational symmetry. Within this framework, it is also equivalent to the recently defined periodic disorder invariant (PDI), which constitutes an integer valued ($\mathbb{Z}$) topological invariant in the presence of chiral symmetry. Finally, we prove that the sign of the Pfaffian of a quadratic Hamiltonian equals the fermion parity of its ground state, establishing a direct physical interpretation of the invariant, in terms of sign of the product of the ground state fermion parity with periodic and anti-periodic boundary conditions. Numerical results confirm the correspondence between sign of the Pfaffian reversals, flux-induced level crossings, and ground-state parity switching in clean and disordered nanowires.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

AI总结：

摘要：

英文摘要：

相关论文