Vestiges of Topological Phase Transitions in Kitaev Quantum Spin Liquids

Abstract

We investigate signatures of topological quantum phase transitions (TQPTs) between the $Z_2$ quantum spin liquids (QSLs). In two spatial dimensions, $Z_2$ QSLs and their TQPTs are only well defined at zero temperature ($T=0$), and it is imperative to clarify their observable signatures under nonzero temperatures. Here, we present the vestiges of TQPTs between $Z_2$ QSLs with Majorana fermions in terms of thermal Hall conductivity $κ_{xy}$ at nonzero temperatures. The $κ_{xy}/T$ shows characteristic temperature dependences around TQPTs. We argue that an exponential upturn near $T=0$ and the peak of $κ_{xy}/T$ around massive excitation energy are observable smoking-gun signals of the TQPTs. Quantum critical fan-shape temperature dependences are uncovered across TQPTs. We also perform the parton mean-field analysis on a modified Kitaev model with next-nearest neighbor interactions finding TQPTs between the phases with different Chern numbers and their vestiges self-consistently. We discuss the implication of our results to the recent experiments in $α$-RuCl$_3$.

6+3 pages (main text+supplemental material), Phys. Rev. Lett., in press