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 ($N=2$).

6 pages + bibliography, 5 figures

References in corpus (6)

• Framing Anomaly in the Effective Theory of Fractional Quantum Hall Effect
• Low-energy effective theory in the bulk for transport in a topological phase
• Band mass anisotropy and the intrinsic metric of fractional quantum Hall systems
• Transference of Transport Anisotropy to Composite Fermions
• Fractional quantum Hall states in two-dimensional electron systems with anisotropic interactions
• Composite Fermions with a Warped Fermi Contour

Cited by in corpus (5)

• Composite Fermi Liquid at Zero Magnetic Field in Twisted MoTe${}_2$
• Anisotropic Pseudopotential Characterization of Quantum Hall Systems under Tilted Magnetic Field
• Fermi surfaces of composite fermions
• Anisotropy and quench dynamics of quasiholes in fractional quantum Hall liquids
• Probing Non-Fermi-Liquid Behaviour of Composite Fermi Liquid via Efficient Thermal Simulations