Spin relaxation in quantum Hall systems

TL;DR

This paper investigates spin relaxation mechanisms in a two-dimensional electron gas near filling factor one under strong magnetic fields, deriving nonlinear kinetic equations that reveal power-law relaxation at zero temperature.

Contribution

It introduces a new set of nonlinear kinetic equations for spin density that replace traditional Bloch equations in quantum Hall systems.

Findings

At zero temperature, spin relaxation follows a power-law decay.

The relaxation behavior depends on the filling factor and phonon bath temperature.

Conventional exponential relaxation is replaced by power-law decay at zero temperature.

Abstract

We study the spin relaxation in an interacting two--dimensional electron gas in a strong magnetic field for the case that the electron density is close to filling just one Landau sub--level of one spin projection, i.e., for filling factor near one. Assuming the relaxation to be caused by scattering with phonons, we derive the kinetic equations for the electron's spin--density which replace the Bloch equations in our case. These equations are non--linear and their solution depends crucially on the filling factor and on the temperature of the phonon bath. In the limit of zero temperature and for filling factor 1, the solution relaxes asymptotically with a power law inversely proportional to time, instead of following the conventional exponential behavior.