Discrete Spectrum of the Bilayer Graphene Operator

TL;DR

This paper analyzes the spectral properties of a perturbed bilayer graphene operator, deriving asymptotic formulas for the number of eigenvalues crossing a fixed point as the perturbation strength increases.

Contribution

It provides new asymptotic formulas for the eigenvalue count of the bilayer graphene operator under large perturbations.

Findings

Asymptotic formulas for eigenvalue counts as perturbation strength grows

Analysis of eigenvalue crossings at regular spectral points

Insights into spectral stability of the bilayer graphene operator

Abstract

We consider the graphene operator $D_m$ perturbed by a decaying potential $\alpha V$, where $\alpha$ is a coupling constant. We study the number $N(\lambda,\alpha)$ of eigenvalues of the operator $D(t)=D_m-tV$ passing through a regular point $\lambda\in\rho(D_m)$ as $t$ changes from $0$ to $\alpha$. We obtain asymptotic formulas for $N(\lambda,\alpha)$ as $\alpha\to\infty$.