Coulomb center instability in bilayer graphene

TL;DR

This paper investigates supercritical Coulomb impurity instability in bilayer graphene, emphasizing the importance of screening effects and revealing the absence of fall-to-center phenomena despite supercriticality.

Contribution

It demonstrates that screening effects prevent the wave function collapse in bilayer graphene, contrasting with traditional expectations of fall-to-center in supercritical regimes.

Findings

Screening effects are crucial in bilayer graphene.

Critical impurity charge remains finite as gap approaches zero.

No fall-to-center phenomenon occurs despite supercritical instability.

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.