Topological phase transitions in superconductors with chiral symmetry

TL;DR

This paper investigates topological phase transitions in one-dimensional chiral symmetric superconductors, identifying conditions under which gapless systems can transition into topological phases capable of hosting Majorana bound states.

Contribution

It introduces the concept of marginal topological superconductors, showing how small perturbations can induce topological transitions without breaking chirality.

Findings

Identified conditions for topological transitions in gapless chiral superconductors.

Demonstrated that small perturbations can induce topological phases in these systems.

Analyzed specific cases including p-wave and s-wave superconductors with magnetic interactions.

Abstract

We study topological transitions in one dimensional superconductors that can harbor multiple edge Majorana bound states protected by chiral symmetry. The chiral symmetry arises due to the structure of the internal spin degrees of freedom of the superconductor and it can be guided by the coupling of the superconductor with sources of time-reversal symmetry breaking. We then consider distinct regions of the phase diagram in the parameters space that are marked by gapless excitations in the spectrum and evaluate the conditions for inducing a topological transition. We show that for gapless chiral symmetric superconductors one can identify a class of physical perturbations that enable a gap opening in the spectrum, without breaking chirality, and turn the system into a topological state. This type of superconductor is dubbed marginal topological superconductor because an infinitesimally small perturbation is able to induce a transition into a topological nontrivial phase. To explicitly demonstrate and evaluate the character of the transitions from gapless to topological gapfull phases we explore different physical cases including p-wave superconductor in the presence of an applied magnetic field or proximity-coupled to a ferromagnet, and s-wave superconductor in a noncollinear magnetic ordering.