Collapse of Spin-Splitting in the Quantum Hall Effect

TL;DR

This paper investigates the collapse of spin-splitting in the quantum Hall effect at low magnetic fields, attributing it to disorder disrupting exchange enhancement, and models this as a phase transition with explicit sample-dependent predictions.

Contribution

It introduces a mean-field model explaining the collapse of spin-splitting as a second-order phase transition influenced by disorder and provides explicit formulas for critical parameters based on sample properties.

Findings

Spin-splitting collapse occurs at a critical Landau level index $N_c$.

The transition is modeled as a second-order phase transition.

Explicit expression for $N_c$ in terms of sample parameters.

Abstract

It is known experimentally that at not very large filling factors $\nu$ the quantum Hall conductivity peaks corresponding to the same Landau level number $N$ and two different spin orientations are well separated. These peaks occur at half-integer filling factors $\nu = 2 N + 1/2$ and $\nu = 2 N + 3/2$ so that the distance between them $\delta\nu$ is unity. As $\nu$ increases $\delta\nu$ shrinks. Near certain $N = N_c$ two peaks abruptly merge into a single peak at $\nu = 2N + 1$. We argue that this collapse of the spin-splitting at low magnetic fields is attributed to the disorder-induced destruction of the exchange enhancement of the electron $g$-factor. We use the mean-field approach to show that in the limit of zero Zeeman energy $\delta\nu$ experiences a second-order phase transition as a function of the magnetic field. We give explicit expressions for $N_c$ in terms of a sample's parameters. For example, we predict that for high-mobility heterostructures $N_c = 0.9 d n^{5/6} n_i^{-1/3},$ where $d$ is the spacer width, $n$ is the density of the two-dimensional electron gas, and $n_i$ is the two-dimensional density of randomly situated remote donors.