Excitonic Effects in Two-Dimensional Massless Dirac Fermions

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.

16 pages, 18 figures

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Cited by in corpus (19)

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• Optical Response and Ground State of Graphene
• Absence of dynamical gap generation in suspended graphene
• Screening effects on the excitonic instability in graphene
• Excitonic pairing and insulating transition in two-dimensional semi-Dirac semimetals
• Gapped phase in AA stacked bilayer graphene
• Finite-size version of the excitonic instability in graphene quantum dots
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• Pair states in one-dimensional Dirac systems
• Zero-energy vortices in Dirac materials
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• Quantum critical phenomena of the excitonic insulating transition in two dimensions
• Excitonic physics in a Dirac quantum dot