Valley Stoner Instability of the Composite Fermi Sea

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 $\nu =1/2$.

7 pages, 4 figures

References in corpus (20)

• Fermi liquid instabilities in the spin channel
• Density Matrix Renormalization Group Study of Incompressible Fractional Quantum Hall States
• Composite Fermions and Broken Symmetries in Graphene
• Time-Reversal Symmetry Breaking and Spontaneous Anomalous Hall Effect in Fermi Fluids
• Spin polarization of the $\nu =5/2$ quantum Hall state
• Nematic Valley Ordering in Quantum Hall Systems
• Composite fermi liquids in the lowest Landau level
• Transference of Transport Anisotropy to Composite Fermions
• Entanglement entropy of the $\nu =1/2$ composite fermion non-Fermi liquid state
• Transference of Fermi Contour Anisotropy to Composite Fermions
• Composite Fermions on a Torus
• Composite fermion valley polarization energies: Evidence for particle-hole asymmetry
• Contrast between spin and valley degrees of freedom
• Quantum Hall ferroelectrics and nematics in multivalley systems
• Numerical study of anisotropy in a composite Fermi liquid
• Composite Fermions with a Warped Fermi Contour
• Composite fermions in bands with N-fold rotational symmetry
• Connection between Fermi contours of zero-field electrons and $\nu =\frac{1}{2}$ composite fermions in two-dimensional systems
• Anisotropic composite fermions and fractional quantum Hall effect
• Temperature dependence of piezoresistance of composite Fermions with a valley degree of freedom

Cited by in corpus (9)

• Observation of spontaneous valley polarization of itinerant electrons
• Widely Tunable Quantum Phase Transition from Moore-Read to Composite Fermi Liquid in Bilayer Graphene
• Is the composite fermion state of Graphene a doped Chern insulator?
• Interaction-dependent anisotropy of fractional quantum Hall states
• Fractional quantum Hall valley ferromagnetism in the extreme quantum limit
• Charge density waves and their transitions in anisotropic quantum Hall systems
• Anisotropic quantum Hall states in the presence of interactions with fourfold rotational symmetry
• $2{\mathbf{k}}_{\mathbf{F}}$ Density Wave Instability of Composite Fermi Liquid
• False Vacuum Decay in Flat-Band Ferromagnets: Role of Quantum Geometry and Chiral Edge States