Bound state energy of a Coulomb impurity in gapped bilayer graphene: "Hydrogen atom with a Mexican hat"

TL;DR

This paper investigates how a perpendicular electric field in bilayer graphene creates a 'Mexican hat' dispersion, affecting the bound state energies of electrons around Coulomb impurities, revealing unique quantum behaviors.

Contribution

It provides the first calculation of hydrogen-like bound state energies in gapped bilayer graphene considering the Mexican hat dispersion structure.

Findings

Ground state energy varies with interlayer voltage and fine structure constant.

Wavefunction exhibits many nodes even in the ground state.

Electron states undergo atomic collapse at certain voltages.

Abstract

Application of a perpendicular electric field induces a band gap in bilayer graphene, and it also creates a "Mexican hat" structure in the dispersion relation. This structure has unusual implications for the hydrogen-like bound state of an electron to a Coulomb impurity. We calculate the ground state energy of this hydrogen-like state as a function of the applied interlayer voltage and the effective fine structure constant. Unlike in the normal hydrogen atom, the resulting wavefunction has many nodes even in the ground state. Further, the electron state undergoes "atomic collapse" into the Dirac continuum both at small and large voltage.