Connection between Fermi contours of zero-field electrons and $\nu =\frac{1}{2}$ composite fermions in two-dimensional systems

Abstract

We investigate the relation between the Fermi sea (FS) of zero-field carriers in two-dimensional systems and the FS of the corresponding composite fermions which emerge in a high magnetic field at filling $\nu =\frac{1}{2}$, as the kinetic energy dispersion is varied. We study cases both with and without rotational symmetry, and find that there is generally no straightforward relation between the geometric shapes and topologies of the two FSs. In particular, we show analytically that the composite Fermi liquid (CFL) is completely insensitive to a wide range of changes to the zero-field dispersion which preserve rotational symmetry, including ones that break the zero-field FS into multiple disconnected pieces. In the absence of rotational symmetry, we show that the notion of `valley pseudospin' in many-valley systems is generically not transferred to the CFL, in agreement with experimental observations. We also discuss how a rotationally symmetric band structure can induce a reordering of the Landau levels, opening interesting possibilities of observing higher-Landau-level physics in the high-field regime.

7 pages + references, 7 figures. Added many-body DMRG calculation

References in corpus (10)

• Valley splitting of AlAs two-dimensional electrons in a perpendicular magnetic field
• Infinite density matrix renormalization group for multicomponent quantum Hall systems
• Observation of a Nematic Quantum Hall Liquid on the Surface of Bismuth
• Band mass anisotropy and the intrinsic metric of fractional quantum Hall systems
• Fractional quantum Hall states in two-dimensional electron systems with anisotropic interactions
• Quantum Hall Phase Diagram of Half-filled Bilayers in the Lowest and the Second Orbital Landau Levels: Abelian versus Non-Abelian Incompressible Fractional Quantum Hall States
• Transference of Fermi Contour Anisotropy to Composite Fermions
• Numerical study of anisotropy in a composite Fermi liquid
• Composite Fermions with a Warped Fermi Contour
• Signatures of an annular Fermi sea

Cited by in corpus (13)

• Composite Fermi Liquid at Zero Magnetic Field in Twisted MoTe${}_2$
• Chiral Gravitons in Fractional Quantum Hall Liquids
• Composite fermions in bands with N-fold rotational symmetry
• Geometric Resonance of Four-Flux Composite Fermions
• Valley Stoner Instability of the Composite Fermi Sea
• Geometry of flux attachment in anisotropic fractional quantum Hall states
• Interaction-dependent anisotropy of fractional quantum Hall states
• Valley-tunable, even-denominator fractional quantum Hall state in the lowest Landau level of an anisotropic system
• Phase classification in the long-range Harper model using machine learning
• 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
• Fermi surfaces of composite fermions
• Probing Non-Fermi-Liquid Behaviour of Composite Fermi Liquid via Efficient Thermal Simulations