Finite-wavevector Electromagnetic Response in Lattice Quantum Hall Systems

TL;DR

This paper explores how lattice effects modify the finite-wavevector electromagnetic response in quantum Hall systems, introducing a new derivation and a universal formalism to connect lattice and continuum behaviors.

Contribution

It provides a quantum mechanical derivation of finite-wavevector Hall conductivity on lattices and develops a universal formalism linking lattice and continuum quantum Hall physics.

Findings

Lattice corrections significantly alter wavefunctions and transport at moderate fields.

The formalism allows inference of finite-field behavior from zero-field band structure.

Continuum Landau levels are smoothly connected to lattice wavefunctions at weak fields.

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.