Discrete Spectrum of the Bilayer Graphene Operator

Siyu Gao; Oleg Safronov

Discrete Spectrum of the Bilayer Graphene Operator

Spectral Theory 2025-07-01 v1

Authors: Siyu Gao , Oleg Safronov

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 $\alpha\to\infty$ .

Keywords

bilayer graphene operator discrete spectrum decaying potential eigenvalue asymptotics coupling constant

Cite

@article{arxiv.2506.22998,
  title  = {Discrete Spectrum of the Bilayer Graphene Operator},
  author = {Siyu Gao and Oleg Safronov},
  journal= {arXiv preprint arXiv:2506.22998},
  year   = {2025}
}

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