Effective description of Chern insulators

Abstract

The Berry curvature in Chern insulators appears to be a non-gauge-invariant quantity and does not immediately allow local length characterization. However, in two examples of 2- and 3-band models that we discuss, we find high-symmetry points in the Brillouin zone that have Berry curvature invariant under diagonal gauge transformations, and may serve as expansion points of geometrical description. On the basis of the geometrical description, in the case of Dirac based 2-band Chern insulators like Haldane model we conclude that the characteristic length based on the value of the Berry curvature at the expansion point plays the role of the magnetic length in the expression for the Hall viscosity. In the case of 2-band models the characteristic "cyclotron" spin is equal to 1/2, while in the 3-band kagome case this spin is likely non-quantized and non-universal.

arXiv comment10 pages, 7 figures

References in corpus (15)

• Berry Phase Effects on Electronic Properties
• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• Viscosity of Quantum Hall Fluids
• Geometrical Description of the Fractional Quantum Hall Effect
• Hall viscosity, orbital spin, and geometry: paired superfluids and quantum Hall systems
• Zoology of Fractional Chern Insulators
• Torsional Anomalies, Hall Viscosity, and Bulk-boundary Correspondence in Topological States
• Torsional Response and Dissipationless Viscosity in Topological Insulators
• Abelian and Non-Abelian Quantum Geometric Tensor
• Field theory of the quantum Hall nematic transition
• Momentum space metric, non-local operator, and topological insulators
• Electron Dynamics in Slowly Varying Antiferromagnetic Texture
• Field Theory of Nematicity in the Spontaneous Quantum Anomalous Hall effect

Cited by in corpus (8)

• Geometric stability of topological lattice phases
• Viscoelastic response of topological tight-binding models in two and three dimensions
• Torsion, Parity-odd Response and Anomalies in Topological States
• Contrasting lattice geometry dependent versus independent quantities: ramifications for Berry curvature, energy gaps, and dynamics
• Generalized Bloch theorem and topological characterization
• Interplay of Band Geometry and Topology in Ideal Chern Insulators in Presence of External Electromagnetic Fields
• Hall effect, edge states and Haldane exclusion statistics in two-dimensional space
• Quantum geometric tensors from sub-bundle geometry