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Article overview
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Height correlation of rippled graphene and Lundeberg-Folk formula for magnetoresistance | | Kazuyuki Genma
; Makoto Katori
; | | Date: |
9 Nov 2012 | | Abstract: | Application of an in-plane magnetic field to rippled graphene will make the
system be a plane with randomly distributed vector potentials. Massless Dirac
fermions carrying charges on graphene are scattered by the vector potentials
and magnetoresistance is induced proportional to the square of amplitude of
in-plane magnetic field $B_{parallel}^2$. Recently, Lundeberg and Folk
proposed a formula showing dependence of the magnetoresistance on carrier
density, in which the coefficient of $B_{parallel}^2$ is given by a functional
of the height-correlation function $c(r)$ of ripples. In the present paper, we
give exact and explicit expressions of the coefficient for the two cases such
that $c(r)$ is (i) exponential and (ii) Gaussian. The results are given using
well-known special functions. Application of the present solutions in the
vicinity of charge neutrality point should be careful because of the possible
strong density inhomogeneity in rippled graphene. Here our analytic expressions
are proposed, however, as trial interpolation formulas connecting the positive
high-carrier-density regime and the negative one for magnetoresistance.
Numerical fitting of our solutions to experimental data were performed. It is
shown that the experimental data are well-described by the formula for the
Gaussian height-correlation of ripples in the whole region of carrier density.
The standard deviation $Z$ of ripple height and the correlation length $R$ of
ripples are evaluated, which can be compared with direct experimental
measurements. | | Source: | arXiv, 1211.2046 | | Services: | Forum | Review | PDF | Favorites | |
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