Numerical study of anisotropy in a composite Fermi liquid

Abstract

We perform density-matrix renormalization group studies of a two-dimensional electron gas in a high magnetic field and with an anisotropic band mass. At half-filling in the lowest Landau level, such a system is a Fermi liquid of composite fermions. By measuring the Fermi surface of these composite fermions, we determine a relationship between the anisotropy of composite fermion dispersion, ${\alpha }_{CF}$, and the original anisotropy ${\alpha }_F$ of the fermion dispersion at zero magnetic field. For systems where the electrons interact via a Coulomb interaction, we find ${\alpha }_{CF}=\sqrt{{\alpha }_F}$ within our numerical accuracy. The same result has been found concurrently in recent experiments. We also show results with other forms of the electron-electron interaction; this allows us (a) to benchmark our procedure against known exact results and (b) to show that the relationship between the anisotropies is dependent on the form of the interaction.

4 pages + references, 4 figures

References in corpus (8)

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Cited by in corpus (22)

• Composite Fermi Liquid at Zero Magnetic Field in Twisted MoTe${}_2$
• Chiral Gravitons in Fractional Quantum Hall Liquids
• Anisotropic effects in two-dimensional materials
• Transference of Fermi Contour Anisotropy to Composite Fermions
• Anisotropy Driven Transition from Moore-Read State to Quantum Hall Stripes
• Evolution of quantum entanglement with disorder in fractional quantum Hall liquids
• Composite fermions in bands with N-fold rotational symmetry
• Geometric Resonance of Four-Flux Composite Fermions
• Connection between Fermi contours of zero-field electrons and $\nu =\frac{1}{2}$ composite fermions in two-dimensional systems
• Screening, Friedel oscillations, RKKY interaction, and Drude transport in anisotropic two-dimensional systems
• Valley Stoner Instability of the Composite Fermi Sea
• Geometry of flux attachment in anisotropic fractional quantum Hall states
• Universal Fermi-surface anisotropy renormalization for interacting Dirac fermions with long-range interactions
• Interaction-dependent anisotropy of fractional quantum Hall states
• Tuning of Fermi Contour Anisotropy in GaAs (001) 2D Holes via Strain
• Corner Charge Fluctuations and Many-Body Quantum Geometry
• Charge density waves and their transitions in anisotropic quantum Hall systems
• Anisotropic quantum Hall states in the presence of interactions with fourfold rotational symmetry
• Anisotropy and quench dynamics of quasiholes in fractional quantum Hall liquids
• $2{\mathbf{k}}_{\mathbf{F}}$ 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