Symmetry of boundary conditions of the Dirac equation for electrons in carbonnanotubes

Abstract

We consider the effective mass model of spinless electrons in single-wall carbon nanotubesthat is equivalent to the Dirac equation for massless fermions. Within this framework wederive all possible energy independent hard wall boundary conditions that are applicable tometallic tubes. The boundary conditions are classified in terms of their symmetryproperties and we demonstrate that the use of different boundary conditions will result invarying degrees of valley degeneracy breaking of the single-particle energy spectrum.