$PT$-symmetric graphene under a magnetic field

TL;DR

This paper introduces a $PT$-symmetric deformation of the graphene tight-binding model under magnetic fields, analyzing spectral properties and eigenvector behavior in different symmetry regions, revealing asymmetries and eigenvector completeness issues.

Contribution

It presents a novel $PT$-symmetric deformation of the graphene model and studies its spectral and eigenvector properties, highlighting effects on zero-energy states and biorthogonality.

Findings

Deformation causes asymmetry in zero-energy states

Eigenvector completeness breaks down in $PT$-broken regions

Biorthogonality properties differ between symmetry regions

Abstract

We propose a $PT$-symmetrically deformed version of the graphene tight-binding model under a magnetic field. We analyze the structure of the spectra and the eigenvectors of the Hamiltonians around the $K$ and $K'$ points, both in the $PT$-symmetric and $PT$-broken regions. In particular we show that the presence of the deformation parameter $V$ produces several interesting consequences, including the asymmetry of the zero-energy states of the Hamiltonians and the breakdown of the completeness of the eigenvector sets. We also discuss the biorthogonality of the eigenvectors, which {turns out to be} different in the $PT$-symmetric and $PT$-broken regions.