Hall Viscosity and Momentum Transport in Lattice and Continuum Models of the Integer Quantum Hall Effect in Strong Magnetic Fields

TL;DR

This paper introduces a new method to compute Hall viscosity in lattice systems under strong magnetic fields, compares it to continuum models, and explores how lattice symmetry affects the results.

Contribution

It develops a momentum transport-based method for lattice Hall viscosity and compares lattice and continuum models, highlighting the effects of magnetic length and lattice symmetry.

Findings

Agreement between lattice and continuum Hall viscosity when magnetic length is large

Deviations increase with stronger magnetic fields and broken lattice symmetry

Lattice Dirac model's Hall viscosity matches continuum when magnetic length is large

Abstract

The Hall viscosity describes a non-dissipative response to strain in systems with broken time-reversal symmetry. We develop a new method for computing the Hall viscosity of lattice systems in strong magnetic fields based on momentum transport, which we compare to the method of momentum polarization used by Tu et al. [Phys. Rev. B 88 195412 (2013)] and Zaletel et al. [Phys. Rev. Lett. 110 236801 (2013)] for non-interacting systems. We compare the Hall viscosity of square-lattice tight-binding models in magnetic field to the continuum integer quantum Hall effect (IQHE) showing agreement when the magnetic length is much larger than the lattice constant, but deviation as the magnetic field strength increases. We also relate the Hall viscosity of relativistic electrons in magnetic field (the Dirac IQHE) to the conventional IQHE. The Hall viscosity of the lattice Dirac model in magnetic field agrees with the continuum Dirac Hall viscosity when the magnetic length is much larger than the lattice constant. We also show that the Hall viscosity of the lattice model deviates further from the continuum model if the $C_4$ symmetry of the square lattice is broken to $C_2$, but the deviation is again minimized as the magnetic length increases.