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Application of an in-plane magnetic field to rippled graphene will make thesystem be a plane with randomly distributed vector potentials. Massless Diracfermions carrying charges on graphene are scattered by the vector potentialsand magnetoresistance is induced proportional to the square of amplitude ofin-plane magnetic field $B_{\parallel}^2$. Recently, Lundeberg and Folkproposed a formula showing dependence of the magnetoresistance on carrierdensity, in which the coefficient of $B_{\parallel}^2$ is given by a functionalof the height-correlation function $c(r)$ of ripples. In the present paper, wegive exact and explicit expressions of the coefficient for the two cases suchthat $c(r)$ is (i) exponential and (ii) Gaussian. The results are given usingwell-known special functions. Numerical fitting of our solutions toexperimental data were performed. It is shown that the experimental data arewell-described by the formula for the Gaussian height-correlation of ripples inthe whole region of carrier density. The standard deviation $Z$ of rippleheight and the correlation length $R$ of ripples are evaluated, which can becompared with direct experimental measurements.

Height correlation of rippled graphene and Lundeberg-Folk formula for magnetoresistance