Spin Bottlenecks in the Quantum Hall Regim

TL;DR

This paper develops a theory for time-dependent tunneling between a metal and a partially spin-polarized 2DES in the quantum Hall regime, revealing how spin dynamics influence leakage currents and tunneling rates.

Contribution

It introduces a model linking spin-dependent tunneling conductances and quantum corrections to the electrostatic capacitance with leakage current behavior in quantum Hall systems.

Findings

Leakage current is a sum of two exponential contributions.

The ratio of fast to slow leakage rates is predicted to be (2K+1)^2.

The model applies to high-mobility, homogeneous 2DES at Landau level filling factor ν=1.

Abstract

We present a theory of time-dependent tunneling between a metal and a partially spin-polarized two-dimensional electron system (2DES). We find that the leakage current which flows to screen an electric field between the metal and the 2DES is the sum of two exponential contributions whose relative weights depend on spin-dependent tunneling conductances, on quantum corrections to the electrostatic capacitance of the tunnel junction, and on the rate at which the 2DES spin-polarization approaches equilibrium. For high-mobility and homogeneous 2DES's at Landau level filling factor $\nu=1$, we predict a ratio of the fast and slow leakage rates equal to $(2K+1)^2$ where $K$ is the number of reversed spins in the skyrmionic elementary charged excitations.