Valley Stoner instability of the composite Fermi sea

Abstract

We study two-component electrons in the lowest Landau level at total filling factor ν[subscript T] = 1/2 with anisotropic mass tensors and principal axes rotated by π/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 m[subscript x]/m[subscript y]∼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 wave functions 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 ν = 1/2.