Finite-wavevector Electromagnetic Response in Lattice Quantum Hall Systems
arXiv:1807.00970 · doi:10.1103/PhysRevB.98.245303
Abstract
In a quantum Hall system, the finite-wavevector Hall conductivity displays an intriguing dependence on the Hall viscosity, a coefficient that describes the non-dissipative response of the fluid to a velocity gradient. In this paper, we pursue this connection in detail for quantum Hall systems on a lattice, noting that the neat continuum relation breaks down and develops corrections due to the broken rotational symmetry. In the process, we introduce a new, quantum mechanical derivation of the finite-wavevector Hall conductivity for the integer quantum Hall effect, which allows terms to arbitrary order in the wavevector expansion to be calculated straightforwardly. We also develop a universal formalism for studying quantum Hall physics on a lattice, and find that at weak applied magnetic fields, generic lattice wavefunctions connect smoothly to the Landau levels of the continuum. At moderate field strengths, the lattice corrections can be significant and perturb the wavefunctions, energy levels, and transport properties from their continuum values. Our approach allows the finite-field behaviour of a system to be inferred directly from the zero-field band structure.
arXiv comment17 pages, 3 figures. v2: published version
References in corpus (33)
- Two-Dimensional Gas of Massless Dirac Fermions in Graphene
- Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
- Berry Phase Effects on Electronic Properties
- Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
- Artificial gauge potentials for neutral atoms
- Hofstadter's butterfly in moire superlattices: A fractal quantum Hall effect
- Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices
- Cloning of Dirac fermions in graphene superlattices
- Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices
- Fractional quantum Hall states at zero magnetic field
- Nearly-flat bands with nontrivial topology
- Fractional quantum Hall effect in the absence of Landau levels
- Topological Flat Band Models and Fractional Chern Insulators
- Fractional Quantum Hall Physics in Topological Flat Bands
- Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and p_x+ip_y paired superfluids
- Observation of topological surface state quantum Hall effect in an intrinsic three-dimensional topological insulator
- Viscosity of Quantum Hall Fluids
- Hall Viscosity and Electromagnetic Response
- Band geometry of fractional topological insulators
- Hall viscosity, orbital spin, and geometry: paired superfluids and quantum Hall systems
- Kubo formulas for viscosity: Hall viscosity, Ward identities, and the relation with conductivity
- Hydrodynamic Electron Flow and Hall Viscosity
- NiCl3 Monolayer: Dirac Spin-Gapless Semiconductor and Chern Insulator
- Fractional Chern Insulators and the W-Infinity Algebra
- Non-local transport and the Hall viscosity of 2D hydrodynamic electron liquids
- Geometric stability of topological lattice phases
- Bimetric Theory of Fractional Quantum Hall States
- Transport signatures of Hall viscosity
- Perturbative Approach to Flat Chern Bands in the Hofstadter Model
- Quantum geometry and stability of the fractional quantum Hall effect in the Hofstadter model
- Geometry of Landau orbits in the absence of rotational symmetry
- Hall Viscosity Revealed via Density Response
- Semiclassical theory of viscosity in quantum Hall states