Topological phase transitions in Graphene under periodic kicking

Abstract

We consider a periodically $\delta$-kicked Graphene system with the kicking applied in the $\hat{z}$ direction. This is known to open a gap at the Dirac points by breaking inversion symmetry through the introduction of a time-varying staggered sub-lattice potential. We look here at the topological properties of the gap closing-opening transition that occurs as functions of the driving amplitude. The dependence of the driving induced mass-term and the Berry curvature on the strength of the driving is computed. The Chern number for the gapped-out points is computed numerically and it's variation with the driving amplitude is studied. We observe that though the z-kicked Graphene system being time-reversal invariant remains topologically trivial in the bulk, it still permits a quantification of the topological changes that occur at individual gaps with changes in the sign of the mass term. Note:In Sec.II C,page 5, equations 10 & 11 have typos (in the denominators of these equations ,the parentheses appearing after ${\cos }^2({\alpha }_z)$ should appear before it).Eq.12 has a missing term which is independent of the wavevector.This follows from there being typos in eq.9 where in the numerators of the coefficients of $\hat{x}$ and $\hat{y}$ the ${\alpha }_z$ multiplied to the second term has to be dropped in both cases.This follows through to eqs. 10,11 and 12.

arXiv commentThe results reported were generally found to not constitute novel findings of any kind. The Chern number was accorded an unphysical and ambiguous role of quantifying topology around individual Dirac points