Power law Kohn anomalies and the excitonic transition in graphene

Abstract

Dirac electrons in graphene in the presence of Coulomb interactions of strength $\beta$ have been shown to display power law behavior with $\beta$ dependent exponents in certain correlation functions, which we call the mass susceptibilities of the system. In this work, we first discuss how this phenomenon is intimately related to the excitonic insulator transition, showing the explicit relation between the gap equation and response function approaches to this problem. We then provide a general computation of these mass susceptibilities in the ladder approximation, and present an analytical computation of the static exponent within a simplified kernel model, obtaining ${\eta }_0=\sqrt{1-\beta /{\beta }_c}$ . Finally we emphasize that the behavior of these susceptibilities provides new experimental signatures of interactions, such as power law Kohn anomalies in the dispersion of several phonons, which could potentially be used as a measurement of $\beta$.

arXiv commentExtended version of 1109.6375

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Cited by in corpus (9)

• Fano resonance in Raman scattering of graphene
• Emergence of a ZO Kohn anomaly in quasi-freestanding epitaxial graphene
• Excitonic pairing and insulating transition in two-dimensional semi-Dirac semimetals
• Spectroscopic investigations of phonons in epitaxial graphene
• Dynamical gap generation in 2D Dirac semimetal with deformed Dirac cone
• Higher-order renormalization of graphene many-body theory
• Robustness of the semimetal state of Na3Bi and Cd3As2 against Coulomb interaction
• Quantum critical phenomena of the excitonic insulating transition in two dimensions
• Excitonic pairing of two-dimensional Dirac fermions near the antiferromagnetic quantum critical point