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Algebraic solution of a graphene layer in a transverse electric and perpendicular magnetic fields
We present an exact algebraic solution of a single graphene plane in
transverse electric and perpendicular magnetic fields. The method presented
gives both the eigen-values and the eigen-functions of the graphene plane. It
is shown that the eigen-states of the problem can be casted in terms of
coherent states, which appears in a natural way from the formalism.Comment: 11 pages, 5 figures, accepted for publication in Journal of Physics
Condensed Matte
Conductivity of suspended and non-suspended graphene at finite gate voltage
We compute the DC and the optical conductivity of graphene for finite values
of the chemical potential by taking into account the effect of disorder, due to
mid-gap states (unitary scatterers) and charged impurities, and the effect of
both optical and acoustic phonons. The disorder due to mid-gap states is
treated in the coherent potential approximation (CPA, a self-consistent
approach based on the Dyson equation), whereas that due to charged impurities
is also treated via the Dyson equation, with the self-energy computed using
second order perturbation theory. The effect of the phonons is also included
via the Dyson equation, with the self energy computed using first order
perturbation theory. The self-energy due to phonons is computed both using the
bare electronic Green's function and the full electronic Green's function,
although we show that the effect of disorder on the phonon-propagator is
negligible. Our results are in qualitative agreement with recent experiments.
Quantitative agreement could be obtained if one assumes water molelcules under
the graphene substrate. We also comment on the electron-hole asymmetry observed
in the DC conductivity of suspended graphene.Comment: 13 pages, 11 figure
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