# Emergent chirality in multi-lead Luttinger-liquid junctions out of equilibrium

## TL;DR

This paper investigates how nonequilibrium conditions induce emergent chirality in multi-lead Luttinger-liquid junctions, revealing mechanisms that generate current asymmetries and rectification effects without magnetic fields or explicit symmetry breaking.

## Contribution

It uncovers two novel mechanisms of emergent chirality in biased Luttinger-liquid junctions, linked to effective magnetic flux and parity asymmetry, under nonequilibrium conditions.

## Key findings

- Bias voltage induces a tip current proportional to |V|.
- Emergent effective magnetic flux breaks time-reversal symmetry.
- Parity-breaking asymmetry leads to rectification effects.

## Abstract

We study charge transport through $N$-lead junctions ($N\geq 3$) of spinless Luttinger liquid wires with bias voltages applied to Fermi-liquid reservoirs. In particular, we consider a Y junction, which is a setup characteristic of the tunneling experiment. In this setup, the strength of electron-electron interactions in one of the arms ("tunneling tip") is different from that in the other two arms (which form together the "main wire"). For a generic single-particle $S$ matrix of the junction, we find that the bias voltage $V$ applied---even symmetrically---to the main wire generates a current proportional to $|V|$ in the tip wire. We identify two mechanisms of this nonequilibrium-induced "emergent chirality" in a setup characterized by the time-reversal and parity symmetric Hamiltonian of the junction. These are: (i) the emergence of an effective magnetic flux, which breaks time-reversal symmetry, and (ii) the emergence of parity-breaking asymmetry of the setup, both proportional to the interaction strength and the sign of the voltage. The current in the tip wire generated by mechanism (i) is reminiscent of the Hall current in the linear response of a system the Hamiltonian of which breaks time-reversal symmetry; however, in the absence of any magnetic field or a local magnetic moment. Similarly, mechanism (ii) can be thought of as an emergent "photogalvanic effect"; however, in the presence of inversion symmetry within the main wire. The nonequilibrium chirality implies a rectification of the current in the tip when the main wire is biased by $\it ac$ voltage.