Eigenvalues of the bilayer graphene operator with a complex valued potential

TL;DR

This paper investigates how the eigenvalues of a bilayer graphene operator are affected by a complex-valued potential, showing they cluster near the spectrum edges of the unperturbed system.

Contribution

It provides new insights into the spectral behavior of non-selfadjoint operators in bilayer graphene models with complex potentials.

Findings

Eigenvalues are located near the spectrum edges of the unperturbed operator.

The spectrum is influenced by the non-selfadjoint matrix potential.

Eigenvalue distribution is characterized in the complex plane.

Abstract

We study the spectrum of a system of second order differential operator perturbed by a non-selfadjoint matrix valued potential. We prove that eigenvalues of the perturbed operator are located near the edges of the spectrum of the unperturbed operator.