Abstract
Starting from the four component-Dirac equation for free, ballistic electrons with finite mass, driven by a constant d.c. field, we derive a basic model of scalar quantum conductivity, capable of yielding simple analytic forms, also in the presence of magnetic and polarization effects. The classical Drude conductivity is recovered as a limit case. A quantum-mechanical evaluation is provided for parabolic and linear dispersion, as in graphene, recovering currently used expressions as particular cases. Numerical values are compared with the ones from the literature in the case of graphene under d.c. applied field. In particular, the effect of the sample length and field strength on the conductivity are highlighted.
Highlights
Graphene has recently attracted intense attention in the research community due to its extraordinary mechanical, electronic and optical properties [1,2,3,4,5]
We introduce a Dirac equation- based, free electron, ballistic model with finite mass under the action of a d.c. electric field in a highly idealized 2D-geometry
It has to be remarked that the Kubo–Drude formulation can only deal with the case of a constant applied voltage (i), whereas the present method is quite more general and deals with a potential varying along the graphene domain
Summary
Graphene has recently attracted intense attention in the research community due to its extraordinary mechanical, electronic and optical properties [1,2,3,4,5]. [32] is found a useful synthesis of the peculiar features of currents at the nanoscale In evaluating this kind of situations with finite electron mass, use is currently made of Schrödinger equation from quantum mechanics in the framework of a free electron model, where the electron is described by a scalar wave-function. It is well appreciated, that such description is incomplete when polarization/magnetization aspects become important, e.g., in the very practical situation of applied electromagnetic fields, where using a four-component spinor description becomes necessary
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