Dirac and Klein-Gordon particles in one-dimensional periodic potentials

By M. Barbier, François M. Peeters, P. Vasilopoulos, J. M. Pereira. 2008

173 citations recorded by the source corpus.

We evaluate the dispersion relation for massless fermions, described by the Dirac equation, and for zero-spin bosons, described by the Klein-Gordon equation, moving in two dimensions and in the presence of a one-dimensional periodic potential. For massless fermions the dispersion relation shows a zero gap for carriers with zero momentum in the direction parallel to the barriers in agreement with the well-known "Klein paradox". Numerical results for the energy spectrum and the density of states are presented. Those for fermions are appropriate to graphene in which carriers behave relativistically with the "light speed" replaced by the Fermi velocity. In addition, we evaluate the transmission through a finite number of barriers for fermions and zero-spin bosons and relate it with that through a superlattice.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/cf388136239e02261b5a4470559767484f20dab0

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In Atomic and Molecular Physics, and Optics

In Materials Chemistry

Citations in the corpus

Emergence of superlattice Dirac points in graphene on hexagonal boron nitride (2012, background): “On the analytical side, one-dimensional potentials render particle propagation anisotropic [2, 3, 11, 14] and generate new Dirac points, where the electron and hole bands meet, at energies ±~vF|G|/2 given by the reciprocal superlattice vectors G [2, 3], and at zero energy for potentials with strengt”