BITS Faculty Publications
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Item Topological phase transitions in Graphene under periodic kicking(ARXIV, 2017-09) Bandyopadhyay, Jayendra N.; Sarkar, Tapomoy GuhaWe consider a periodically δ-kicked Graphene system with the kicking applied in the 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 cos2(αz) 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 x^ and y^ the αz multiplied to the second term has to be dropped in both cases.This follows through to eqs. 10,11 and 12.Item Floquet analysis of pulsed Dirac systems: a way to simulate rippled graphene(Springer, 2015-09) Bandyopadhyay, Jayendra N.The low energy continuum limit of graphene is effectively known to be modeled using the Dirac equation in (2 + 1) dimensions. We consider the possibility of using a modulated high frequency periodic driving of a two-dimensional system (optical lattice) to simulate properties of rippled graphene. We suggest that the Dirac Hamiltonian in a curved background space can also be effectively simulated by a suitable driving scheme in an optical lattice. The time dependent system yields, in the approximate limit of high frequency pulsing, an effective time independent Hamiltonian that governs the time evolution, except for an initial and a final kick. We use a specific form of 4-phase pulsed forcing with suitably tuned choice of modulating operators to mimic the effects of curvature. The extent of curvature is found to be directly related to ω −1 the time period of the driving field at the leading order. We apply the method to engineer the effects of curved background space. We find that the imprint of curvilinear geometry modifies the electronic properties, such as LDOS, significantly. We suggest that this method shall be useful in studying the response of various properties of such systems to non-trivial geometry without requiring any actual physical deformations.