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Register a new userQuantum Thermal Hall effect of chiral spinons on a Kagome strip
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We develop a theory for the thermal Hall coefficient in a spin-$frac{1}{2}$ system on a strip of Kagome lattice, where a chiral spin-interaction term is present. To this end, we model the Kagome strip as a three-leg $XXZ$ spin-ladder, and use Bosonization to derive a low-energy theory for the spinons in this system. Introducing further a Dzyaloshinskii-Moriya interaction ($D$) and a tunable magnetic field ($B$), we identify three distinct $B$-dependent quantum phases: a valence-bond crystal (VBC), a metallic spin liquid (MSL) and a chiral spin liquid (CSL). In the presence of a temperature difference $Delta T$ between the top and the bottom edges of the strip, we evaluate the net heat current $J_h$ along the strip, and consequently the thermal Hall conductivity $kappa_{xy}$. We find that the VBC-MSL-CSL transitions are accompanied by a pronounced qualitative change in the behavior of $kappa_{xy}$ as a function of $B$. In particular, analogously to the quantum Hall effect, $kappa_{xy}$ in the CSL phase exhibits a quantized plateau centered around a commensurate value of the spinon filling factor $ u_spropto B/D$.
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The search for exotic quantum spin liquid states in simple yet realistic spin models remains a central challenge in the field of frustrated quantum magnetism. Here we consider the canonical nearest-neighbor kagome Heisenberg antiferromagnet restricted to a quasi-1D strip consisting entirely of corner-sharing triangles. Using large-scale density matrix renormalization group calculations, we identify in this model an extended gapless quantum phase characterized by central charge $c=2$ and power-law decaying spin and bond-energy correlations which oscillate at tunably incommensurate wave vectors. We argue that this intriguing spin liquid phase can be understood as a marginal instability of a two-band spinon Fermi surface coupled to an emergent U(1) gauge field, an interpretation which we substantiate via bosonization analysis and Monte Carlo calculations on model Gutzwiller variational wave functions. Our results represent one of the first numerical demonstrations of emergent fermionic spinons in a simple SU(2) invariant nearest-neighbor Heisenberg model beyond the strictly 1D (Bethe chain) limit.
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.
The recent observation of a half-integer quantized thermal Hall effect in $alpha$-RuCl$_3$ is interpreted as a unique signature of a chiral spin liquid with a Majorana edge mode. A similar quantized thermal Hall effect is expected in chiral topological superconductors. The unavoidable presence of gapless acoustic phonons, however, implies that, in contrast to the quantized electrical conductivity, the thermal Hall conductivity $kappa_xy$ is never exactly quantized in real materials. Here, we investigate how phonons affect the quantization of the thermal conductivity focusing on the edge theory. As an example we consider a Kitaev spin liquid gapped by an external magnetic field coupled to acoustic phonons. The coupling to phonons destroys the ballistic thermal transport of the edge mode completely, as energy can leak into the bulk, thus drastically modifying the edge-picture of the thermal Hall effect. Nevertheless, the thermal Hall conductivity remains approximately quantized and we argue, that the coupling to phonons to the edge mode is a necessary condition for the observation of the quantized thermal Hall effect. The strength of this edge coupling does, however, not affect the conductivity. We argue that for sufficiently clean systems the leading correction to the quantized thermal Hall effect, $Delta kappa_{xy}/T sim text{sign(B)} , T^2$, arises from a intrinsic anomalous Hall effect of the acoustic phonons due to Berry phases imprinted by the chiral (spin) liquid in the bulk. This correction depends on the sign but not the amplitude of the external magnetic field.
Using a two-dimensional square lattice Heisenberg model with a Rashba-type Dzyaloshinskii-Moriya interaction, we demonstrate that chiral spin fluctuations can give rise to a thermal Hall effect in the absence of any static spin texture or momentum space topology. It is shown by means of Monte Carlo and stochastic spin dynamics simulations that the thermal Hall response is finite at elevated temperature outside of the linear spin wave regime and consistent with the presence of thermal fluctuation-induced nontrivial topology. Our result suggests that the high-fluctuation phases outside of the conventional regime of magnonics may yet be a promising area of exploration for spin-based electronics.
The spinon continues to be an elusive elementary excitation of frustrated antiferromagnets. To solidify evidence for its existence, we address the question of what will be the Angle Resolved Photoemission Spectroscopy (ARPES) signatures of single crystal samples of Herbertsmithite assuming it is described by the Dirac spin liquid state. In particular, we show that the electron spectral function will have a linear in energy dependence near specific wave vectors and that this dependence is expected even after fluctuations to the mean field values are taken into account. Observation of this unique signature in ARPES will provide very strong evidence for the existence of spinons in greater than one dimension.
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