Transport in honeycomb lattice with random π fluxes: Implications for low-temperature thermal transport in Kitaev spin liquids

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(K) similar to T(3)e(Delta upsilon/kBT) when k(B)T << Delta(upsilon), and suggest the possible occurrence of strong Majorana localization kappa(K)/T << k(B)(2)/2 pi h when k(B)T similar to Delta(upsilon), where Delta(upsilon) is the vison gap.