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Disorder upon disorder: localization effects in the Kitaev spin liquid

In recent years, several magnetic Mott insulators with strong spin-orbit couplings were suggested to be proximate to the Kitaev quantum spin liquid (QSL) whose one of the most exciting features is the fractionalization of spin excitations into itinerant Majorana fermions and static $Z_2$ fluxes. Motivated by the emergence of this plethora of 4d and 5d transition metal Kitaev materials and by the fact that some level of disorder is inevitable in real materials, here we study how the Kitaev QSL responds to various forms of disorder, such as vacancies, impurities, and bond randomness. First, we argue that the presence of the quenched disorder in the Kitaev QSL can lead to the Anderson localization of Majorana fermions and the appearance of Lifshitz tails. We point out that the Anderson localization of low-energy states is particularly strong in the extended Kitaev model with the time reversal symmetry breaking term. Second, we show that the disorder effects on the low-energy Majorana fermion modes can be detected in thermal transport. Third, we show that at finite temperatures the $Z_2$ fluxes become thermally excited and give rise to an additional disorder for the Majorana fermions. This source of the disorder dominates at high temperatures. Fourth, we demonstrate that both the structure of the energy spectrum and the thermal transport properties of the disordered Kitaev QSL depend strongly on the character of disorder. While we find that both the site disorder and the bond randomness suppress the longitudinal thermal conductivity, the low-energy localization is stronger in the case of the site disorder.