Tunable tilted anisotropy of massless Dirac fermion in magnetic Kronig-Penney-type graphene

Abstract

Modulation effects of alternating periodic electrostatic scalar and magnetic vector potentials on the anisotropic and the tilt characteristics of Dirac cone in a semi-infinite graphene was theoretically investigated using the transfer matrix technique. To study its anisotropic behavior, we characterized the geometry deformation of superlattice Dirac cone by introducing the tilt parameter, eccentricity, and group velocity. We found that the Dirac cone anisotropy and tilt effect depend on the amplitude of the periodically modulated scalar and/or vector potentials. As the results of tuning the coupled periodic scalar and vector potentials, four different phases of Dirac fermions emerged and were categorized through a phase diagram of the tilt parameter. For a strong coupled modulation, the tilt parameter becomes larger than one and the type-II Dirac cone phase emerged. We also found that pairs of extra Dirac points can be induced by a very high periodic scalar modulation coupled with a low periodic vector modulation. Moreover, strong modulation caused the Fermi contour to deform from a closed contour into an opened contour, introducing an electron-hole pocket on the graphene. Our results demonstrate the possibility to control the anisotropic behavior of the electronic structure of graphene, which might lead to an artificial tilted Dirac cone material and direction-dependent quantum devices.