Floquet topological phase transitions in a kicked Haldane-Chern insulator

Abstract

We consider a periodically δ-kicked Haldane type Chern insulator with the kicking applied in theẑ direction. This is known to behave as an inversion symmetry breaking perturbation, since it introduces a time-dependent staggered sub-lattice potential. We study here the effects of such driving on the topological phase diagram of the original Haldane model of a Hall effect in the absence of a net magnetic field. The resultant Floquet band topology is again that of a Chern insulator with the driving parameters, frequency and amplitude, influencing the inversion breaking mass M of the undriven Haldane model. A family of such, periodically related, 'Semenoff masses' is observed to occur which support a periodic repetition of Haldane like phase diagrams along the inversion breaking axis of the phase plots. Out of these it is possible to identify two in-equivalent masses in the reduced zone scheme of the Floquet quasienergies, which form the centres of two inequivalent phase diagrams. Further, variation in the driving amplitude's magnitude alone is shown to effect the topological properties by linearly shifting the phase diagram of the driven model about the position of the undriven case. A phenomenon that allows the study of Floquet topological phase transitions in the system. Finally, we also discuss some issues regarding the modifications to Haldane's condition for preventing band overlaps at the Dirac point touchings in the Brillouin zone, in the presence of kicking. * tridev.mishra@pilani.bits-pilani.ac.in

Floquet dynamical quantum phase transitions in transverse XY spin chains under periodic kickings

“…[50] As we know, δ -function periodic kicking is another special periodic driving and may provide an interesting analytical solvable model, which may also change the system and induce new phenomena, for instance, periodic behavior may result in a new phase diagram in a topological system, changes the critical point of the quantum phase transition, etc. [55][56][57][58] It is an interesting topic to consider effect of periodic kickings in Floquet systems with DQPTs.…”

Floquet engineering of low-energy dispersions and dynamical localization in a periodically kicked three-band system

“…The impact of such driving protocol has far reaching consequences. This type of driving has been used to study a wide range of spectacular phenomena including non-equilibrium phase transition in a Dicke Model [85], local-ization effect in a chain of hard core bosons [86], semimetalic phases in Harper models [87], edge modes in quantum Hall systems [88], low energy band engineering in graphene [89], Majorana edge mode in one dimensional systems [90] as well as in Kitaev model [91] on a honeycomb lattice, topological properties of Chern insulator [92], topological phase transition in Haldane-Chern insulator [93], generation of higher order topological insulator from a lower order topological insulating phase [94] and many more. Another interesting effect of periodic δ-function driving on the quantum systems is to achieve dynamical localization of the quasiparticles.…”

Chiral Luttinger liquids in graphene tuned by irradiation

“…Floquet engineering [12][13][14][15][16][17][18][19] or the generation of new Hamiltonians that are not present in static systems but emerge in driven systems, have recently become a very important field of study. In the case of graphene, it has been realised that the possibility of tuning the band gap by shining light greatly increases the potential of applications and there has been considerable work [20][21][22][23][24][25][26][27][28][29] on new topological phases obtained by shining light on graphene, as well as bilayer graphene [30][31][32][33] . Recent experimental observation of anomalous Hall effect in irradiated graphene confirms the Floquet bands and their non-trivial Berry curvature 34 .…”