Absence of dynamical gap generation in suspended graphene

TL;DR

This study uses Dyson-Schwinger equations to analyze whether Coulomb interactions can induce a gap in suspended graphene, concluding it remains a semimetal due to insufficient interaction strength.

Contribution

The paper provides a self-consistent analysis including velocity renormalization and screening effects, showing no gap formation at realistic interaction levels in suspended graphene.

Findings

Critical interaction strength exceeds physical value

Suspended graphene remains a semimetal at zero temperature

Dynamical screening suppresses gap generation

Abstract

There is an interesting proposal that the long-range Coulomb interaction in suspended graphene can generate a dynamical gap, which leads to a semimetal-insulator phase transition. We revisit this problem by solving the self-consistent Dyson-Schwinger equations of wave function renormalization and fermion gap. In order to satisfy the Ward identity, a suitable vertex function is introduced. The impacts of singular velocity renormalization and dynamical screening on gap generation are both included in this formalism, and prove to be very important. We obtain a critical interaction strength, $3.2 < \alpha_{c} < 3.3$, which is larger than the physical value $\alpha = 2.16$ for suspended graphene. It therefore turns out that suspended graphene is a semimetal, rather than insulator, at zero temperature.