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

Bo Yang, Z. Papić, E. H. Rezayi, R. N. Bhatt, F. D.M. Haldane

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87 Scopus citations


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 wave functions 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 wave functions 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 is 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 n2 Landau levels, mass anisotropy selects and enhances stripe ordering with compatible wave vectors at partial 1/3 and 1/2 fillings.

Original languageEnglish (US)
Article number165318
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number16
StatePublished - Apr 24 2012

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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