Nuclear spin polaron-formation: anisotropy effects and quantum phase transition

TL;DR

This paper theoretically investigates the formation of nuclear-spin polarons in semiconductor nanosystems, highlighting the effects of anisotropy and identifying a quantum phase transition between two polaron states.

Contribution

It develops a Lindblad equation framework for anisotropic hyperfine interactions and characterizes the quantum phase transition in nuclear-spin polaron formation.

Findings

Identification of two distinct polaron states separated by a quantum phase transition.

Correlation of polaron formation with low-temperature quantum fluctuations.

Predictions for spin-noise measurements to observe the transition.

Abstract

We study theoretically the formation of the nuclear-spin polaron state in semiconductor nanosystems within the Lindblad equation approach. To this end, we derive a general Lindblad equation for the density operator that complies with the symmetry of the system Hamiltonian and address the nuclear-spin polaron formation for localized charge carriers subject to an arbitrarily anisotropic hyperfine interaction when optically cooling the nuclei. The steady-state solution of the density matrix for an anisotropic central spin model is presented as a function of the electron and nuclear spin bath temperature. Results for the electron-nuclear spin correlator as well as data for the nuclear spin distribution function serve as a measure of spin-entanglement. The features in both of them clearly indicate the formation of the nuclear polaron state at low temperatures where the crossover regime coincides with an enhancement of quantum fluctuations and agrees with the mean-field prediction of the critical temperature line. We can identify two distinct polaron states dependent upon the hyperfine anisotropy which are separated by a quantum phase transition at the isotropic point. These states are reflected in the temporal spin auto-correlation functions accessible in experiment via spin-noise measurements.