Screening effects on the excitonic instability in graphene

TL;DR

This paper studies how screening effects influence the excitonic instability in graphene, revealing that dynamical screening lowers the critical interaction strength needed for exciton condensation, which may be attainable in real samples.

Contribution

It provides a detailed analysis of screening effects on excitonic instability in graphene, highlighting the importance of dynamical screening in lowering the critical coupling.

Findings

Static screening increases the critical coupling to approximately 2.09.

Dynamical screening reduces the critical coupling to approximately 0.99.

The results suggest exciton condensation could occur at realistic interaction strengths in graphene.

Abstract

We investigate the excitonic instability in the theory of Dirac fermions in graphene with long-range Coulomb interaction. We analyze the electron-hole vertex relevant for exciton condensation in the ladder approximation, showing that it blows up at a critical value of the interaction strength \alpha = e^2/4\pi v_F sensitive to further many-body corrections. Under static screening of the interaction, we find that taking into account electron self-energy corrections increases the critical coupling to \alpha_c \approx 2.09, for a number N = 4 of two-component Dirac fermions. We show that the dynamical screening of the interaction has however the opposite effect of enhancing the instability, which turns out to develop then at \alpha_c \approx 0.99 for N = 4, bringing the question of whether that critical value can be reached by the effective coupling in real graphene samples at the low-energy scales of the exciton condensation.