Dynamical fermion mass generation and exciton spectra in graphene

TL;DR

This paper investigates how Coulomb interactions induce dynamical mass generation and exciton spectra in graphene, revealing the effects of small bare masses on symmetry breaking and exciton properties using QCD-inspired methods.

Contribution

It applies Dyson-Schwinger equations and QCD sum rule techniques to analyze exciton spectra and symmetry breaking in graphene with small bare fermion masses.

Findings

Critical Coulomb interaction strength is reduced for exciton formation.

Dynamical fermion mass is significantly enhanced.

Exciton masses are larger than bare mass but smaller than dynamical mass gap.

Abstract

The Coulomb interaction between massless Dirac fermions may induce dynamical chiral symmetry breaking by forming excitonic pairs in clean graphene, leading to semimetal-insulator transition. If the Dirac fermions have zero bare mass, an exact continuous chiral symmetry is dynamically broken and thus there are massless Goldstone excitons. If the Dirac fermions have a small bare mass, an approximate continuous chiral symmetry is dynamically broken and the resultant Goldstone type excitons become massive, which is analogous to what happens in QCD. In this paper, after solving Dyson-Schwinger gap equation in the presence of a small bare fermion mass, we found a remarkable reduction of the critical Coulomb interaction strength for excitonic pair formation and a strong enhancement of dynamical fermion mass. We then calculate the masses of Goldstone type excitons using the SVZ sum rule method and operator product expansion technique developed in QCD and find that the exciton masses are much larger than bare fermion mass but smaller than dynamical fermion mass gap. We also study the spin susceptibilities and estimate the masses of non-Goldstone type excitons using the same tools.