2008/03/25 by M. Barbier, Michaël Barbier, F. M. Peeters +3 · 5 citations
Materials Science · Physics and Astronomy · #Boson #Dirac (video compression format) #Dirac equation #Dirac fermion #Dispersion relation #Fermi energy #Fermion #Graphene research and applications #Massless particle #Mathematical physics #Momentum (technical analysis) #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum electrodynamics #Quantum mechanics #Spin (aerodynamics) #Superlattice #Topological Materials and Phenomena #Zero (linguistics) #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevb.77.115446
published as Phys. Rev. B 77, 115446 (2008) · 9 pages, 12 figures
openalex publication_date 2008/03/25 · arxiv created 2011/01/20 · arxiv updated 2015/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.