Quantum Charged Spinning Massless Particles in 2+1 dimensions

Abstract

Motivated 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, fromwhich 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.

30 pages, 14 figures, Mathematica code annexed as an ancillary file. Version v2: Paragraph added in the introduction. Three new references. Version v3: Final version, publihshed in Eur. Phys. J

References in corpus (12)

• The electronic properties of graphene
• Chiral tunneling and the Klein paradox in graphene
• Andreev reflection and Klein tunneling in graphene
• Quantum interference and Klein tunneling in graphene heterojunctions
• Selective transmission of Dirac electrons and ballistic magnetoresistance of \textit{n-p} junctions in graphene
• Evidence of Klein tunneling in graphene p-n junctions
• Modeling Klein tunneling and caustics of electron waves in graphene
• Semiclassical theory of potential scattering for massless Dirac fermions
• Symmetry breaking and (pseudo)spin polarization in Veselago lenses for massless Dirac fermions
• Scattering of charge carriers in graphene induced by topological defects
• Graphene and Black Holes: novel materials to reach the unreachable
• Behaviour of Charged Spinning Massless Particles