任意边界条件下二次费米子哈密顿量的精确解
Exact Solution of Quadratic Fermionic Hamiltonians for Arbitrary Boundary Conditions
摘要：
我们提出了一个严格对角化有限范围的二次费米子哈密顿任意边界条件的D维之一，并在其余的D-1周期。关键是一个哈密顿依赖的分离的大部分从边界。通过结合两者的信息，我们确定了一个矩阵函数，完全表征的解决方案，并允许确定散装边界对应的指标。作为一个例子，我们展示了我们的方法如何正确地描述了零能量马约拉纳模式的时间反演不变的s波超导体的约瑟夫森环配置，并预测，分数4 π约瑟夫森效应只能观察到的阶段托管奇数马约拉纳对。
英文摘要：
We present a procedure for exactly diagonalizing finite-range quadratic fermionic Hamiltonians with arbitrary boundary conditions in one of D dimensions, and periodic in the remaining D-1. The key is a Hamiltonian-dependent separation of the bulk from the boundary. By combining information from the two, we identify a matrix function that completely characterizes the solutions, and allow to identify an indicator of bulk-boundary correspondence. As an illustration, we show how our method correctly describes the zero-energy Majorana modes of a time-reversal-invariant s-wave superconductor in a Josephson ring configuration, and predicts that a fractional 4 pi Josephson effect can only be observed in phases hosting an odd number of Majorana pairs.
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