Exceptional point description of one-dimensional chiral topological superconductors/superfluids in BDI class

TL;DR

This paper introduces a novel method using exceptional points in complex wave vector space to identify topological phase transitions and quantify Majorana zero modes in 1D chiral topological superconductors in the BDI class.

Contribution

It proposes a generic formula based on exceptional points to determine the number of Majorana zero modes, providing an alternative to the traditional winding number invariant.

Findings

Exceptional points identify topological phase transitions.

A formula quantifies Majorana zero modes from exceptional point properties.

The method offers an alternative to the winding number invariant.

Abstract

We show that certain singularities of the Hamiltonian in the complex wave vector space can be used to identify topological quantum phase transitions for $1D$ chiral topological superconductors/superfluids in the BDI class. These singularities fall into the category of the so-called exceptional points ($EP$'s) studied in the context of non-Hermitian Hamiltonians describing open quantum systems. We also propose a generic formula in terms of the properties of the $EP$'s to quantify the exact number of Majorana zero modes in a particular chiral topological superconducting phase, given the values of the parameters appearing in the Hamiltonian. This formula serves as an alternative to the familiar integer ($\mathbb{Z}$) winding number invariant characterizing topological superconductor/superfluid phases in the chiral BDI class.