# Topology by Dissipation: Transport properties

## TL;DR

This paper investigates how engineered dissipation can create topological 2D Chern insulator states, analyzing their transport properties and revealing differences from equilibrium systems, including conditions for quantized Hall conductance.

## Contribution

It demonstrates the emergence of topological phases via dissipation without Hamiltonian tuning and explores their transport properties using open quantum systems tools.

## Key findings

- Dissipative engineering can produce topological states efficiently.
- The relation between Chern number and Hall conductance can be broken in non-equilibrium.
- Conditions for quantized Hall conductance are identified.

## Abstract

Topological phases of matter are the center of much current interest, with promising potential applications in, e.g., topologically-protected transport and quantum computing. Traditionally such states are prepared by tuning the system Hamiltonian while coupling it to a generic bath at very low temperatures; This approach is often ineffective, especially in cold-atom systems. It was recently shown that topological phases can emerge much more efficiently even in the absence of a Hamiltonian, by properly engineering the interaction of the system with its environment, to directly drive the system into the desired state. Here we concentrate on dissipatively-induced 2D Chern insulator (lattice quantum Hall) states. We employ open quantum systems tools to explore their transport properties, such as persistent currents and the conductance in the steady state, in the presence of various Hamiltonians. We find that, in contrast with equilibrium systems, the usual relation between the Chern topological number and the Hall conductance is broken. We explore the intriguing edge behaviors and elucidate under which conditions the Hall conductance is quantized.