Transport in honeycomb lattice with random $\pi$-fluxes: implications for low-temperature thermal transport in the Kitaev spin liquids

TL;DR

This study investigates how random $\pi$-fluxes affect thermal transport in honeycomb lattices, revealing localization effects and implications for low-temperature behavior in Kitaev spin liquids.

Contribution

It introduces a numerical analysis of transport in a honeycomb lattice with random $\pi$-fluxes, connecting flux disorder to localization and thermal conductivity in Kitaev models.

Findings

DC conductivity is quadratic in Fermi momentum and inversely proportional to flux density.

Localization length due to random fluxes is quantified.

Thermal conductivity diverges as temperature approaches zero, with implications for Majorana localization.

Abstract

Motivated by the thermal transport problem in the Kitaev spin liquids, we consider a nearest-neighbor tight-binding model on the honeycomb lattice in the presence of random uncorrelated $\pi$-fluxes. We employ different numerical methods to study its transport properties near half-filling. The zero-temperature DC conductivity away from the Dirac point is found to be quadratic in Fermi momentum and inversely proportional to the flux density. Localization due to the random $\pi$-fluxes is observed and the localization length is extracted. Our results imply that, for realistic system size, the thermal conductivity of a pure Kitaev spin liquid diverges as $\kappa_\text{K}\sim T^3 e^{\Delta_v/k_BT}$ when $k_B T\ll \Delta_v$, and suggest the possible occurrence of strong Majorana localization $\kappa_\text{K}/T\ll k_B^2/2\pi\hbar$ when $k_B T\sim \Delta_v$, where $\Delta_v$ is the vison gap.