اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدHalf-integer quantized anomalous thermal Hall effect in the Kitaev material $alpha$-RuCl$_3$
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Heat transport mediated by Majorana edge modes in a magnetic insulator leads to a half-integer thermal quantum Hall conductance, which has recently been reported for the two-dimensional honeycomb material $alpha$-RuCl$_3$. While the conventional electronic Hall effect requires a perpendicular magnetic field, we find that this is not the case in $alpha$-RuCl$_3$. Strikingly, the thermal Hall plateau appears even for a magnetic field with no out-of-plane components. The field-angular variation of the quantized thermal Hall conductance has the same sign structure of the topological Chern number, which is either $pm$1, as the Majorana band structure of the pure Kitaev spin liquid. This observation of a half-integer anomalous thermal Hall effect firmly establishes that the Kitaev interaction is primarily responsible and that the non-Abelian topological order associated with fractionalization of the local magnetic moments persists even in the presence of non-Kitaev interactions in $alpha$-RuCl$_3$.
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We have investigated the sample dependence of the half-integer thermal Hall effect in $alpha$-RuCl$_3$ under a magnetic field tilted 45 degree from the $c$ axis to the $a$ axis. We find that the sample with the largest longitudinal thermal conductivi
ty ($kappa_{xx}$) shows the half-integer quantized thermal Hall effect expected in the Kitaev model. On the other hand, the quantized thermal Hall effect was not observed in the samples with smaller $kappa_{xx}$. We suggest that suppressing the magnetic scattering effects on the phonon thermal conduction, which broaden the field-induced gap protecting the chiral edge current of the Majorana fermions, is important to observe the quantized thermal Hall effect.
The Kitaev quantum spin liquid displays the fractionalization of quantum spins into Majorana fermions. The emergent Majorana edge current is predicted to manifest itself in the form of a finite thermal Hall effect, a feature commonly discussed in top
ological superconductors. Here we report on thermal Hall conductivity $kappa_{xy}$ measurements in $alpha$-RuCl$_3$, a candidate Kitaev magnet with the two-dimensional honeycomb lattice. In a spin-liquid (Kitaev paramagnetic) state below the temperature characterized by the Kitaev interaction $J_K/k_B sim 80$ K, positive $kappa_{xy}$ develops gradually upon cooling, demonstrating the presence of highly unusual itinerant excitations. Although the zero-temperature property is masked by the magnetic ordering at $T_N=7$ K, the sign, magnitude, and $T$-dependence of $kappa_{xy}/T$ at intermediate temperatures follows the predicted trend of the itinerant Majorana excitations.
The honeycomb Kitaev model in a magnetic field is a source of a topological quantum spin liquid with Majorana fermions and gauge flux excitations as fractional quasiparticles. We present experimental results for the thermal Hall effect of the materia
l $alpha$-RuCl$_{3}$ which recently emerged as a prime candidate for realizing such physics. At temperatures above long-range magnetic ordering $Tgtrsim T_Napprox8$ K, we observe with an applied magnetic field $B$ perpendicular to the honeycomb layers a sizeable positive transversal heat conductivity $kappa_{xy}$ which increases linearly with $B$. Upon raising the temperature, $kappa_{xy}(T)$ increases strongly, exhibits a broad maximum at around 30 K, and eventually becomes negligible at $Tgtrsim 125$ K. Remarkably, the longitudinal heat conductivity $kappa_{xx}(T)$ exhibits a sizeable positive thermal magnetoresistance effect. Thus, our findings provide clear-cut evidence for longitudinal and transverse magnetic heat transport and underpin the unconventional nature of the quasiparticles in the paramagnetic phase of $alpha$-RuCl$_{3}$.
The quantum Hall effect (QHE) in two-dimensional (2D) electron gases, which is one of the most striking phenomena in condensed matter physics, involves the topologically protected dissipationless charge current flow along the edges of the sample. Int
eger or fractional electrical conductance are measured in units of $e^2/2pihbar$, which is associated with edge currents of electrons or quasiparticles with fractional charges, respectively. Here we discover a novel type of quantization of the Hall effect in an insulating 2D quantum magnet. In $alpha$-RuCl$_3$ with dominant Kitaev interaction on 2D honeycomb lattice, the application of a parallel magnetic field destroys the long-range magnetic order, leading to a field-induced quantum spin liquid (QSL) ground state with massive entanglement of local spins. In the low-temperature regime of the QSL state, we report that the 2D thermal Hall conductance $kappa_{xy}^{2D}$ reaches a quantum plateau as a function of applied magnetic field. $kappa_{xy}^{2D}/T$ attains a quantization value of $(pi/12)(k_B^2/hbar)$, which is exactly half of $kappa_{xy}^{2D}/T$ in the integer QHE. This half-integer thermal Hall conductance observed in a bulk material is a direct signature of topologically protected chiral edge currents of charge neutral Majorana fermions, particles that are their own antiparticles, which possess half degrees of freedom of conventional fermions. These signatures demonstrate the fractionalization of spins into itinerant Majorana fermions and $Z_2$ fluxes predicted in a Kitaev QSL. Above a critical magnetic field, the quantization disappears and $kappa_{xy}^{2D}/T$ goes to zero rapidly, indicating a topological quantum phase transition between the states with and without chiral Majorana edge modes. Emergent Majorana fermions in a quantum magnet are expected to have a major impact on strongly correlated topological quantum matter.
High-resolution thermal expansion and magnetostriction measurements were performed on single crystals of $alpha$-RuCl$_3$ in magnetic fields applied parallel to the Ru-Ru bonds. The length changes were measured in the direction perpendicular to the h
oneycomb planes. Our data show clear thermodynamic characteristics for the field-induced phase transition at the critical field $mu_0H_{c1} = 7.8(2)$ T where the antiferromagnetic zigzag order is suppressed. At higher fields, a kink in the magnetostriction coefficient signals an additional phase transition around $mu_0H_{c2} approx 11$ T. The extracted Gruneisen parameter shows typical hallmarks for quantum criticality near $H_{c1}$, but also displays anomalous behavior above $H_{c1}$. We compare our experimental data with linear spin-wave calculations employing a minimal Kitaev-Heisenberg model in the semiclassical limit. Most of the salient features are in agreement with each other, however, the peculiar features in the high-field region above $H_{c1}$ cannot be accounted for in our modelling and hence suggest a genuine quantum nature. We construct a phase diagram for $alpha$-RuCl$_3$ showing two low-temperature transitions induced by an in-plane field along the Ru-Ru bonds.
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