Roughness of undoped graphene and its short-range induced gauge field

Abstract

We present both numerical and analytical study of graphene roughness with a crystal structure including $500\times 500$ atoms. The roughness can effectively result in a random gauge field and has important consequences for its electronic structure. Our results show that its height fluctuations in small scales have scaling behavior with a temperature dependent roughness exponent in the interval of $0.6<\chi <0.7$. The correlation function of height fluctuations depends upon temperature with characteristic length scale of $\approx 90\mathring{A}$ (at room temperature). We show that the correlation function of the induced gauge field has a short-range nature with correlation length of about $\simeq 2-3\mathring{A}$. We also treat the problem analytically by using the Martin-Siggia-Rose method. The renormalization group flows did not yield any delocalized-localized transition arising from the graphene roughness. Our results are in good agreement with recent experimental observations.

5 Pages, 5 figures

References in corpus (8)

• Two Dimensional Atomic Crystals
• The structure of suspended graphene sheets
• Strong suppression of weak (anti)localization in graphene
• Magnetic confinement of massless Dirac fermions in graphene
• Intervalley scattering, long-range disorder, and effective time reversal symmetry breaking in graphene
• Effect of Disorder on Transport in Graphene
• Chirality and Correlations in Graphene
• Graphene: A Pseudochiral Fermi Liquid

Cited by in corpus (9)

• The electronic properties of graphene
• Ripple Texturing of Suspended Graphene Atomic Membranes
• Electron scattering on microscopic corrugations in graphene
• Formation of atomic nanoclusters on graphene sheets
• Rippling of Graphene
• Anderson Transition in Disordered Graphene
• Effect of disorder on the ground-state properties of graphene
• Quasiparticle properties of graphene in the presence of disorder
• Dirac fermions in a power-law-correlated random vector potential