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Fractional quantum Hall (FQH) states can exhibit a nematic phase. This study models the FQH nematic transition using the standard Coulomb potential model, revealing its mechanism via gap closure.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Hall Effect

Background:

  • Fractional quantum Hall (FQH) states are topological phases of matter.
  • Geometric fluctuations can lead to a nematic FQH phase with broken rotational symmetry.
  • Experimental signatures of nematic FQH states exist, but a realistic theoretical model was lacking.

Purpose of the Study:

  • To develop a realistic model for the FQH nematic transition.
  • To investigate the mechanism driving the transition in the standard FQH model.

Main Methods:

  • Utilized exact diagonalization and variational wave functions.
  • Analyzed the standard model of particles in the lowest Landau level with Coulomb interaction.
  • Investigated the effect of reducing the shortest-range Haldane pseudopotential.

Main Results:

  • The FQH nematic transition is realized in the standard model.
  • The transition occurs when the neutral gap closes at long wavelengths while the charge gap remains open.
  • Confirmed symmetry breaking through a "circular moat" potential and identified geometric character via nematic susceptibility and Hall viscosity fluctuations.

Conclusions:

  • The standard Coulomb potential model accurately describes the FQH nematic transition.
  • The transition is driven by specific gap dynamics and exhibits clear symmetry-breaking characteristics.