Effect of Coulomb interaction on the gap in monolayer and bilayer graphene

TL;DR

This study investigates how Coulomb interactions influence the spectral gap in monolayer and bilayer graphene near charge neutrality, revealing fixed points and the role of the gap in renormalization flow saturation.

Contribution

It provides a detailed analysis of Coulomb effects on the spectral gap in graphene using the functional renormalization-group method, including fixed points and flow saturation mechanisms.

Findings

Coulomb interaction supports the gap once it is open.

Identifies a fixed point related to a quantum phase transition at infinite Coulomb strength.

Shows the gap introduces a length scale that saturates renormalization flow.

Abstract

We study effects of a repulsive Coulomb interaction on the spectral gap in monolayer and bilayer graphene in the vicinity of the charge neutrality point by employing the functional renormalization-group technique. In both cases Coulomb interaction supports the gap once it is open. For monolayer graphene we correctly reproduce results obtained previously by several authors, e.g., an apparent logarithmic divergence of the Fermi velocity and the gap as well as a fixed point corresponding to a quantum phase transition at infinitely large Coulomb interaction. On the other hand, we show that the gap introduces an additional length scale at which renormalization flow of diverging quantities saturates. An analogous analysis is also performed for bilayer graphene with similar results. We find an additional fixed point in the gapless regime with linear spectrum corresponding to the vanishing electronic band mass. This fixed point is unstable with respect to gap fluctuations and can not be reached as soon as the gap is opened. This preserves the quadratic scaling of the spectrum and finite electronic band mass.