Quantum charged spinning massless particles in 2 + 1 dimensions

Author:

Morales IvanORCID,Neves Bruno,Oporto Zui,Piguet Olivier

Abstract

AbstractMotivated by the conduction properties of graphene discovered and studied in the last decades, we consider the quantum dynamics of a massless, charged, spin 1/2 relativistic particle in three dimensional space-time, in the presence of an electrostatic field in various configurations such as step or barrier potentials and generalizations of them. The field is taken as parallel to the y coordinate axis and vanishing outside of a band parallel to the x axis. The classical theory is reviewed, together with its canonical quantization leading to the Dirac equation for a 2-component spinor. Stationary solutions are numerically found for each of the field configurations considered, from which we calculate the mean quantum trajectories of the particle and compare them with the corresponding classical trajectories, the latter showing a classical version of the Klein phenomenon. Transmission and reflection probabilities are also calculated, confirming the Klein phenomenon.

Funder

Fundação de Amparo a Pesquisa do Estado de Minas Gerais - FAPEMIG, Brazil

Coordenação de Aperfeiçoamento de Pessoal de Nivel Superior - CAPES, Brasil

Conselho Nacional de Desenvolvimento Cientifico e Tecnologico - CNPq, Brazil

Grupo de Sistemas Complejos de la Carrera de Física de la Universidad Mayor de San Andrés, UMSA, Bolivia

Publisher

Springer Science and Business Media LLC

Subject

Physics and Astronomy (miscellaneous),Engineering (miscellaneous)

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