Driving protocol for a Floquet topological phase without static counterpart

Abstract

Periodically driven systems play a prominent role in optical lattices. In these ultracold atomic systems, driving is used to create a variety of interesting behaviours, of which an important example is provided by topological states of matter. Such Floquet topological phases have a richer classification than their equilibrium counterparts. Although there exist analogues of the equilibrium topological phases that are characterised by a Chern number, the corresponding Hall conductivity, and protected edge states, there is an additional possibility. This is a phase that has a vanishing Chern number and no Hall conductivity, but nevertheless hosts anomalous topological edge states (Rudner et al (2013 Phys. Rev. X 3 031005)). Due to experimental difficulties associated with the observation of such a phase, it has not been experimentally realised in optical lattices so far. In this paper, we show that optical lattices prove to be a good candidate for its realisation and observation, because they can be driven in a controlled manner. Specifically, we present a simple shaking protocol that serves to realise this special Floquet phase, discuss the specific properties that it has, and propose a method to experimentally detect this fascinating topological phase that has no counterpart in equilibrium systems.

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

“…N γ = N + . Using (21) the path from −π → π gives the winding number ν. Since f k is periodic in k → k + 2π, the two contributions from π → π + i∞ and −π + i∞ → −π cancel each other.…”

Strongly Disordered Floquet Topological Systems

“…For Floquet systems, the latter is sometimes associated to a transport observable, and usually coincides with the bulk index (whose physical meaning is sometimes associated to magnetization, see below) through the celebrated bulk-edge correspondence [24,25,15]. Originally designed to induce topological properties on a trivial sample through the periodic driving [20], Floquet topological systems have recently become a topic of intense study when it was realized that this driving also allowed to engineer new topological phases of matter that have no static counterpart [24]; some proposals for experimental observation of these phases in cold atoms were recently suggested [19,22].…”

Chiral flow in one-dimensional Floquet topological insulators

“…In particular, driven systems of free fermions have been found to form dynamical analogues of TIs known as Floquet topological insulators (FTIs) [17][18][19][20][21][22][23][24][25][26][27][28][29][30], and several of these phases have now been realised experimentally [31][32][33][34][35][36]. FTI phases exhibit bulk-boundary correspondence in a similar vein to their static counterparts, although the resulting edge modes can be very different: Remarkably, dynamical edge modes analogous to those of the QHE or TIs can exist even if the bulk bands are topologically trivial [19,37]. In this way, bulk-boundary correspondences for driven systems are far richer than in static systems, and in most cases remain unexplored.…”