Collective excitations in a large- d model for graphene

Francisco Guinea (1) , Pierre Le Doussal (2) , Kay Joerg Wiese (2)

1 School of Physics and Astronomy [Manchester]
2 LPTENS - Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure]

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.

Domaines: Physique [physics]; Matière Condensée [cond-mat]; Systèmes mésoscopiques et effet Hall quantique [cond-mat.mes-hall]

Francisco Guinea, Pierre Le Doussal, Kay Joerg Wiese. Collective excitations in a large- d model for graphene. Physical Review B: Condensed Matter and Materials Physics (1998-2015), 2014, 89 (12), ⟨10.1103/PhysRevB.89.125428⟩. ⟨hal-02281090⟩