TOPOLOGICAL PHENOMENA IN TWO AND THREE DIMENSIONAL SYSTEMS: AN INTERPLAY AMONG PERIODIC DRIVING, QUANTUM COHERENCE AND DISORDER

Abstract

Topology played a crucial role in enhancing our understanding in many areas of physics. Initially, I will discuss about interband coherence induced correction to Thouless pumping. In Thouless pump, the charge transport in a one-dimensional insulator over an adiabatic cycle is topologically quantized. For nonequilibrium initial states, however, interband coherence will induce a previously unknown contribution to Thouless pumping. By examining adiabatic pumping both theoretically and numerically, I will discuss the importance of the interband coherence in Thouless pumping.

Further, I will discuss topological features associated with periodically driven Weyl semimetal. I will demonstrate many new Floquet band touching points at Floquet quasienergies zero and pi will start to appear. and show that edge states analogous to Fermi arcs in static Weyl semimetal systems are observed in these systems. Also, I will argue that by designing an adiabatic pumping scheme, the chirality of the Floquet-band Weyl points can be manifested.

Finally, I will discuss about the effect of disorder on the topological phases. Because of the periodic kicking, Qi-Wu-Zhang model exhibits new topological phases compared to the static system. I will discuss how the topological phases transit between different topological phases due to the impact of the disorder.