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

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