Coulomb center instability in bilayer graphene

Abstract

In the low-energy two-band as well as four-band continuum models, we study the supercritical instability in gapped bilayer graphene in the field of a charged impurity. It is found that the screening effects are crucially important in bilayer graphene. If they are neglected, then the critical value for the impurity charge as the lowest-energy bound state dives into the lower continuum tends to zero as the gap $\Delta$ vanishes. If the screened Coulomb interaction is considered, then the critical charge tends to a finite value for $\Delta \to 0$. The different scalings of the kinetic energy of quasiparticles and the Coulomb interaction with respect to the distance to the charged impurity ensure that the wave function of the electron bound state does not shrink toward the impurity as its charge increases. This results in the absence of the fall-to-center phenomenon in bilayer graphene although the supercritical instability is realized.

15 pages, 6 figures

References in corpus (13)

• Unconventional quantum Hall effect and Berry's phase of 2pi in bilayer graphene
• Is graphene in vacuum an insulator?
• The Coulomb impurity problem in graphene
• Vacuum Polarization and Screening of Supercritical Impurities in Graphene
• Atomic Collapse and Quasi-Rydberg States in Graphene
• Quantum Anomalous Hall State in Bilayer Graphene
• Optical conductivity of bilayer graphene with and without an asymmetry gap
• Local Compressibility Measurements of Correlated States in Suspended Bilayer Graphene
• Screening of a hypercritical charge in graphene
• On the eigenvalues of operators with gaps. Application to Dirac operators
• Supercritical Coulomb center and excitonic instability in graphene
• Monte-Carlo study of the electron transport properties of monolayer graphene within the tight-binding model
• Dynamical polarization of monolayer graphene in a magnetic field

Cited by in corpus (2)

• Electron states for gapped pseudospin-1 fermions in the field of charged impurity
• Electron binding energy of a donor in bilayer graphene with gate-tunable gap