Discrete Spectrum of the Bilayer Graphene Operator

Siyu Gao; Oleg Safronov

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arXiv · 2506.22998

Discrete Spectrum of the Bilayer Graphene Operator

Siyu Gao·Oleg Safronov

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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 $\alpha\to\infty$.

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Siyu Gao, Oleg Safronov. 2025-06-28. Discrete Spectrum of the Bilayer Graphene Operator. https://arxiv.org/abs/2506.22998

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