Electron dynamics in graphene with spin-orbit couplings and periodic potentials

Ranjani Seshadri, Diptiman Sen

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We use both continuum and lattice models to study the energy-momentum dispersion and the dynamics of a wave packet for an electron moving in graphene in the presence of spin-orbit couplings and either a single potential barrier or a periodic array of potential barriers. Both Kane-Mele and Rashba spin-orbit couplings are considered. A number of special things occur when the Kane-Mele and Rashba couplings are equal in magnitude. In the absence of a potential, the dispersion then consists of both massless Dirac and massive Dirac states. A periodic potential is known to generate additional Dirac points; we show that spin-orbit couplings generally open gaps at all those points, but if the two spin-orbit couplings are equal, some of the Dirac points remain gapless. We show that the massless and massive states respond differently to a potential barrier; the massless states transmit perfectly through the barrier at normal incidence while the massive states reflect from it. In the presence of a single potential barrier, we show that there are states localized along the barrier. Finally, we study the time evolution of a wave packet in the presence of a periodic potential. We discover special points in momentum space where there is almost no spreading of a wave packet; there are six such points in graphene when the spin-orbit couplings are absent.

Original languageEnglish
Article number155303
JournalJournal of Physics Condensed Matter
Issue number15
StatePublished - 13 Mar 2017
Externally publishedYes


  • grapheme
  • spin-orbit couplings
  • wave packet dynamics

ASJC Scopus subject areas

  • Materials Science (all)
  • Condensed Matter Physics


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