Spectroscopic signatures of tetralayer graphene polytypes

Tetralayer graphene has recently become a new addition to the family of few-layer graphene with versatile electronic properties. This material can be realised in three distinctive stacking configurations, for which we determine spectroscopic signatures in angle-resolved photoemission spectroscopy (ARPES), dynamical optical conductivity, and Raman spectra of inter-band excitations. The reported library of spectral features of tetralayer graphenes can be used for the non-invasive identification of the stacking order realised in a particular film.Comment: Pages 11, figures

Symmetry of boundary conditions of the Dirac equation for electrons in carbon nanotubes.

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