Exact results for model wave functions of anisotropic composite fermions in the fractional quantum Hall effect

Abstract

The microscopic wave functions of the composite fermion theory can incorporate electron mass anisotropy by a trivial rescaling of the coordinates. These wave functions are very likely adiabatically connected to the actual wave functions of the anisotropic fractional quantum Hall states. We show in this article that they possess the nice property that their energies can be analytically related to the previously calculated energies for the isotropic states through a universal scale factor, thus allowing an estimation of several observables in the thermodynamic limit for all fractional quantum Hall states. The rather weak dependence of the scale factor on the anisotropy provides insight into why fractional quantum Hall effect and composite fermions are quite robust to electron mass anisotropy. We discuss how better, though still approximate, wave functions can be obtained by introducing a variational parameter, following Haldane [Phys. Rev. Lett. {\bf 107}, 116801 (2011)], but the resulting wave functions are not readily amenable to calculations. Our considerations are also applicable, with minimal modification, to the case where the dielectric function of the background material is anisotropic.

11 pages, 2 figures, published version

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• 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
• Tunnel transport and interlayer excitons in bilayer fractional quantum Hall systems
• Non-Abelian quasiholes in lattice Moore-Read states and parent Hamiltonians
• Anisotropic composite fermions and fractional quantum Hall effect
• Geometry of flux attachment in anisotropic fractional quantum Hall states
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• 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
• Tuning of Fermi Contour Anisotropy in GaAs (001) 2D Holes via Strain
• Pairing instabilities of Dirac composite fermions
• Charge density waves and their transitions in anisotropic quantum Hall systems
• Collective excitations of quantum Hall states under tilted magnetic field
• 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
• Exchange effect and magneto-plasmon mode dispersion in an anisotropic two-dimensional electronic system