Band mass anisotropy and the intrinsic metric of fractional quantum Hall systems

Abstract

It was recently pointed out that topological liquid phases arising in the fractional quantum Hall effect (FQHE) are not required to be rotationally invariant, as most variational wavefunctions proposed to date have been. Instead, they possess a geometric degree of freedom corresponding to a shear deformation that acts like an intrinsic metric. We apply this idea to a system with an anisotropic band mass, as is intrinsically the case in many-valley semiconductors such as AlAs and Si, or in isotropic systems like GaAs in the presence of a tilted magnetic field, which breaks the rotational invariance. We perform exact diagonalization calculations with periodic boundary conditions (torus geometry) for various filling fractions in the lowest, first and second Landau levels. In the lowest Landau level, we demonstrate that FQHE states generally survive the breakdown of rotational invariance by moderate values of the band mass anisotropy. At 1/3 filling, we generate a variational family of Laughlin wavefunctions parametrized by the metric degree of freedom. We show that the intrinsic metric of the Laughlin state adjusts as the band mass anisotropy or the dielectric tensor are varied, while the phase remains robust. In the n=1 Landau level, mass anisotropy drives transitions between incompressible liquids and compressible states with charge density wave ordering. In n>=2 Landau levels, mass anisotropy selects and enhances stripe ordering with compatible wave vectors at partial 1/3 and 1/2 fillings.

9 pages, 8 figures

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Cited by in corpus (14)

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• Fractional quantum Hall states in two-dimensional electron systems with anisotropic interactions
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• Composite Fermions with a Warped Fermi Contour
• Anisotropic Pseudopotential Characterization of Quantum Hall Systems under Tilted Magnetic Field
• Competition between fractional quantum Hall liquid and Wigner solid at small fillings: Role of layer thickness and Landau level mixing
• Bilayer mapping of the paired quantum Hall state: Instability toward anisotropic pairing
• Composite fermions in bands with N-fold rotational symmetry
• Existence of strong-pairing quantum Hall phase in bilayer cold atom systems with dipolar interactions
• Anisotropic composite fermions and fractional quantum Hall effect
• Tilt-Induced Phase Transitions in Even-Denominator Fractional Quantum Hall States at the ZnO Interface
• Phase transition and intrinsic metric of the dipolar fermions in quantum Hall regime
• Exact Mappings in Condensed Matter Physics