Coherent States of Graphene Layer with and without a PT-symmetric Chemical Potential

TL;DR

This paper constructs coherent and bicoherent states for a graphene model under magnetic fields and PT-symmetric chemical potentials, addressing ground state issues and analyzing PT-symmetry effects.

Contribution

It introduces ladder operators for the graphene system with PT-symmetry and demonstrates Hamiltonian factorization, advancing the understanding of coherent states in this context.

Findings

Existence of ladder operators enabling Hamiltonian factorization.

Construction of coherent and bicoherent states for graphene with magnetic field.

Analysis of PT-symmetry breaking and its impact on the system.

Abstract

In this paper we construct different classes of coherent and bicoherent states for the graphene tight-binding model in presence of a magnetic field, and for a deformed version where we include a $\mathcal{P}\mathcal{T}$-symmetric chemical potential $V$. In particular, the problems caused by the absence of a suitable ground state for the system is taken into account in the construction of these states, for $V=0$ and for $V\neq0$. We introduce ladder operators which work well in our context, and we show, in particular, that there exists a choice of these operators which produce a factorization of the Hamiltonian. The role of broken and unbroken $\mathcal{P}\mathcal{T}$-symmetry is discussed, in connection with the strength of $V$.