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At least 1,351 records · Page 75

Reaching 1.5 and 2.0 °C global surface temperature targets using stratospheric aerosol geoengineering

A new set of stratospheric aerosol geoengineering (SAG) model experiments has been performed with Community Earth System Model version 2 (CESM2) with the Whole Atmosphere Community Climate Model (WACCM6) that are based on the Coupled Model Intercomparison Project phase 6 (CMIP6) overshoot scenario (SSP5-34-OS) as a baseline scenario to limit global warming to 1.5 or 2.0 °C above 1850–1900 conditions. The overshoot scenario allows us to applying a peak-shaving scenario that reduces the needed duration and amount of SAG application compared to a high forcing scenario. In addition, a feedback algorithm identifies the needed amount of sulfur dioxide injections in the stratosphere at four pre-defined latitudes, 30 °N, 15 °N, 15 °S, and 30 °S, to reach three surface temperature targets: global mean temperature, and interhemispheric and pole-to-Equator temperature gradients. These targets further help to reduce side effects, including overcooling in the tropics, warming of high latitudes, and large shifts in precipitation patterns. These experiments are therefore relevant for investigating the impacts on society and ecosystems. Comparisons to SAG simulations based on a high emission pathway baseline scenario (SSP5-85) are also performed to investigate the dependency of impacts using different injection amounts to offset surface warming by SAG. We find that changes from present-day conditions around 2020 in some variables depend strongly on the defined temperature target (1.5 °C vs. 2.0 °C). These include surface air temperature and related impacts, the Atlantic Meridional Overturning Circulation, which impacts ocean net primary productivity, and changes in ice sheet surface mass balance, which impacts sea level rise. Others, including global precipitation changes and the recovery of the Antarctic ozone hole, depend strongly on the amount of SAG application. Furthermore, land net primary productivity as well as ocean acidification depend mostly on the global atmospheric CO 2 concentration and therefore the baseline scenario. Multi-model comparisons of experiments that include strong mitigation and carbon dioxide removal with some SAG application are proposed to assess the robustness of impacts on societies and ecosystems.

42 ENGINEERING↗

Predicting Thermal Excursions During in situ Oxidative Regeneration of Packed Bed Catalytic Fast Pyrolysis Catalyst

Ex situ catalytic fast pyrolysis (CFP) uses a secondary reactor to upgrade biomass pyrolysis vapors to stabilized CFP oils with reduced oxygen content. In one configuration, the secondary reactor is operated as a packed-bed swing reactor system which allows coke-deactivated beds to be decarbonized in situ while other beds remain online for vapor upgrading. In situ decarbonization must be done carefully to avoid irreversible deactivation and/or physical degradation of catalyst pellets. Given that packed bed reactors are well known to have poor heat transfer characteristics, this is a critical issue impacting scaleability and commercial viability of the technology. To predict thermal excursions during regeneration, finite element computational models have been built to assist in scaling up oxidative decarbonization of a Pt/TiO2 CFP catalyst (0.5 mm spheres) from a bench scale packed bed with 100 g of catalyst to a pilot scale packed bed with 2 kg of catalyst and internal cooling tubes. Based on transient measurements of outlet temperature and effluent CO2 concentration, and using an assumed coke profile and activation energy, this paper demonstrates that specific combinations of effective thermal conductivity and wall heat transfer coefficient can fit bench scale oxidative regeneration data equally well. For the upscaled 2 kg bed, four bench-scale “best fit” parameter pairs give different predictions for location and magnitude of thermal excursions, with the maximum computed bed temperature gradients ranging from 30 °C cm-1 to as high as 3000 °C cm-1. The larger the fraction of heat removal by conduction through the cooling tubes, the greater the differences between the parameter pairs. The modelling results presented in this paper cast doubt on the industrial viability of the proposed combination of catalyst, bed and regeneration process, and point to the need for alternate reactor designs. However, there is considerable uncertainly in some of the key model parameters. The reliability of model predictions can be increased by adding more temperature measurements at key bed locations, testing additional variations in process conditions, performing careful bed dissections to determine the true coke profile, and perhaps most importantly, directly measuring the effective thermal conductivity of the catalyst pellets.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Low-gravity experiments on Liquid Phase Miscibility Gap (LPMG) alloys: Materials Experiments Assembly (MEA)

Space shuttle experiments which study the massive separation which occurred during sounding rocket Al-In alloy tests are described. The gradient cool experiment studies surface tension driven droplet migration and particle pushing in an LPMG alloy. Isothermal experiments on the Te-Tl alloys test the hypothesis that LPMG systems with low surface energies produce relatively fine, and uniform emulsions and dispersions. It also examines the effect of droplet concentration on phase separation kinetics. Isothermal plunger experiments on Al-In alloys determine whether surface tension driven convection currents originating at a free surface contribute to massive separation. They ascertain whether In-rich droplets migrate under the action of a temperature gradient when they are not influenced by the crucible walls.

Gelles, S. H.↗

C III density diagnostics in nonequilibrium plasmas

Mass flow through a temperature gradient can produce substantial departures of the ionization states from their equilibrium values and can change the character of line emission. The effect of such flows on extreme ultraviolet intensities in the solar atmosphere is evaluated for the beryllium-sequence ion C III, which is an easily observed and powerful diagnostic of electron density in a collisionally dominated plasma. A downflow of material in a transition region can lead to an underestimate of the electron density; outflow of material, as in a stellar or solar wind passing from chromospheric to coronal temperatures, yields a reliable density diagnostic. Ambiguities in the analysis of ultraviolet emission lines can be circumvented by measurement of several transitions.

Raymond, J. C.↗

Modeling of heat transfer, fluid flow and solidification microstructure of nickel-base superalloy fabricated by laser powder bed fusion

Laser-Powder Bed Fusion (L-PBF), an additive manufacturing process, produces a distinctive microstructure that closely resembles the weld metal microstructure but at a much finer scale. The solidification parameters, particularly temperature gradient and solidification rate, are important to study the as-built microstructure. In the present paper, a computational framework with meso-scale resolution is developed for L-PBF of Inconel ® 718 (IN718), a Ni-base superalloy. The framework combines a powder packing model based on Discrete Element Method and a 3-D transient heat and fluid flow simulation. The latter, i.e., the molten pool model, captures the interaction between laser beam and individual powder particles including free surface evolution, surface tension and evaporation. The solidification parameters, calculated from the temperature fields, are used to assess the solidification morphology and grain size using existing theoretical models. The IN718 coupon built by L-PBF are characterized using optical and scanning electron microscopies. Finally, the experimental data of molten pool size and solidification microstructure are compared to the corresponding simulation results.

36 MATERIALS SCIENCE↗

Separate effects irradiation testing of miniature fuel specimens

We report that qualification of new nuclear fuels is necessary for their deployment and requires a thorough understanding of fuel behavior under irradiation. Traditionally, nuclear fuels have been qualified by performing exhaustive integral tests under a limited range of prototypic conditions designed for their specific reactor application. While some integral fuel testing is essential, basic data on behavior and property evolution under irradiation can be obtained from separate effects tests. These irradiations could offer reduced cost, reduced complexity, and in the case of accelerated testing, reduced time to achieve a given burnup. Furthermore, it may be desirable to design test irradiations capable of deconvoluting the myriad effects of burnup, temperature gradients, and other factors inherent to integral irradiation tests. Oak Ridge National Laboratory has developed an experimental capability to perform separate effects irradiation testing of miniature fuel specimens in the High Flux Isotope Reactor (HFIR): the “MiniFuel” irradiation vehicle. The small size (<4 mm 3 ) of the fuel specimens simplifies the design, analysis, and post-irradiation examination. By reducing the fuel mass, the total heat generated inside the experiment vehicle can be dominated by gamma heating in the structural materials instead of fission heating in the fuel. This essentially decouples the fuel temperature from the fission rate, allowing for highly accelerated testing (3X-18X the burnup rate of a typical light water reactor for 235 U enrichments varying from 0.22 wt% to 8 wt%) and an extremely flexible experiment design that can accommodate a wide range of fuel temperatures (~100 °C to >1200 °C), compositions, enrichments, and even geometries without requiring detailed analyses for each fuel variant. In conclusion, this paper summarizes the experiment design concept, evaluates potential applications for specific fuel forms, and briefly describes the first set of experiments on uranium nitride kernels that have been assembled and are currently being irradiated in the HFIR.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Bentonite buffer under high temperature: laboratory experiments and coupled process modeling

Abstract. Bentonite buffer in a geological repository will be simultaneously heated from decaying radioactive waste and hydrated from the surrounding host rock, triggering complex and coupled THMC (thermal–hydrological–mechanical–chemical) processes. Understanding the THMC behavior of bentonite-based engineered barrier system (EBS) is key to the evaluation and prediction of its long-term performance. Studies on the THMC process have been focused on conditions under 100 ∘C, as most design concepts impose a thermal limit of 100 ∘C in bentonite. Recently, studies under high-temperature conditions have been conducted to evaluate the possibility of raising the thermal limit and expanding the data/knowledge base to increase the confidence level. In this abstract, we present a series of bench-scale laboratory experiments at high temperatures (up to 200 ∘C) and the corresponding modeling work. Two sets of column tests were conducted, and each set consisted of two test columns: a control column undergoing only hydration (non-heated) and an experiment column experiencing both heating and hydration (heated). During the experiment, frequent X-ray computed tomography (CT) images were collected to provide a 3D visualization of the density distribution and present the spatiotemporal evolution of (1) hydration/dehydration, (2) clay swelling/shrinkage, (3) displacement, and (4) mineral precipitation. The two sets of tests differ with respect to several experimental conditions, such as bentonite type, compacted density and water content, water chemistry, and hydration pressure, but the important difference is that the first set used bentonite powder with a dry density of 1.28 g cm−3, whereas the second set used granulated bentonite (mixture of pellets and powder) with a dry density of 1.45–1.5 g cm−3. In both sets of experiments, a comprehensive post-dismantling characterization of bentonite samples was carried out after the column tests had been running for 1.5 years. Comparing non-heated and heated columns, the temperature gradient led to lower degree of homogenization of bentonite after bentonite became fully saturated; comparing the first and second sets, granulated and powdered bentonite exhibited drastically different hydration behavior. A THM model with a 2D axisymmetric grid system was used to interpret the data from the first set of tests. The model considers the combined impact of saturation, fluid pressure, and porosity change due to swelling/compression on the spatiotemporal distribution of bulk density and movement of the thermocouple modules. Observations from the tests help us understand the early perturbation of bentonite buffer under high temperature, and data from these tests improve the calibration of key constitutive hydrological and mechanical models and, therefore, enhance the modeling capability with respect to calculating the long-term evolution of bentonite buffer.

Zheng, Liange↗

Thermocapillary Flows with Low Frequency g-Jitter

A thermocapillary parallel flow is established in a fluid filled slot with an applied temperature gradient. Low frequency jitter is imposed in arbitrary directions. Vertical jitter proves to be relatively uninteresting, merely augmenting or opposing the basic thermocapillary flow. Streamwise jitter still produces parallel flows, but these now exhibit boundary layers or layered cellular structures for large Rayleigh number as the applied stratification alternates between stable and unstable. Runaways are possible for unstable stratification and these correspond to resonant excitation of stationary long wave Rayleigh-Benard modes. Spanwise jitter produces fully three dimensional motion. A spanwise-streamwise circulation results for weak spanwise jitter, which advects the interfacial temperature establishing a subsidiary spanwise thermocapillary flow. This flow is strong at small Biot number when advected temperature is trapped in the slot, and has a counter-intuitive dependence on the spanwise-streamwise aspect ratio.

Grassia, P.↗

Weakening of the Extratropical Storm Tracks in Solar Geoengineering Scenarios

Solar geoengineering that aims to offset global warming could nonetheless alter atmospheric temperature gradients and humidity and thus affect the extratropical storm tracks. Here, we first analyze climate model simulations from experiment G1 of the Geoengineering Model Intercomparison Project, in which a reduction in incoming solar radiation balances a quadrupling of CO 2 . The Northern Hemisphere extratropical storm track weakens by a comparable amount in G1 as it does for increased CO2 only. The Southern Hemisphere storm track also weakens in G1, in contrast to a strengthening and poleward shift for increased CO 2 . Using mean available potential energy, we show that the changes in zonal-mean temperature and humidity are sufficient to explain the different responses of storm-track intensity. We also demonstrate similar weakening in a more complex geoengineering scenario. Here, our results offer insight into how geoengineering affects storm tracks, highlighting the potential for geoengineering to induce novel climate changes.

54 ENVIRONMENTAL SCIENCES↗

Determination of the effects of heating on modal characteristics of an aluminum plate with application to hypersonic vehicles

The structural integrity of proposed high speed aircraft can be seriously affected by the extremely high surface temperatures and large temperature gradients throughout the vehicle's structure. Variations in the structure's elastic characteristics as a result of thermal effects can be seen by changes in vibration characteristics. Analysis codes that predict these changes must be correlated and verified with experimental data. Analytical and experimental modal test results are given from uniform, nonuniform, and transient thermoelastic vibration tests of a 12 x 50 x 0.19 aluminum plate. The data show the effect of heat on the modal characteristics of the plate. The results showed that frequencies decreased, damping increased, and mode shapes remained unchanged as the temperature of the plate increased. Analytical predictions provided good correlation with experimental results.

Snyder, H. Todd↗

X-ray spectroscopy of multi-temperature plasmas using the differential emission measure formalism

We present a theoretical construct that nominally underlies spectroscopic data analysis of multi-temperature plasmas, known as the differential emission measure (DEM). From a data analytic perspective, the DEM formalism is used to derive temperature distributions from line spectra that are formed in the presence of temperature gradients and by time integrations of evolving plasmas. From a modeling perspective, DEMs are convenient intermediaries between radiation hydrodynamics simulations and spectroscopic measurements acquired in the laboratory. The DEM concept and its associated methodologies were originally developed by spectroscopists working with astrophysical data. We borrow from these earlier investigations. In this manuscript, intended primarily as a tutorial, we discuss the basic concepts, but also augment various aspects of the theory by the way of extension and example, including a detailed treatment of various weighting and averaging schemes, intended to mitigate ambiguities that often arise when reporting temperature information. We focus on high-temperature plasmas that are not in local thermodynamic equilibrium and the x-ray spectra that they produce, although the core ideas presented here are applicable to spectroscopy in other energy bands. A few examples involving the derivation and manipulation of model DEMs in simple geometries are provided.

Liedahl, Duane A. [Lawrence Livermore National Lab↗

Observation of Vector Spin Seebeck Effect in a Noncollinear Antiferromagnet

Spintronic phenomena to date have been established in magnets with collinear moments, where the spin injection through the spin Seebeck effect (SSE) is always along the out-of-plane direction. Here, we report the observation of a vector SSE in a noncollinear antiferromagnet (AF) LuFeO 3 , where temperature gradient along the out-of-plane and also the in-plane directions can both inject a pure spin current and generate a voltage in the heavy metal via the inverse spin Hall effect (ISHE). We show that the thermovoltages are due to the magnetization from canted spins in LuFeO 3 . Furthermore, in contrast to the challenges of generating, manipulating, and detecting spin current in collinear AFs, the vector SSE in LuFeO 3 is readily viable in zero magnetic field and can be controlled by a small magnetic field of about 150 Oe at room temperature. Furthermore, the noncollinear AFs expand new realms for exploring spin phenomena and provide a new route to low-field antiferromagnetic spin caloritronics and magnonics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Direct selective laser sintering of hexagonal barium titanate ceramics

Abstract A direct selective laser sintering (SLS) process was combined with a laser preheating procedure to decrease the temperature gradient and thermal stress, which was demonstrated as a promising approach for additive manufacturing of BaTiO 3 ceramics. The phase compositions in BaTiO 3 ceramics fabricated by SLS were investigated by X‐ray and neutron diffractions. The surface morphologies and cross‐section microstructures were characterized by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). A dense hexagonal h‐BaTiO 3 layer was formed on the surface and extended to a depth of 500 μm, with a relative density higher than 97% and absence of pores or microcracks. SLS resulted in the formation of the high‐temperature phase, h‐BaTiO 3 , which was retained at room temperature possibly due to the high cooling rate. The grain boundaries of SLSed h‐BaTiO 3 ceramics consist of a Ti‐rich secondary phase. Compared with that of the pressureless sintered t‐BaTiO 3 ceramics, the Vickers hardness of SLSed h‐BaTiO 3 is 70% higher.

Zhang, Xiang↗

Use of rotation to suppress thermosolutal convection in directionally solidified binary alloys

Effects of rotation on onset of convection during plane-front directional solidification of Pb-Sn and the pseudobinary system mercury cadmium telluride (Hg(1-x)Cd(x)Te), and on dendritic solidification of Pb-Sn have been studied by means of linear stability analysis. Incorporating Coriolis and centrifugal accelerations into the momentum equation of Coriell et al., we find that under realistic processing conditions, a large degree of stabilization can be achieved using modest rotation rates for both Pb-Sn and mercury cadmium telluride. At a growth velocity of 5 micron/sec and nominal liquid-side temperature gradient of 200 K/cm in Pb-Sn, rotation at 500 rpm results in a hundredfold increase in the critical Sn concentration. Large increases in the maximum allowable growth velocity at fixed melt composition are also attainable with modest rotation rates. The effect is amplified under conditions of reduced gravitational acceleration. For Hg(1-x)Cd(x)Te, we have also studied the nonrotating case. The key differences are due to the existence of a composition range for Hg(1-x)Cd(x)Te in which the melt density has a local maximum as a function of temperature. When the melt solidifies by cooling from below, the liquid density may initially increase with distance above the interface, before ultimately decreasing as the melt temperature increases above the value at which the local density maximum occurs. In contrast to the Pb-Sn case where density depends monotonically on temperature and composition, for Hg(1-x)Cd(x)Te there exists a critical value of the growth velocity above which plane-front solidification is unstable for all bulk CdTe mole fractions. Again, rotation leads to significant inhibition of onset. We identify the predicted stabilization with the Taylor-Proudman mechanism by which rotation inhibits thermal convection in a single-component fluid heated from below. In a binary liquid undergoing solidification, rotation inhibits the onset of buoyancy-driven convection, and has no effect on the short-wavelength morphological instability. At large growth velocities, the plane-front interface between liquid and solid becomes unstable with respect to a morphological instability and solidification occurs dendritically, with a mushy zone of dendrites and interdendritic fluid separating the solid from the melt. For the Pb-Sn system, rotation substantially suppresses the onset of convection in the mushy zone and in the overlying liquid, holding open the promise that rotation can suppress freckling and other macrosegregation defects.

Pearlstein, Arne J.↗

SWIFT BAT Loop Heat Pipe Thermal System Characteristics and Ground/Flight Operation Procedure

The SWIFT Burst Alert Telescope (BAT) Detector Array has a total power dissipation of 208 W. To meet the stringent temperature gradient and thermal stability requirements in the normal operational mode, and heater power budget in both the normal operational and safehold modes, the Detector Array is thermally well coupled to eight constant conductance heat pipes (CCHPs) embedded in the Detector Array Plate (DAP), and two loop heat pipes (LHPs) transport heat fiom the CCHPs to a radiator. The CCHPs have ammonia as the working fluid and the LHPs have propylene as the working fluid. Precision heater controllers, which have adjustable set points in flight, are used to control the LHP compensation chamber and Detector Array XA1 ASIC temperatures. The radiator has the AZ-Tek AZW-LA-II low-alpha white paint as the thermal coating and is located on the anti-sun side of the spacecraft. This paper presents the characteristics, ground operation and flight operation procedures of the LHP thermal system.

Choi, Michael K.↗

Quantifying the Uncertainty in Deterministic Phonon Transport Calculations of Thermal Conductivity using Polynomial Chaos Expansions

The nature of computational simulations requires the inclusion of an uncertainty analysis, as we have limited knowledge of all physically determined input parameters for a computationally simulated problem. We rely on uncertainty quantification (UQ) to characterize our confidence in the outcomes. Quantifying uncertainty can provide a basis for certifications in high-consequence decisions, such as nuclear reactor design, and is a fundamental component of model validation. We employ a previously developed method of uncertainty quantification, polynomial chaos expansion with stochastic collocation (PCE-SC), applied to deterministic phonon transport simulations. In these simulations, we use the neutron transport code Rattlesnake, which solves the Self-Adjoint Angular Flux (SAAF) formulation of the transport equation with a continuous finite element (CFEM) spatial discretization and discrete ordinates, spherical harmonics angular discretizations. Rattlesnake was developed in the multi-physics object oriented simulation environment (MOOSE) framework. We have previously shown Rattlesnake to be effective in simulating phonon transport. We aim to provide a deterministic phonon transport framework for heterogeneous nuclear fuel with fission product defects to predict thermal conductivity (?). A first principles, physics-based calculation of thermal conductivity must involve factors such as the microstructure of nuclear fuel, which constantly changes during the fission process through the formation of isotopic decay products. Heat transport in oxide nuclear fuels is dominated by phonon transport. Impurities in the bulk material influence the transport of energy at the fundamental level, altering the scattering behavior of phonons and electrons. Conventionally, heat transport follows classical physics based on the heat equation derived from Fourier's law q = -k∇T, where q is heat flux, k is thermal conductivity and ∇T is a temperature gradient. However, Fourier's law is a macroscopic empirical law in which the thermal conductivity? does not have a mechanistic connection to the underpinning heat transport processes. Thermal conductivity of a material depends both on the material's intrinsic ability to transport heat and a variety of resistive effects caused by defects in the material. Thus ab initio prediction of the macroscopic conductivity - the property of interest for safe reactor operation - requires simulating detailed processes of heat transport, and then determining the effective thermal conductivity of the simulated material from the resulting heat flux under the imposed temperature difference. The thermal conductivity of a bulk, homogeneous, dielectric material can be well estimated by the mechanistically derived expression: k{sub bulk} = 1/3 C{sub ν}νgλ (2), where C{sub ν}, νg, and λ are the volumetric specific heat, phonon speed, and phonon mean free path, respectively. In these problems the relevant parameter is the material's acoustic thickness, its characteristic distance L relative to the phonon mean free path λ. In Eq. (2) the largest source of uncertainty is λ. While propagating uncertainty in λ to uncertainty in k through Eq. (2) is trivial, systems with extrinsic scattering require more sophisticated approaches. At the microscopic level, uncertainty in λ changes both a material's intrinsic thermal conductivity. Our goal is to propagate the uncertainty in λ through the deterministic transport computation of k. Because there are a small number of uncertain input quantities, we use the method of polynomial chaos expansion (PCE), which expresses solutions in the form of spectral expansions of an uncertain variable. This approach combines both intrusive and nonintrusive methods of uncertainty propagation techniques and results in a unique formulation which is very effective and efficient for problems with few uncertain parameters. Uncertainty Quantification and Sensitivity Analysis We use PCE-SC to measure propagation of uncertainty in a 3-D phonon transport problem of homogeneous silicon, to compute the mean and variance in temperature, heat flux and thermal conductivity. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Satellite and Skin Layer Effects on the Accuracy of Sea Surface Temperature Measurements from the GOES Satellites

The latest Geostationary Operational Environmental Satellites (GOES) have facilitated significant improvements in our ability to measure sea surface temperature (SST) from geostationary satellites. Nonetheless, difficulties associated with sensor calibration and oceanic near-surface temperature gradients affect the accuracy of the measurements and our ability to estimate and interpret the diurnal cycle of the bulk SST. Overall, measurements of SST from the GOES Imagers on the GOES 8-10 satellites are shown to have very small bias (less than 0.02 K) and rms differences of between 0.6 and 0.9 K relative to buoy observations. Separate consideration of individual measurement times, however, demonstrates systematic bias variations of over 0.6 K with measurement hour. These bias variations significantly affect both the amplitude and shape of estimates of the diurnal SST cycle. Modeled estimates of the temperature difference across the oceanic cool skin and diurnal thermocline show that bias variations up to 0.3 K can result from variability in the near-surface layer. Oceanic near-surface layer and known "satellite midnight" calibration effects, however, explain only a portion of the observed bias variations, suggesting other possible calibration concerns. Methods of explicitly incorporating skin layer and diurnal thermocline effects in satellite bulk SST measurements were explored in an effort to further improve the measurement accuracy. While the approaches contain more complete physics, they do not yet significantly improve the accuracy of bulk SST measurements due to remaining uncertainties in the temperature difference across the near-surface layer.

Wick, Gary A.↗

Quantization of the Thermal Hall Conductivity at Small Hall Angles

We consider the effect of coupling between phonons and a chiral Majorana edge in a gapped chiral spin liquid with Ising anyons (e.g., Kitaev’s non-Abelian spin liquid on the honeycomb lattice). This is especially important in the regime in which the longitudinal bulk heat conductivity κ x x due to phonons is much larger than the expected quantized thermal Hall conductance $κ$ $^{q}_{xy}$ = (πT/12)($k$ $^{2}_{B}$/ℏ) 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 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 >> ℓ, where ℓ is a thermalization length. We obtain ℓ ~ 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. Furthermore, our results may explain recent experiments observing a quantized thermal Hall conductivity in the regime of small Hall angle, κ xy /κ xx ~ 10 –3 , in α–RuCl 3 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗