Biasing topological charge injection in topological matter

TL;DR

This paper develops a thermodynamic framework for injecting topological charges in nonequilibrium conditions, highlighting the role of edge modes in connecting reservoirs to bulk transport, with implications for Majorana fermion manipulation.

Contribution

It introduces a novel thermodynamic description of topological charge injection, linking momentum-space topology to real-space transport and proposing methods to control Majorana fermions.

Findings

Edge modes connect reservoirs to bulk charge transport.

Injection of skyrmions and vortices can be controlled via external bias.

Majorana zero modes exhibit fractional entropy enabling manipulation.

Abstract

We explore the interplay between topologies in the momentum and real spaces to formulate a thermodynamic description of nonequilibrium injection of topological charges under external bias. We show that the edge modes engendered by the momentum-space topology can play a functional role of connecting the external reservoirs to the bulk transport of topological charges in the real space. We illustrate our general results with two examples: the spin-torque injection of skyrmions in an electrically-biased integer quantum Hall system, and the vortex injection in a topological $p\,+\,i\,p$ superconductor coupled to heat reservoirs. Based on the universal fractional entropy of the Majorana zero modes bound to the vortices, their controllable injection proposed in this work could provide a route for creating and manipulating Majorana fermions.