Valley Stoner Instability of the Composite Fermi Sea

TL;DR

This paper investigates a quantum phase transition in a two-component electron system at half filling, revealing a Stoner-like transition to a valley-polarized state driven by mass anisotropy in AlAs quantum wells.

Contribution

It introduces the concept of a valley Stoner instability in the composite Fermi sea and provides trial wavefunctions capturing the transition from two-component to single-component states.

Findings

Identifies a critical mass anisotropy of ~7 for the phase transition.

Proposes a Stoner transition mechanism for valley polarization.

Provides experimental evidence for Stoner magnetism in Jain states near ν=1/2.

Abstract

We study two-component electrons in the lowest Landau level at total filling factor $\nu _T=1/2$ with anisotropic mass tensors and principal axes rotated by $\pi/2$ as realized in Aluminum Arsenide (AlAs) quantum wells. Combining exact diagonalization and the density matrix renormalization group we demonstrate that the system undergoes a quantum phase transition from a gapless state in which both flavors are equally populated to another gapless state in which all the electrons spontaneously polarize into a single flavor beyond a critical mass anisotropy of {\bf $m_x/m_y \sim 7$}. We propose that this phase transition is a form of itinerant Stoner transition between a two-component and a single-component composite fermi sea states and describe a set of trial wavefunctions which successfully capture the quantum numbers and shell filling effects in finite size systems as well as providing a physical picture for the energetics of these states. Our estimates indicate that the composite Fermi sea of AlAs is the analog of an itinerant Stoner magnet with a finite spontaneous valley polarization. We pinpoint experimental evidence indicating the presence of Stoner magnetism in the Jain states surrounding $\nu=1/2$.