Three-dimensional two-band Floquet topological insulator with Z2 index

Abstract

We present a class of three dimensional (3D) two-band Floquet topological insulators constructed from two-dimensional Floquet topological insulators with a Z topological index. It is shown that the 3D two-band Floquet topological insulator has a Z2 topological index, whose value can be obtained by numerical calculations or by using a relation to the winding number. The classification of the 3D Z2 Floquet topological insulator, however, cannot be attributed to the stable homotopy groups. Thus, it is an example outside the proposed K-theory classifications of Floquet topological insulators. We also analyze the edge modes of the 3D Z2 Floquet topological insulator and find the parity of the number of edge modes reflects the bulk Z2 index.

Realizing Hopf Insulators in Dipolar Spin Systems

“…Hopf map [15,19]. Despite a recent resurgence of interest in HIs [15][16][17][18][20][21][22][23][24][25][26][27][28][29][30][31][32], fundamental difficulties have led to only a few proposals for their physical implementation [16].…”

“…There has recently been a burst of theoretical interest in Hopf insulators and their possible extensions, including non-hermitian generalizations [31], the survival of topology under quantum quenches [32], crystal symmetries [18,27], and generalizations to periodically-driven Floquet systems [28,30]. These ideas motivate the possibility of experimentally realizing the Hopf insulator phase, which would allow one to test the above predictions, and, more tantalizingly, could probe regimes of Hopf insulating physics that are much harder for theory to handle.…”

Quench dynamics of Hopf insulators

“…[29]. This technique first embeds the SU(2) unitary loop operator into an extended three-band unitary space U(3) [59,60]…”

Floquet higher-order Weyl and nexus semimetals

“…Given that even an otherwise topologically trivial system can be converted into a topological nontrivial phase via periodic driving [1,14], nonequilibrium strategies that utilize the time dimension significantly expand the domain of topological phases and at the same time lead us to many possible applications of topological matter in photonics [5,[15][16][17][18][19], acoustics [20], quantum information etc [21,22]. Three-dimensional (3D) periodically driven (Floquet) topological phases include Floquet Weyl semimetals [10,[23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40] and Floquet topological insulators [41][42][43]. Floquet Weyl semimetals may support a single Weyl point, thus constituting an excellent platform to investigate the chiral magnetic effect [37,38].…”

“…Floquet Weyl semimetals may support a single Weyl point, thus constituting an excellent platform to investigate the chiral magnetic effect [37,38]. The so-called Floquet Hopf insulator, whose full topological description requires one Z type Hopf linking number and another intrinsically dynamic Z 2 invariant [42,43], is another fascinating example that has advanced the notion of topological insulators.…”