Determination of the Fermi Contour and Spin-polarization of $\nu=3/2$ Composite Fermions via Ballistic Commensurability Measurements

TL;DR

This study uses ballistic commensurability measurements to analyze the Fermi contour and spin polarization of $ u=3/2$ composite fermions, revealing their shape, size, and spin state dependence on quantum well width and parallel magnetic field.

Contribution

It provides the first quantitative analysis of the Fermi contour shape and spin polarization of $ u=3/2$ composite fermions using ballistic transport measurements.

Findings

CFs are formed by minority carriers in the upper spin state.

Wider quantum wells increase CF spin polarization.

Parallel magnetic fields distort the CF Fermi contour and enhance spin polarization.

Abstract

We report ballistic transport commensurability minima in the magnetoresistance of $\nu =3/2$ composite fermions (CFs). The CFs are formed in high-quality two-dimensional electron systems confined to wide GaAs quantum wells and subjected to an in-plane, unidirectional periodic potential modulation. We observe a slight asymmetry of the CF commensurability positions with respect to $\nu=3/2$, which we explain quantitatively by comparing three CF density models and concluding that the $\nu=3/2$ CFs are likely formed by the minority carriers in the upper energy spin state of the lowest Landau level. Our data also allow us to probe the shape and size of the CF Fermi contour. At a fixed electron density of $\simeq 1.8 \times 10^{11}$ cm$^{-2}$, as the quantum well width increases from 30 to 60 nm, the CFs show increasing spin-polarization. We attribute this to the enhancement of the Zeeman energy relative to the Coulomb energy in wider wells where the latter is softened because of the larger electron layer thickness. The application of an additional parallel magnetic field ($B_{||}$) leads to a significant distortion of the CF Fermi contour as $B_{||}$ couples to the CFs' out-of-plane orbital motion. The distortion is much more severe compared to the $\nu=1/2$ CF case at comparable $B_{||}$. Moreover, the applied $B_{||}$ further spin-polarizes the $\nu=3/2$ CFs as deduced from the positions of the commensurability minima.