S. Palpacelli, M. Mendoza, H. J. Herrmann, S. Succi
In this paper, we study Klein tunneling in random media. To this purpose, we simulate the propagation of a relativistic Gaussian wavepacket through a graphene sample with randomly distributed potential barriers (impurities). The simulations, based on a relativistic quantum lattice Boltzmann method, permit to compute the transmission coefficient across the sample, thereby providing an estimate for the conductivity as a function of impurity concentration and strength of the potentials. It is found that the conductivity loss due to impurities is significantly higher for wave-packets of massive particles, as compared to massless ones. A general expression for the loss of conductivity as a function of the impurity percentage is presented and successfully compared with the Kozeny-Carman law for disordered media in classical fluid dynamics.
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http://arxiv.org/abs/1202.6217
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