Nonequilibrium phase transition in transport through a driven quantum point contact

TL;DR

This paper investigates how a driven quantum point contact can undergo a nonequilibrium phase transition where heating ceases above a critical frequency, enabling frequency-controlled quantum switching.

Contribution

It demonstrates a nonequilibrium phase transition in driven QPCs, showing heating rate vanishes above a critical frequency and revealing potential for quantum switching applications.

Findings

Heating rate vanishes when driving frequency exceeds the chain bandwidth.

The phase transition is analytically established for specific QPCs and numerically verified for generic cases.

Certain QPCs exhibit zero current above the critical frequency despite bias, acting as quantum switches.

Abstract

We study transport of noninteracting fermions through a periodically driven quantum point contact (QPC) connecting two tight-binding chains. Initially, each chain is prepared in its own equilibrium state, generally with a bias in chemical potentials and temperatures. We examine the heating rate (or, alternatively, energy increase per cycle) in the nonequilibrium time-periodic steady state established after initial transient dynamics. We find that the heating rate vanishes identically when the driving frequency exceeds the bandwidth of the chain. We first establish this fact for a particular type of QPC where the heating rate can be calculated analytically. Then we verify numerically that this nonequilibrium phase transition is present for a generic QPC. Finally, we derive this effect perturbatively in leading order for cases when the QPC Hamiltonian can be considered as a small perturbation. Strikingly, we discover that for certain QPCs the current averaged over the driving cycle also vanishes above the critical frequency, despite a persistent bias. This shows that a driven QPC can act as a frequency-controlled quantum switch.