Topological Floquet Phases in Driven Coupled Rashba Nanowires

Abstract

We consider periodically driven arrays of weakly coupled wires with conduction and valence bands of Rashba type and study the resulting Floquet states. This nonequilibrium system can be tuned into nontrivial phases such as topological insulators, Weyl semimetals, and dispersionless zero-energy edge mode regimes. In the presence of strong electron-electron interactions, we generalize these regimes to the fractional case, where elementary excitations have fractional charges e=m with m being an odd integer. DOI: 10.1103/PhysRevLett.116.176401 Introduction.-Topological effects in condensed matter systems have attracted attention for many years. From the quantum Hall effect over topological insulators (TIs) [1][2][3][4][5][6][7][8][9][10][11][12] and Weyl semimetals [13][14][15][16][17], to Majorana fermions and parafermions [39][40][41][42][43][44][45][46][47][48][49], the interest is driven both by fundamental physics and the promise for topological quantum computation. Despite the many proposals for topological systems, the search for the most optimal material still continues unabated.While most studies were focused on static structures, it has recently been proposed to extend topological phases to nonequilibrium systems, described by Floquet states . Remarkably, this approach no longer relies on given material properties, such as strong spin orbit interactions (SOIs), typically necessary for reaching topological regimes, but instead allows one to turn initially nontopological materials such as graphene [50] and non-bandinverted semiconducting wells into TIs [52] by applying an external driving field.An even bigger challenge is to describe topological effects that involve fractional excitations. This requires the presence of strong electron-electron interactions. However, given the difficulties in the search for conventional TIs, it would be even more surprising to expect such phases to occur naturally. Moreover, even if they existed, twodimensional (2D) systems with electron-electron interactions are difficult to describe analytically and often progress can come only from numerics [61].Here, we circumvent this difficulty by considering strongly anisotropic 2D systems [71][72][73][74] formed by weakly coupled Rashba wires (see Fig. 1), where each of them can be treated as a one-dimensional Luttinger liquid by bosonization [75][76][77][78][79][80][81][82][83][84][85][86]. This will allow us to introduce the Floquet version not only of TIs but also of Weyl semimetals in driven 2D systems. Importantly, in this way we can also address fractional regimes and are able to obtain the Floquet version of fractional TIs and Weyl semimetals.

Helical Floquet Channels in 1D Lattices

“…1(a)]. Harnessing the unique properties of periodically driven quantum systems [12][13][14][15][16][17], here we show how these limitations can be circumvented: we find perfect spin-momentum locking in the stroboscopic dynamics of a periodically driven 1D lattice model. While conventional helical edge states require a time reversal symmetric topological 2D bulk [19], the spin-momentum locking in our 1D setting stems from topological properties in combined time-momentum (Floquet) space [see Fig.…”

Topological invariants for Floquet-Bloch systems with chiral, time-reversal, or particle-hole symmetry

“…More recently, unconventional topological phases in periodically driven systems [7][8][9][10][11][12] have moved into focus. Driving allows for non-trivial topological phases even if each individual Floquet band is topologically trivial.…”

Effects of local periodic driving on transport and generation of bound states

“…57. It is known that interactions can lead to a variety of topological phases (some of which have elementary excitations with fractional charges) in driven Rashba nanowires 58,59 , and to a chaotic and topologically trivial phase in the periodically driven Kitaev model 60 . The effects of periodic driving on the stability of a bosonic fractional Chern insulator has been investigated 61 .…”