Driven quantum many-body systems and out-of-equilibrium topology

TL;DR

This review explores driven and out-of-equilibrium topological quantum systems, focusing on their dynamical preparation, effects of periodic driving, and transport phenomena in various topological phases.

Contribution

It provides a comprehensive overview of recent developments in driven topological systems, including dynamical state preparation and transport in complex topological materials.

Findings

Periodic driving can induce topological phase transitions.

Majorana modes influence transport properties in Kitaev chains.

Hybridization affects surface state transport in topological insulators.

Abstract

In this review we present some of the work done in India in the area of driven and out-of-equilibrium systems with topological phases. After presenting some well-known examples of topological systems in one and two dimensions, we discuss the effects of periodic driving in some of them. We discuss the unitary as well as the non-unitary dynamical preparation of topologically non-trivial states in one and two dimensional systems. We then discuss the effects of Majorana end modes on transport through a Kitaev chain and a junction of three Kitaev chains. Transport through the surface states of a three-dimensional topological insulator is discussed. The effects of hybridization between the top and bottom surfaces and the application of electromagnetic radiation on a strip-like region on the top surface are described. Two unusual topological systems are mentioned briefly, namely, a spin system on a kagome lattice and a Josephson junction of three superconducting wires. We have also included a pedagogical discussion on topology and topological invariants in the appendices, where the connection between topological properties and the intrinsic geometry of quantum states is also elucidated.