Excitonic Effects in Two-Dimensional Massless Dirac Fermions

TL;DR

This paper investigates excitonic effects in 2D massless Dirac fermions with Coulomb interactions, revealing a phase transition indicated by a change in response behavior and enhanced Friedel oscillations.

Contribution

It introduces a detailed analysis of excitonic effects using the Bethe-Salpeter equation, highlighting a phase transition driven by interaction strength in 2D Dirac systems.

Findings

Power law behavior of the 4-leg vertex changes from real to complex with increasing coupling.

Antisymmetric response exhibits critical-like power law behavior at small wavevectors.

Exciton correlations significantly enhance Friedel oscillations around impurities.

Abstract

We study excitonic effects in two-dimensional massless Dirac fermions with Coulomb interactions by solving the ladder approximation to the Bethe-Salpeter equation. It is found that the general 4-leg vertex has a power law behavior with the exponent going from real to complex as the coupling constant is increased. This change of behavior is manifested in the antisymmetric response, which displays power law behavior at small wavevectors reminiscent of a critical state, and a change in this power law from real to complex that is accompanied by poles in the response function for finite size systems, suggesting a phase transition for strong enough interactions. The density-density response is also calculated, for which no critical behavior is found. We demonstrate that exciton correlations enhance the cusp in the irreducible polarizability at $2k_F$, leading to a strong increase in the amplitude of Friedel oscillations around a charged impurity.