Supercritical Coulomb center and excitonic instability in graphene

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 α=e^2/κ\hbar v_F leading to instability of the system. In the random-phase approximation, the critical coupling is estimated to be α_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.

17 pages, 4 figures

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• A Strongly-Interacting Dirac Liquid on the Surface of a Topological Kondo Insulator
• Coulomb impurity problem of graphene in magnetic fields
• Scattering theory and ground-state energy of Dirac fermions in graphene with two Coulomb impurities
• Power law Kohn anomalies and the excitonic transition in graphene
• Large conduction band and Fermi velocity spin splittings due to Coulomb interactions in single-layer MoS_{2}
• Massless Dirac cones in graphene: experiments and theory
• Two-electron bound states near a Coulomb impurity in gapped graphene
• Bound States and Supercriticality in Graphene-Based Topological Insulators
• Atomic Collapse in Graphene: Lost of Unitarity
• Green functions in graphene monolayer with Coulomb interactions taken into account