Evolution of Majorona zero-energy edge states in a $T^2 = -1$ symmetry protected 1D topological superconductor with dominant spin-orbit coupling

TL;DR

This paper investigates how Rashba spin-orbit coupling influences the evolution of Majorana zero-energy edge states in a 1D topological superconductor protected by $T^2=-1$ time-reversal symmetry, revealing a phase diagram with three distinct phases.

Contribution

It introduces a model combining Kitaev chains with spin-orbit coupling to analyze phase transitions and edge state evolution in a $T^2=-1$ symmetric topological superconductor.

Findings

Rashba spin-orbit coupling induces phase transitions in the system.

The system exhibits three phases characterized by different topological invariants.

Number of Majorana zero modes varies with the phase, from zero to two.

Abstract

We consider a 1D topological superconductor (TSC) constructed by coupling a pair of Kitaev's Majorana chains with opposite spin configurations. Such a 1D lattice model is known to be protected by a $T^2 = -1$ time-reversal symmetry. Furthermore, we consider a modeled Rashba spin-orbit coupling on such a system of $T^2=-1$ time-reversal symmetric TSC. The Rashba spin-orbit coupling together with the chemical potential engineered the phase transitions of the edge states in the system and consequently the number of Majorona's zero-energy edge modes (MZM's) emerging at the edge of the coupled chains. Correspondingly, the topological nature of the system is described by a phase diagram consisting of three different phases. The three phases are characterized by a topological winding number, $\mathcal{W}=1$, $2$ (with one and two MZM's: topological phases) and $\mathcal{W}=0$ (devoid of any MZM: trivial insulating phase).