Nonreciprocal electrical transport in linear systems with balanced gain and loss in the bulk

TL;DR

This paper demonstrates that linear quantum wires with balanced gain and loss exhibit nonreciprocal electrical transport when parity symmetry is broken, with inelastic scattering being essential for this effect.

Contribution

It reveals that nonreciprocal transport arises in linear systems with balanced gain and loss, highlighting the role of inelastic scattering and parity-breaking in such phenomena.

Findings

Nonreciprocal current occurs when parity symmetry is broken.

Inelastic scattering is essential for nonreciprocity.

Nonreciprocity oscillates with wire length and can vanish at specific lengths.

Abstract

We investigate electrical transport in a quantum wire of $N$ sites connected to an equal number $(N_i/2)$ of sources and drains of charges in bulk. Each source and drain injects and extracts charges at the same rate, respectively. We show that the linear-response electrical current is nonreciprocal in such a system when the arrangement of sources and drains breaks the system's parity. We prove that inelastic scattering is essential for nonreciprocity in this system. For this, we invoke a master equation description of classical charge transport in a similar system. The nonreciprocal current in quantum wire matches that in the classical model for $N_i/N \sim 1$, generating a finite scattering length much smaller than the length of the wire. The nonreciprocity in the quantum wire oscillates with wire length when $N_i/N \ll 1$, and it can vanish at specific lengths.