Antilinear spectral symmetry and the vortex zero-modes in topological insulators and graphene

TL;DR

This paper extends the Dirac Hamiltonian to include antilinear reflection symmetry, analyzing zero-energy vortex modes in topological insulators and graphene, revealing conditions for their existence and providing analytical solutions.

Contribution

It introduces a generalized Hamiltonian framework that preserves antilinear symmetry and explores zero-mode conditions in topological systems and graphene.

Findings

Zero-mode exists only when Zeeman coupling is below a critical threshold.

Analytical zero-energy wave functions are derived for graphene.

The extended Hamiltonian applies to various physical realizations of topological systems.

Abstract

We construct the general extension of the four-dimensional Jackiw-Rossi-Dirac Hamiltonian that preserves the antilinear reflection symmetry between the positive and negative energy eigenstates. Among other systems, the resulting Hamiltonian describes the s-wave superconducting vortex at the surface of the topological insulator, at a finite chemical potential, and in the presence of both Zeeman and orbital couplings to the external magnetic field. Here we find that the bound zero-mode exists only when the Zeeman term is below a critical value. Other physical realizations pertaining to graphene are considered, and some novel zero-energy wave functions are analytically computed.