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Register a new userSign structure of thermal Hall conductivity for in-plane-field polarized Kitaev magnets
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The appearance of half-quantized thermal Hall conductivity in $alpha$-RuCl$_3$ in the presence of in-plane magnetic fields has been taken as a strong evidence for Kitaev spin liquid. Apart from the quantization, the observed sign structure of the thermal Hall conductivity is also consistent with predictions from the exact solution of the Kitaev model. Namely, the thermal Hall conductivity changes sign when the field direction is reversed with respect to the heat current, which is perpendicular to one of the three nearest neighbor bonds on the honeycomb lattice. On the other hand, it is almost zero when the field is applied along the bond direction. Here, we show that such a peculiar sign structure of the thermal Hall conductivity is a generic property of the polarized state in the presence of in-plane magnetic-fields. In this case, thermal Hall effect arises from topological magnons with finite Chern numbers and the sign structure follows from the symmetries of the momentum space Berry curvature. Using a realistic spin model with bond-dependent interactions, we show that the thermal Hall conductivity can have a magnitude comparable to that observed in the experiments. Hence the sign structure alone cannot make a strong case for Kitaev spin liquid. The quantization at very low temperatures, however, will be a decisive test as the magnon contribution vanishes in the zero temperature limit.
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We study magnetic excitations and thermal Hall effect on the Kitaev-Heisenberg model under magnetic fields. By employing the spin-wave theory for the magnetic orders realized in this model, we examine the topological nature of the spin-wave dispersions and calculate the thermal Hall conductivity. The comprehensive investigations on the field-angle dependence clarify that the thermal Hall conductivity is sensitive to the spin ordered pattern and excitation spectra of magnons; this quantity is enhanced by the noncoplanar spin configurations and small magnon gap in the excitation spectrum. On the other hand, we also find a common feature in the field-angle dependence of the thermal Hall conductivity. It vanishes when the magnetic field is on the planes spanned by the spin axes. We reveal that the behavior is intrinsic to the Kitaev -Heisenberg model in an applied field and demonstrate that the introduction of the off-diagonal spin interaction causes the disappearance of the feature in the thermal Hall conductivity.
In this work we study the phase diagram of 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 multi-band structure characterized by Chern numbers 0, $pm$1, and $pm2$. 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 part 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 $alpha$-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.
Recently, the observation of large thermal Hall conductivities in correlated insulators with no apparent broken symmetry have generated immense interest and debates on the underlying ground states. Here, considering frustrated magnets with bond-dependent interactions, which are realized in the so-called Kitaev materials, we theoretically demonstrate that a large thermal Hall conductivity can originate from a classical ground state without any magnetic order. We discover a novel liquid state of magnetic vortices, which are inhomogeneous spin textures embedded in the background of polarized spins, under out-of-plane magnetic fields. In the classical regime, different configurations of vortices form a degenerate manifold. We study the static and dynamical properties of the magnetic vortex liquid state at zero and finite temperatures. In particular, we show that the spin excitation spectrum resembles a continuum of nearly flat Chern bands, which ultimately leads to a large thermal Hall conductivity. Possible connections to experiments are discussed.
We consider the effect of coupling between phonons and a chiral Majorana edge in a gapped chiral spin liquid with Ising anyons (e.g., Kitaevs non-Abelian spin liquid on the honeycomb lattice). This is especially important in the regime in which the longitudinal bulk heat conductivity $kappa_{xx}$ due to phonons is much larger than the expected quantized thermal Hall conductance $kappa_{xy}^{rm q}=frac{pi T}{12} frac{k_B^2}{hbar}$ of the ideal isolated edge mode, so that the thermal Hall angle, i.e., the angle between the thermal current and the temperature gradient, is small. By modeling the interaction between a Majorana edge and bulk phonons, we show that the exchange of energy between the two subsystems leads to a transverse component of the bulk current and thereby an {em effective} Hall conductivity. Remarkably, the latter is equal to the quantized value when the edge and bulk can thermalize, which occurs for a Hall bar of length $L gg ell$, where $ell$ is a thermalization length. We obtain $ell sim T^{-5}$ for a model of the Majorana-phonon coupling. We also find that the quality of the quantization depends on the means of measuring the temperature and, surprisingly, a more robust quantization is obtained when the lattice, not the spin, temperature is measured. We present general hydrodynamic equations for the system, detailed results for the temperature and current profiles, and an estimate for the coupling strength and its temperature dependence based on a microscopic model Hamiltonian. Our results may explain recent experiments observing a quantized thermal Hall conductivity in the regime of small Hall angle, $kappa_{xy}/kappa_{xx} sim 10^{-3}$, in $alpha$-RuCl$_3$.
A clear thermal Hall signal ($kappa_{xy}$) was observed in the spin liquid phase of the $S=1/2$ kagome antiferromagnet Ca kapellasite (CaCu$_3$(OH)$_6$Cl$_2cdot 0.6$H$_2$O). We found that $kappa_{xy}$ is well reproduced, both qualitatively and quantitatively, using the Schwinger-boson mean-field theory with the Dzyaloshinskii--Moriya interaction of $D/J sim 0.1$. In particular, $kappa_{xy}$ values of Ca kapellasite and those of another kagome antiferromagnet, volborthite, converge to one single curve in simulations modeled using Schwinger bosons, indicating a common temperature dependence of $kappa_{xy}$ for the spins of a kagome antiferromagnet.
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