Nematic quantum phase transition of composite Fermi liquids in half-filled Landau levels and their geometric response

Abstract

We present a theory of the isotropic-nematic quantum phase transition in the composite Fermi liquid arising in half-filled Landau levels. We show that the quantum phase transition between the isotropic and the nematic phase is triggered by an attractive quadrupolar interaction between electrons, as in the case of conventional Fermi liquids. We derive the theory of the nematic state and of the phase transition. This theory is based on the flux attachment procedure which maps an electron liquid in half-filled Landau levels into the composite Fermi liquid close to a nematic transition. We show that the local fluctuations of the nematic order parameters act as an effective dynamical metric interplaying with the underlying Chern-Simons gauge fields associated with the flux attachment. Both the fluctuations of the Chern-Simons gauge field and the nematic order parameter can destroy the composite fermion quasiparticles and drive the system into a non-Fermi liquid state. The effective field theory for the isotropic-nematic phase transition has $z=3$ dynamical exponent due to Landau damping effects. We show that there is a Berry phase type term which governs the effective dynamics of the nematic order parameter fluctuations, which can be interpreted as a non-universal "Hall viscosity" of the dynamical metric. We show that the effective field theory has a Wen-Zee-type term. Both terms originate from the time-reversal breaking fluctuation of the Chern-Simons gauge fields. We present a perturbative computation of the Hall viscosity and also show that this term is also obtained by a Ward identity. We show that the disclination of the nematic fluid, carries an electric charge. We show that a resonance observed in radio-frequency conductivity experiments can be interpreted as a Goldstone nematic mode gapped by lattice effects.

v2. mildly edited version. 5 new references. 31 pages, 8 figures, 113 references. published version

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• Evidence of a fractional quantum Hall nematic phase in a microscopic model
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• Dirac Composite Fermions and Emergent Reflection Symmetry about Even Denominator Filling Fractions
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• Unconventional anisotropic even-denominator fractional quantum Hall state in a system with mass anisotropy
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• Onset of Quantum Criticality in the Topological-to-Nematic Transition in a Two-dimensional Electron Gas at Filling Factor $\nu =5/2$
• Nematic fluctuations balancing the zoo of phases in half-filled quantum Hall systems
• Regularizing 3D conformal field theories via anyons on the fuzzy sphere
• Vortex and disclination structures in a nematic-superconductor state
• Competition of Pairing and Nematicity in the Two-Dimensional Electron Gas
• Hall Viscosity of the Composite-Fermion Fermi Seas for Fermions and Bosons
• Partial filled Landau Level at even denominator, a vortex metal with Berry phase
• Distinguishing XY from Ising Electron Nematics
• Possible continuous transition from fractional quantum Hall to stripe phase at ${\nu }_e=7/3$
• Nematic order on the surface of a three-dimensional topological insulator
• Observation of the novel type of ordering: Spontaneous ferriquadrupolar order
• Composite Fermion States around 2D Hole Landau Level Filling Factor 3/2 in Tilted Magnetic Fields
• Exploring Quantum Hall Physics at Ultra-Low Temperatures and at High Pressures