Quantum theory for edge current and noise in 2D topological superconductors

TL;DR

This paper investigates edge current and noise in 2D topological superconductors, revealing that noise correlates with the Chern number and peaks during topological phase transitions, providing insights into topological properties.

Contribution

The study introduces a method to relate edge noise to the Chern number, linking topological invariants with measurable noise characteristics in 2D topological superconductors.

Findings

Edge current is zero for non-chiral states and non-zero for chiral states.

Edge noise is always non-zero regardless of chirality.

Bulk noise peaks at topological phase transitions, indicating strong fluctuations.

Abstract

We calculate the edge current and its fluctuations, i.e. noise, in a 2D topological superconductor using the T-matrix and the Green function techniques. We show that the current is zero for non-chiral edge states and non-zero for chiral edge states, while the edge noise is non-zero whatever the chirality of the edge states. By applying our results to toy models with chiral edge states, we find that the noise is closely related to the Chern number. The edge noise is non-zero only when the Chern number is non-zero, and the bulk noise exhibits a peak each time the Chern number varies, meaning that there is strong current fluctuations when a topological phase transition occurs. Our results suggest that the bulk noise could be seen as a topological susceptibility.