Graphene thermopower

Start date 01/01/2006
Temperature dependence of (a) the charge conductance, (b) the heat conductance, and (c) the thermopower for three values of the impurity density n_imp. The solid and broken lines are for a large impurity potential V_imp=20Ec, while the dotted lines are for the strict unitary limit V_imp -> infinity. In (a)-(b) we have normalized the conductivities by the lowtemperature asymptotics sigma0=4e^2/ (pi h) and kappa0=4pi k_B^2 T/(3h). In (d) we show the details at low temperatures. The dotted lines are the thermopower computed through the Mott relation. In (e) we show the Lorenz ration L=kappa/(sigma T) in units of the value L0=(pi^2/3)/(k_B^2/e^2) appearing in the Wiedeman-Franz law. We used Ec=1eV -> 11605 K to convert the temperature scale to Kelvin. The order of magnitude S~k_B/e~100 micro-Volt/ Kelvin is in agreement with recent experiments on graphene and earlier experimentes on carbon nanotubes.
The experimental isolation of graphene, one monolayer of graphite, has generated great interest partly because of the potential of carbon-based nano-scale electronics but also for fundamental reasons. Experiments have shown that the charge conductivity of graphene reaches a minimal value of order e2/h. It has also been found that the conductivity is linearly dependent on the electron density. Furthermore, an unconventional half-integer quantum Hall effect has been discovered. These experiments are in qualitative agreement with theoretical results based on the effective low-energy Dirac theory of graphene.
Measurements of other quantities than the charge conductance can provide additional and valuable information of graphene properties. In a recent study we have predicted that the thermopower can provide information about impurities in graphene[1], which has been qualitatively confirmed experimentally very recently. Current efforts include extensions to nanostructured graphene, such as nanoribbons[2]. [1] T. Löfwander and M. Fogelström, Phys.
[1] T. Löfwander and M. Fogelström, Phys. Rev. B 76, 193401 (2007)
[2] V. Ebrahimi, M.Sc. thesis, Chalmers 2008
​Swedish Research Council (VR)

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