CONSTRUCTION AND CHARACTERIZATION OF FLOQUET TOPOLOGICAL INSULATORS AND WEYL SEMIMETALS

Abstract

Topological phases of matter have gained unprecedented attention after the discovery of intriguing physical phenomena such as the Quantum (spin) Hall effect. These phases of matter are characterized by some nonzero invariants connected to the topological structures, such as Berry curvature or Weyl nodes, to name a few. Materials that possess such robust properties may serve as promising candidates for the construction of devices that show resistance to imperfections. In this thesis, we investigate periodically driven phases of topological insulators and Weyl semimetals. We first considered a two-dimensional system that can exhibit an arbitrary number of counterpropagating edge states at its edges. The bulk boundary correspondence is then established by a combination of longitudinal conductance and dynamical winding invariant. Next, we study the dynamical characterization of gapless Weyl semimetal phases. In this regard, we show that the dynamical winding invariant over a closed two-dimensional surface captures the net chirality of Weyl nodes enclosed by that surface. In addition to this, we show that periodic driving can induce rich Weyl semimetal phases such as hybrid multi-Weyl semimetals and higher-order Weyl semimetals where Weyl nodes appear at the interface of different topological trivial and nontrivial phases.