Recent experiments on Kitaev spin liquid candidate materials reported nonmonotonic behavior of thermal conductivity as a function of magnetic field, which lead to conflicting interpretations of its origin. Motivated by this development, we study the magnetic field dependence of thermal conductivity of a generalized Kitaev model, which allows the phase transitions between different flux sectors as a function of the magnetic field. The thermal conductivity due to Majorana fermions shows dip-bump structures as the magnetic field increases, which is caused by either the transitions between different flux sectors of Kitaev spin liquids or the topological transitions that change the Majorana Chern number within the same flux sector. It is shown that the change of Chern number is closely related to the four-Majorana-fermion interaction induced by the magnetic field. The nonmonotonic behavior in thermal conductivity emerges at finite temperature, and it becomes weaker when temperature decreases toward zero. Our model provides a generic mechanism for the Kitaev spin liquids to develop nonmonotonic magnetic-field dependence of thermal conductivity while the comparison to realistic materials remains an open question for future investigation.
In this work we study the phase diagram of the Kekul\'e-Kitaev model. The model is defined on a honeycomb lattice with bond-dependent anisotropic exchange interactions, making it exactly solvable in terms of Majorana representation of spins, in close analogy to the Kitaev model. However, the energy spectrum of Majorana fermions has a multiband structure characterized by Chern numbers 0, $\ifmmode\pm\else\textpm\fi{}1$, and $\ifmmode\pm\else\textpm\fi{}2$. We obtained the phase diagram of the model in the plane of exchange couplings and in the presence of a magnetic field and found chiral topological and trivial spin-liquid ground states. In the absence of magnetic field most of the phase diagram is a trivial gapped phase continuously connected to an Abelian phase, while in the presence of the magnetic field a topological phase arises. Furthermore, motivated by recent thermal measurements on the spin-liquid candidate $\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}$, we calculated the thermal Hall conductivity at different regimes of parameters and temperatures and found the latter is quantized over a wide range of temperatures.
There has been great interest in identifying a Kitaev quantum spin liquid state in frustrated magnets with bond-dependent interactions. In particular, the experimental report of a half-quantized thermal Hall conductivity in $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ in the presence of a magnetic field has generated excitement as it could be strong evidence for a field-induced chiral spin liquid. More recent experiments, however, provide a conflicting interpretation advocating for topological magnons in the field-polarized state as the origin of the nonquantized thermal Hall conductivity observed in their experiments. An inherent difficulty in distinguishing between the two scenarios is that the phase transition between a putative two-dimensional spin liquid and the field-polarized state exists only at zero temperature, while the behavior at finite temperature is mostly crossover phenomena. In this work, we provide insights into the finite-temperature crossover behavior between the spin excitation continuum in a quantum spin liquid and topological magnons in the field-polarized state in three different theoretical models with large Kitaev interactions. These models allow for a field-induced phase transition from a spin liquid (or an intermediate field-induced spin liquid) to the field-polarized state in the quantum model. We obtain the dynamical spin structure factor as a function of magnetic field using molecular dynamics simulations and compute thermal Hall conductivity in the field-polarized regime. We demonstrate the gradual evolution of the dynamical spin structure factor exhibiting crossover behavior near magnetic fields where zero-temperature phase transitions occur in the quantum model. We also examine nonlinear effects on topological magnons and the validity of thermal Hall conductivity computed using linear spin wave theory. We discuss the implications of our results for existing and future experiments.
We study quantum phase transitions in the honeycomb Kitaev model under a magnetic field, focusing on the topological nature of Majorana fermion excitations. We find a gapless phase between the low-field gapless quantum spin liquid and the high-field gapped forced-ferromagnetic state for the antiferromagnetic Kitaev model in the [001] field by using the Majorana mean-field theory, in conjunction with the exact diagonalization and the spin-wave theory supporting the validity of this approach. The transition between the two gapless phases is driven by a topological change of the Majorana spectrum---line node formation interconnecting two Majorana cones. The peculiar change of the Majorana band topology is rationalized by a sign change of the effective Kitaev coupling by the magnetic field, which does not occur in the ferromagnetic Kitaev case. Upon tilting the magnetic field away from [001], the two gapless phases become gapped and topologically nontrivial, characterized by nonzero Chern numbers with different signs. The sign change of the Chern number leads to a reversal of the thermal edge current in the half-quantized thermal Hall effect.
We investigate the thermal Hall conductivity in the Kitaev model with additional interactions under a magnetic field, employing a finite-temperature tensor network method benchmarked by a thermal pure quantum state technique. We find that the thermal Hall conductivity divided by temperature,
κxy/T, significantly overshoots the value of the half-integer quantization and exhibits a pronounced hump while decreasing temperature. Moreover, we show that the field-direction dependence of
κxy/T is consistent with the sign of the Chern number associated with the Majorana fermions across a wide range of magnetic fields. We also demonstrate that the additional off-diagonal interactions, known as the
Γ and
Γ′ terms, considerably affect
κxy/T. In particular, we show that positive
Γ and negative
Γ′ lead to a remarkable enhancement in the intermediate temperature region. From the comparison with the classical counterpart, we reveal that the effects of the
Γ term go beyond the classical picture, indicating significant quantum fluctuation effects, while those of the
Γ′ term are well captured at the classical level. These comprehensive analyses indicate that the enhanced thermal Hall response is consistently explained by dominant contributions from topological Majorana fermions, even within the polarized regime beyond the critical field. Our approach not only establishes a robust theoretical framework for understanding the thermal Hall transport in Kitaev materials such as
α-RuCl
3, but also offers a promising pathway to bridge the gap between theories and experiments across a wide range of strongly correlated materials.
We propose a scenario of realizing the toric code phase, which can be potentially utilized for fault-tolerant quantum computation, in candidate materials of Kitaev magnets.It is demonstrated that four-body interactions among Majorana fermions in the Kitaev spin liquid state, which are induced by applied magnetic fields as well as non-Kitaev-type exchange interactions, trigger a nematic phase transition of Majorana bonds without magnetic orders, accompanying the change of the Chern number from ±1 to zero.This gapful spin liquid state with zero Chern number is simply the toric code phase.Our result potentially explains the topological nematic transition recently observed in α-RuCl 3 via heat capacity measurements (O.Tanaka et al.,
We investigate how the Kitaev spin liquid state described by Majorana fermions coupled with
Z2 gauge fields is affected by non-Kitaev interactions which exist in real candidate materials of the Kitaev magnet. It is found that the off-diagonal exchange interaction referred to as the ${\mathrm{\ensuremath{\Gamma}}}^{\ensuremath{'}}$ term dramatically changes the Majorana band structure in the case of the antiferromagnetic Kitaev interaction and gives rise to a topological phase transition from a non-Abelian topological phase with the Chern number equal to $\ifmmode\pm\else\textpm\fi{}1$ to an Abelian phase with the Chern number equal to $\ifmmode\pm\else\textpm\fi{}2$, in which the
Z2 vortices behave as Abelian anyons. On the other hand, other non-Kitaev interactions such as the Heisenberg interaction and the $\mathrm{\ensuremath{\Gamma}}$ term only affect the bandwidth of the Majorana band as long as the spin liquid state is not destabilized.