Chiral one-dimensional Floquet topological insulators beyond the rotating wave approximation

Abstract

We study one-dimensional (1D) Floquet topological insulators with chiral symmetry going beyond the standard rotating wave approximation. The occurrence of many anticrossings between Floquet replicas leads to a dramatic extension of phase diagram regions with stable topological edge states (TESs). We present an explicit construction of all TESs in terms of a truncated Floquet Hamiltonian in frequency space, prove the bulk-boundary correspondence, and analyze the stability of the TESs in terms of their localization lengths. We propose experimental tests of our predictions in curved bilayer graphene. arXiv:1811.12062v1 [cond-mat.mes-hall]

Colloquium: Nonthermal pathways to ultrafast control in quantum materials

“…In this context, twistronics-Moiré potential engineering by twisting adjacent layers-is set to play a crucial role. The twist angle provides a critical handle on designing electronic and structural properties which can be geared with great flexibility (Kennes et al, 2021). Crucially, the relevant kinetic energy scales of the Moiré superlattice can be orders of magnitude smaller than in the bulk material, suggesting that external nonequilibrium perturbations can have an outsized effect in determining electronic phases.…”

“…Crucially, the relevant kinetic energy scales of the Moiré superlattice can be orders of magnitude smaller than in the bulk material, suggesting that external nonequilibrium perturbations can have an outsized effect in determining electronic phases. Combining ultrafast light-matter interaction with twist control of such band structures hence suggests a particularly promising route towards nonequilibrium functionalization, with first explorations already under way (Kennes et al, 2021;Rodriguez-Vega et al, 2020;Topp et al, 2019). These efforts should of course be complemented by more traditional avenues of materials science, such as material synthesis tailored specifically to questions relevant to nonequilibrium control.…”

“…9(b)]. This insight results in the notion of sidebands emerging under periodic driving, which can be used to alter the physical properties of a system dramatically (Kennes et al, 2019b;Oka and Aoki, 2009;Rudner and Lindner, 2020) (Fig. 10).…”

“…These many-body interactions are described through the many-body self-energy. Notable approximations to calculate the self-energy include the so-called GW approximation for screened interactions (Aryasetiawan and Gunnarsson, 1998;Thygesen and Rubio, 2007), nonequilibrium dynamical mean-field theory (DMFT) for strongly correlated systems, including Mott insulators with mainly local self-energies (Aoki et al, 2014;Freericks et al, 2006;Tsuji et al, 2008), and the realtime functional renormalization group (FRG) approach (Kennes et al, 2012). In a nonequilibrium setup these approximation schemes are more difficult to handle than in equilibrium because time-translational invariance cannot be exploited and, in general, two time variables instead of one energy variable must be kept.…”

Floquet Engineering Topological Many-Body Localized Systems

“…Most of the proposals on how topology, disorder, and Floquet engineering can be exploited in the design of quantum devices [14][15][16][17][18][19][20][21][22][23][24][25] either concentrate on one or two of these phenomena separately or use special models. Floquet engineering has been suggested as a route to realizing effective topological systems [26][27][28][29][30][31][32], but those studies neglect two-body interactions and thus ignore the fact that a generic driven system will heat up [33]. Heating can be efficiently suppressed by many-body localization [34,35], but the topological properties of a clean system are normally lost in the presence of strong disorder [36][37][38].…”