Field Theory of Nematicity in the Spontaneous Quantum Anomalous Hall effect

Abstract

We derive from a microscopic model the effective theory of nematic order in a system with a spontaneous quantum anomalous Hall effect in two dimensions. Starting with a model of two-component fermions (a spinor field) with a quadratic band crossing and short range four-fermion marginally relevant interactions we use a 1/N expansion and bosonization methods to derive the effective field theory for the hydrodynamic modes associated with the conserved currents and with the local fluctuations of the nematic order parameter. We focus on the vicinity of the quantum phase transition from the isotropic Mott Chern insulating phase to a phase in which time-reversal symmetry breaking coexists with nematic order, the nematic Chern insulator. The topological sector of the effective field theory is a BF/Chern-Simons gauge theory. We show that the nematic order parameter field couples with the Maxwell-type terms of the gauge fields as the space components of a locally fluctuating metric tensor. The nematic field has $z=2$ dynamic scaling exponent. The low energy dynamics of the nematic order parameter is found to be governed by a Berry phase term. By means of a detailed analysis of the coupling of the spinor field of the fermions to the changes of their local frames originating from long-wavelength lattice deformations we calculate the Hall viscosity of this system and show that in this system is not the same as the Berry phase term in the effective action of the nematic field, but both are related to the concept of torque Hall viscosity which we introduce here.

mildly edited version, one new reference; version to be published in Physical Review B; 22 pages, 3 figures (two with 2 subfigures each), 90 references

References in corpus (19)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Topological Crystalline Insulators
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• Topological Mott Insulators
• Fractional quantum Hall effect in the absence of Landau levels
• Topological Insulators and Nematic Phases from Spontaneous Symmetry Breaking in 2D Fermi Systems with a Quadratic Band Crossing
• Topological Order and Conformal Quantum Critical Points
• Characterizing topological order by studying the ground states of an infinite cylinder
• Quantum Anomalous Hall State in Bilayer Graphene
• Interacting fermions on the honeycomb bilayer: from weak to strong coupling
• Competing Nematic, Anti-ferromagnetic and Spin-flux orders in the Ground State of Bilayer Graphene
• Band mass anisotropy and the intrinsic metric of fractional quantum Hall systems
• Observation of Quantum Hall Valley Skyrmions
• Tilt-Induced Anisotropic to Isotropic Phase Transition at $\nu =5/2$
• Nematic Valley Ordering in Quantum Hall Systems
• Hall viscosity from effective field theory
• Phase transitions in superconductor liquid crystals

Cited by in corpus (19)

• Torsion, Parity-odd Response and Anomalies in Topological States
• A discretized Chern-Simons gauge theory on arbitrary graphs
• Theory of Nematic Fractional Quantum Hall State
• Response Properties of Axion Insulators and Weyl Semimetals Driven by Screw Dislocations and Dynamical Axion Strings
• Nematic, topological and Berry phases when a flat and a parabolic band touch
• Nematic quantum phase transition of composite Fermi liquids in half-filled Landau levels and their geometric response
• Geometric Defects in Quantum Hall States
• Excitonic and Nematic Instabilities on the Surface of Topological Kondo Insulators
• Horava-Lifshitz Gravity and Effective Theory of the Fractional Quantum Hall Effect
• Magic-angle Twisted Bilayer Systems with Quadratic-Band-Touching: Exactly Flat Bands with High-Chern Number
• Geometry defects in Bosonic symmetry protected topological phases
• Emergent dome of nematic order around a quantum anomalous Hall critical point
• Spontaneous mass generation due to phonons in a two-dimensional Dirac fermion system
• Effective description of Chern insulators
• Chern-Simons-Higgs Theory with Visible and Hidden Sectors and its $\mathcal{N}=2$ SUSY Extension
• A critical nematic phase with pseudogap-like behavior in twisted bilayers
• Nematic order on the surface of a three-dimensional topological insulator
• Geometric transport signatures of strained multi-Weyl semimetals
• Effective field theory of an anomalous Hall metal from interband quantum fluctuations