Supercritical instability in graphene with two charged impurities

TL;DR

This paper investigates the supercritical instability in gapped graphene with two charged impurities, focusing on the critical distance at which bound states reach the continuum boundary, using variational and quasiclassical methods.

Contribution

It introduces a variational approach to determine the critical distance for supercritical instability in a two-impurity graphene system, highlighting the dependence on the quasiparticle gap.

Findings

Critical distance increases as the quasiparticle gap decreases.

Derived energy and width of quasistationary states as functions of impurity separation.

Identified the boundary between supercritical and subcritical regimes.

Abstract

We study the supercritical instability in gapped graphene with two charged impurities separated by distance R using the two-dimensional Dirac equation for electron quasiparticles. Attention is paid to a situation when charges of impurities are subcritical, whereas their total charge exceeds a critical one. The critical distance R_{cr} in the system of two charged centers is defined as that at which the electron bound state with the lowest energy reaches the boundary of the lower continuum. A variational calculation of the critical distance R_{cr} separating the supercritical (R<R_{cr}) and subcritical (R>R_{cr}) regimes is carried out. It is shown that the critical distance R_{cr} increases as the quasiparticle gap decreases. The energy and width of a quasistationary state as functions of the distance between two impurities are derived in the quasiclassical approximation.