Signatures of surface Majorana modes in the magnetic response of topological superconductors

TL;DR

This paper investigates how surface Majorana modes in topological superconductors influence magnetic susceptibility, revealing a transition in Dirac cone type and a finite frequency response due to surface curvature effects.

Contribution

It provides a detailed analysis of the magnetic response of surface Majorana modes, including a field-induced transition and curvature effects on susceptibility.

Findings

Transition from type I to type II Dirac cone at critical field H*

Finite current flow and diamagnetic response above H*

Finite frequency magnetic susceptibility due to curvature effects

Abstract

We study the magnetic susceptibility of a two-dimensional cone of Majorana modes localised at the surface of a three-dimensional time-reversal invariant topological superconductor belonging to class DIII. A field parallel to the surface tilts the surface Majorana cone along the supercurrent direction. For fields larger than a critical threshold field $H^*$, $H>H^*$, a transition from type I to type II Dirac cone occurs and a finite current carried by the Majorana modes start to flow, leading to an additional diamagnetic contribution to the surface magnetization. On a curved surface interband transitions are promoted by the Majorana spin connection that couples to the external field, giving rise to a finite frequency magnetic susceptibility.