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

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.

4 pages, 2 figures; references added; misprint fixed, some discussion added; published version

References in corpus (14)

• Biased bilayer graphene: semiconductor with a gap tunable by electric field effect
• Gate-induced insulating state in bilayer graphene devices
• Asymmetry gap in the electronic band structure of bilayer graphene
• The electronic properties of bilayer graphene
• Observing Atomic Collapse Resonances in Artificial Nuclei on Graphene
• Atomic Collapse and Quasi-Rydberg States in Graphene
• Electronic Transport in Dual-gated Bilayer Graphene at Large Displacement Fields
• Screening of a hypercritical charge in graphene
• Supercritical Coulomb center and excitonic instability in graphene
• Supercritical Coulomb Impurities in Gapped Graphene
• Charge transport in dual gated bilayer graphene with Corbino geometry
• Polarization Charge Distribution in Gapped Graphene
• The effect of electron dielectric response on the quantum capacitance of graphene in a strong magnetic field
• Disorder-induced tail states in a gapped bilayer graphene

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• Excitons without effective mass: biased bilayer graphene
• Perspectives for gapped bilayer graphene polaritonics
• Quasi-bound States and Resonant Skew Scattering in Two-Dimensional Materials with a Mexican-Hat Dispersion
• Conductivity of a two-dimensional HgTe layer near the critical width: The role of developed edge states network and random mixture of $p$- and $n$-domains
• Excitons and trions with negative effective masses in two-dimensional semiconductors
• Coulomb center instability in bilayer graphene
• Impurity induced current in a Chern insulator
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• Quantum Oscillations in an Impurity-Band Anderson Insulator
• Anomalous screening in two-dimensional materials with an extremum ring in the dispersion law
• Electronic and Phonon Instabilities in Bilayer Graphene under Applied External Bias
• Long-living excited states of a 2D diamagnetic exciton