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arXiv · 1312.2854

Collective excitations in a large-d model for graphene

Francisco Guinea·Pierre Le Doussal·Kay Joerg Wiese
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Abstract

We consider a model of Dirac fermions coupled to flexural phonons to describe a graphene sheet fluctuating in dimension $2+d$. We derive the self-consistent screening equations for the quantum problem, exact in the limit of large $d$. We first treat the membrane alone, and work out the quantum to classical, and harmonic to anharmonic crossover. For the coupled electron-membrane problem we calculate the dressed two-particle propagators of the elastic and electron interactions and find that it exhibits a collective mode which becomes unstable at some wave-vector $q_{\rm c}$ for large enough coupling $g$. The saddle point analysis, exact at large $d$, indicates that this instability corresponds to spontaneous and simultaneous appearance of gaussian curvature and electron puddles. The relevance to ripples in graphene is discussed.

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Francisco Guinea, Pierre Le Doussal, Kay Joerg Wiese. 2013-12-10. Collective excitations in a large-d model for graphene. https://doi.org/10.1103/physrevb.89.125428

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