Composite fermions in bands with N-fold rotational symmetry

Abstract

We study the effect of band anisotropy with discrete rotational symmetry $C_N$ (where $N\ge 2$) in the quantum Hall regime of two-dimensional electron systems. We focus on the composite Fermi liquid (CFL) at half filling of the lowest Landau level. We find that the magnitude of anisotropy transferred to the composite fermions decreases very rapidly with $N$. We demonstrate this by performing density matrix normalization group calculations on the CFL, and comparing the anisotropy of the composite fermion Fermi contour with that of the (non-interacting) electron Fermi contour at zero magnetic field. We also show that the effective interaction between the electrons after projecting into a single Landau level is much less anisotropic than the band, a fact which does not depend on filling and thus has implications for other quantum Hall states as well. Our results confirm experimental observations on anisotropic bands with warped Fermi contours, where the only detectable effect on the composite Fermi contour is an elliptical distortion ($N=2$).

arXiv comment6 pages + bibliography, 5 figures

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• Chiral Gravitons in Fractional Quantum Hall Liquids
• Geometric quench and nonequilibrium dynamics of fractional quantum Hall states
• Anisotropic Pseudopotential Characterization of Quantum Hall Systems under Tilted Magnetic Field
• 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
• 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