Floquet topological phases with high Chern numbers in a periodically driven extended Su–Schrieffer–Heeger model

Abstract

The high Chern number phases with the Chern number |C| > 1 are observed in this study of a periodically driven extended Su-Schrieffer-Heeger (E-SSH) model with a cyclic parameter. Besides the standard intra-dimer and the nearest-neighbor (NN) inter-dimer hopping of the SSH model, an additional next-nearest-neighbor (NNN) hopping is considered in the E-SSH model. The cyclic parameter, which plays the role of a synthetic dimension, is invoked as a modulation of the hopping strengths. A rigorous analysis of different phase diagrams has shown multiple Floquet topological phase transitions among the high Chern number phases. These phase transitions can be controlled by the strength and frequency of the periodic driving. Instead of applying perturbation theory, the whole analysis is done by Floquet replica technique. This gives a freedom to study high as well as low-frequency effects on the system by considering less or more number of photon sectors. This system can be experimentally realized through a pulse sequence scheme in the optical lattice setup.

Engineering topological phases of any winding and Chern numbers in extended Su–Schrieffer–Heeger models

“…Investigation on this model has been carried out under periodic drive in order to find Floquet topological phase [30]. The Hamiltonian with this parametrization preserve the inversion symmetry in terms of two variables k and θ, since…”

“…In the two-band Haldane model, topological phase is defined by C = ±1, values of opposite signs for the two different energy bands. Realization of topological phase for higher values of Cs continues thereafter by either invoking further neighbour hopping terms 17,18 or imposing periodic drive 19,20 , etc. Experimental realization of QAH phases tunable up to C = ±5 has been reported recently 21 .…”

Controllable Floquet topological phases in the magnetic ladder system

“…In 1D systems, Floquet TIs have exhibited rich topological phases that may differ significantly from their undriven counterparts. For instance, the 1D extended Su-Schrieffer-Heeger (SSH) model has been shown to generate higher Chern numbers [28,29], and singular phenomena, such as anomalous edge states [30,31] between energy bands with zero Chern number, challenging our conventional understanding of TIs. Given that the electric field is typically introduced in a single direction, Floquet dynamics in 1D TIs have been extensively explored, including systems such as the SSH chain, the Kitaev chain with p-wave superconductivity [32,33], and the 1D Creutz ladder model [34,35].…”

Topological phase transition in commensurate multi-frequency Floquet Su-Schrieffer-Heeger model

“…We employ the commensurate frequency framework developed in [33] to express the MF Floquet formalism using a single period, and apply this drive to The Su-Schreiffer-Heeger (SSH) model. Note that single frequency driven SSH variations have already generated great interest in the field [37][38][39][40]. In the adiabatic driving scheme, we map the commensurate drives to the frequency space, resulting in the emergence of new couplings.…”