Theory of Nematic Fractional Quantum Hall State

Understand

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.