Theory of Nematic Fractional Quantum Hall State

TL;DR

This paper develops an effective field theory for the isotropic-nematic transition in fractional quantum Hall states, revealing a Berry phase term, collective excitation behavior, and topological charge properties of disclinations.

Contribution

It introduces a novel effective field theory with a Berry phase term for the nematic transition in FQH states, linking nematic order to geometric and topological responses.

Findings

The GMP mode gap collapses at the transition.

Laughlin quasiparticles remain gapped across the transition.

Disclinations carry unquantized electric charge.

Abstract

We derive an effective field theory for the isotropic-nematic quantum phase transition of fractional quantum Hall (FQH) states. We demonstrate that for a system with an isotropic background the low-energy effective theory of the nematic order parameter has $z=2$ dynamical scaling exponent, due to a Berry phase term of the order parameter, which is related to the non-dissipative Hall viscosity. Employing the composite fermion theory with a quadrupolar interaction between electrons, we show that a sufficiently attractive quadrupolar interaction triggers a phase transition from the isotropic FQH fluid into a nematic fractional quantum Hall phase. By investigating the spectrum of collective excitations, we demonstrate that the mass gap of Girvin-MacDonald-Platzman (GMP) mode collapses at the isotropic-nematic quantum phase transition. On the other hand, Laughlin quasiparticles and the Kohn collective mode remain gapped at this quantum phase transition, and Kohn's theorem is satisfied. The leading couplings between the nematic order parameter and the gauge fields include a term of the same form as Wen-Zee term. A disclination of the nematic order parameter carries an unquantized electric charge. We also discuss the relation between nematic degrees of freedom and the geometrical response of the fractional quantum Hall fluid.