Supercritical Coulomb center and excitonic instability in graphene

TL;DR

This paper investigates how a quasiparticle gap affects the stability of supercritical Coulomb impurities in graphene, revealing excitonic instability and potential condensate formation at strong coupling.

Contribution

It demonstrates that opening a quasiparticle gap stabilizes supercritical Coulomb states and identifies a critical coupling for excitonic instability in graphene.

Findings

Quasiparticle gap decreases the imaginary part of resonant states.

Strong Coulomb interaction leads to tachyonic solutions indicating instability.

Critical coupling for instability is estimated at α_c = 1.62.

Abstract

It is well known that there are resonant states with complex energy for the supercritical Coulomb impurity in graphene. We show that opening of a quasiparticle gap decreases the imaginary part of energy, |ImE|, of these states and stabilizes the system. For gapless quasiparticles with strong Coulomb interaction in graphene, we solve the Bethe-Salpeter equation for the electron - hole bound state and show that it has a tachyonic solution for strong enough coupling \alpha=e^2/\kappa\hbar v_F leading to instability of the system. In the random-phase approximation, the critical coupling is estimated to be \alpha_c =1.62 and is an analogue of the critical charge in the Coulomb center problem. We argue that the excitonic instability should be resolved through the formation of an excitonic condensate and gap generation in the quasiparticle spectrum.