Phase Transitions in Dissipative Quantum Transport and Mesoscopic Nuclear Spin Pumping

TL;DR

This paper explores topological phase transitions in dissipative quantum systems, linking non-Hermitian quantum walks to nuclear spin pumping in quantum dots, revealing a transition driven by spin-orbit and hyperfine interactions that affects nuclear polarization and current.

Contribution

It establishes a novel connection between topological phase transitions in non-Hermitian quantum walks and nuclear spin pumping phenomena in double quantum dots, highlighting the role of spin-orbit and hyperfine interactions.

Findings

Transition occurs when spin-orbit coupling exceeds hyperfine coupling.

Nuclear spin pumping is suppressed beyond the transition point.

Dark states cause reduced current below the transition.

Abstract

Topological phase transitions can occur in the dissipative dynamics of a quantum system when the ratio of matrix elements for competing transport channels is varied. Here we establish a relation between such behavior in a class of non-Hermitian quantum walk problems [M. S. Rudner and L. S. Levitov, Phys. Rev. Lett. 102, 065703 (2009)] and nuclear spin pumping in double quantum dots, which is mediated by the decay of a spin-blockaded electron triplet state in the presence of spin-orbit and hyperfine interactions. The transition occurs when the strength of spin-orbit coupling exceeds the strength of the net hyperfine coupling, and results in the complete suppression of nuclear spin pumping. Below the transition point, nuclear pumping is accompanied by a strong reduction in current due to the presence of non-decaying "dark states" in this regime. Due to its topological character, the transition is expected to be robust against dephasing of the electronic degrees of freedom.