Collective excitations in a large-d model for graphene

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 $q_{\mathrm{c}}$ 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.

23 pages, 30 figures

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Cited by in corpus (22)

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• Buckling of thermalized elastic sheets
• Quantum and classical ripples in graphene
• The flat phase of quantum polymerized membranes
• Critical radius and temperature for buckling in graphene
• Thermal stiffening of clamped elastic ribbons
• Interplay between in-plane and flexural phonons in electronic transport of two-dimensional semiconductors
• Ripples in hexagonal lattices of atoms coupled to Glauber spins
• Bifurcation analysis and phase diagram of a spin-string model with buckled states
• STM driven transition from rippled to buckled graphene in a spin-membrane model
• Bending rigidity, sound propagation and ripples in flat graphene
• Rippling transition from electron-induced condensation of curvature field in graphene
• Thermal ripples in bilayer graphene
• Anomalous thermal expansion in Ising-like puckered sheets
• A numerical study of the rippling instability driven by electron-phonon coupling in graphene
• Large-scale critical behavior of the rippling phase transition for graphene membranes
• Geometrically-induced localization of flexural waves on thin warped physical membranes
• Perturbative renormalization and thermodynamics of quantum crystalline membranes