Frontiers in Thermal Transport and Energy Conversion Proceedings of a Workshop (2020) / Chapter Skim
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THERMAL TRANSPORT AND QUASIPARTICLE HYDRODYNAMICS Kamran Behnia, ESPCI Behnia set the stage with a brief history of the field of thermal and electrical conduction; discussed how different scientific branches view transport; and addressed the hydrodynamics of phonons, electron hydrodynamics, and a possible boundary to thermal diffusivity.
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In the low-temperature limit, the mean free path becomes as large as the sample size. Therefore, the Drude model implies that the bigger the solid, the higher the peak of the thermal conductivity.
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Baggio-Saitovitch, and K Behnia, 2018, Thermal transport and phonon hydrodynamics in strontium titanate, Physical Review Letters (120)
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Electron Hydrodynamics Electron hydrodynamics is harder to observe because the samples have to be extremely pure to meet the ballistic regime. An examination of thermal transport data allows a fresh look at the study of electron hydrodynamics.
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These two components can be considered the counterparts of the two fluids of the superfluid. In response to a question about the thermal diffusivity of glasses, Behnia noted that thermal diffusivity decreases with warming in a glass.
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12 and that, when the mean free path is too short, thermal diffusivity is reminiscent of electrical diffusivity in "bad" metals, which also have short mean free paths.13 Finally, it has been shown that it is possible to violate the Wiedemann-Franz (WF) law, because if WF was true, the electronic contribution would be larger than the total thermal conductivity, which is impossible.14 Physics without quasiparticles brings many new questions, according to Hart nell, such as: How can we determine diffusivity in the absence of quasiparticles?
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DQ-1[s/cm2] "Thermal Diffusivity Above Mott-Ioffe-Regel Limit," revised March 18, 2019, arXiv:1808.07564, used at high temperatu thermal conductivity with permission.
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According to Fourier's law, temperature diffuses. Temperature must be defined by a local thermal equilibrium, which takes time to establish itself; this local ther malization time is the time scale over which everything (except the perturbations)
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This results in hopping in an emergent disordered landscape, allowing the energy change between neighboring parts to take a continuum of values.16 Hartnoll explained that this process creates a way to calculate diffusivity as a function of temperature as well as the Lorentz ratio, whose value is extremely small, because at high temperatures, heat current and electrical current are proportional to each other. Future Challenges Several challenges emerge when moving beyond quasiparticles, although Hartnoll expressed confidence they will be overcome.
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THERMAL HALL EFFECT FROM NEUTRAL SPIN EXCITATIONS IN FRUSTRATED QUANTUM MAGNETS N Phuan Ong, Princeton University Ong discussed applying the thermal Hall effect as a potentially important trans port probe to investigate the state of matter called quantum spin liquids (QSLs)
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The fractional quantum Hall effect is a highly entangled, many-body ground state. Two important models for gapped QSLs are the Toric code model and the Kitaev hexagonal spin-exchange model.19,20 Kitaev's 2003 and 2006 papers, which inform much of this work, introduced many of the concepts (Majorana particles, visons, spinons, fusion rules, braiding rules)
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. In a growing group of frustrated quantum mag nets, there exists a large thermal Hall effect that must arise from spin excitations in the candidate QSL state.
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uncovered a large thermal Hall conductivity which increased monotonically with decreasing temperature (Figure 2.3) .26 This thermal Hall signal -- presumably arising from the intrinsic Berry curvature in the QSL state -- is suppressed in a strong magnetic field that destroys the QSL state altogether by aligning the spins.
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The material resists ordering even at very low temperatures, displaying very large magnetocaloric effects related to weak coupling between the spin excitations and the phonons. 2017, Reentrant phase diagram of Yb2Ti2O7 in a ⟨111⟩ magnetic field, Physical Review Letters (119)
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This new QSL candidate is even more promising than the pyrochlores discussed above, Ong said, but as with the earlier pyrochlores, a strong magnetic field kills the QSL state of interest. Deep in the QSL state, the heat current carried by the spin excitations approaches a very small value as the temperature is decreased to 0.3 Kelvin in a weak magnetic field.
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In an applied temperature gradient, the heat current carried by the transverse edge at the warm end is larger than its opposite counterpart at the cool end. The difference of the transverse currents immediately yields a thermal Hall effect.
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In thermal transport, Hall conductivity and its anti-symmetrized version of the off-diagonal conductivity can uncover properties of these new phases, according to Savary. Experiments in this realm either apply a thermal gradient to a sample or thread an electrical current through a system to achieve a solution to Fourier's law, which relates the energy current to the temperature gradient through the thermal conductivity tensor.
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One platform is spin liquids in a magnetic field, and there may also be some fractional quantum Hall states that are non-Abelian. This is cutting-edge work, and finding a QSL or non-Abelian state would represent a great advance, Savary noted.
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Savary and her team conducted a further experiment, with several different linearized equations and boundary conditions, and reached several conclusions.34 First, the Majorana phonon coupling induces a transverse phonon current which is transferred to the Majoranas. Also, owing to the phase-based constraints, phonon-Majorana oupling, crucial to the quantized Hall effect, becomes less than T-6, and the measured c thermal Hall conductivity vanished at zero temperature, which was unexpected.
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Every heat engine converts random motion into unidirectional motion, essentially functioning as rectifiers. Heremans's talk explored opportunities for improving thermoelectric heat engines, spin-based energy conversion, and magnon-drag thermopower.
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The ZT of a thermoelectric generator is a measurement of the thermal efficiency of that generator in terms of a fraction of the Carnot efficiency: a thermoelectric with a ZT of 1 can have a thermal efficiency about 13 percent of the Carnot efficiency; a ZT of infinity would characterize a generator that meets the Carnot efficiency. Heremans discussed three possible routes toward increased ZT, suggested by equations in which the figure of merit appears as a function of the square of the Seebeck coefficient, S, also known as the thermoelectric power or thermopower, and of the conduction electrons' thermal conductivity (κE)
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This setup attains a spin-Seebeck effect of 2 mV/K in InSb, when the InSb electrons are spin polarized by an external magnetic field. Using aluminum instead of Pt as contact to the InSb shrinks the effect by an order of magnitude, because the electrons in alu minum do not give rise to an inverse spin-Hall effect; in that case, the voltage is only due to the thermoelectric voltage in the InSb.
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Here, the conservation of linear momentum impels a moment to the electrons from the magnon flux, which gives rise to a voltage directly, the magnon-drag thermopower. In principle, the conservation of spin angular momentum should give rise to a transverse voltage in ferromagnets with strong spinorbit coupling as well, but experimental proof for that effect has not yet been found.
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, so is thermal conductivity, and so the ZT is not good. In cobalt, the power factor is about 5 times greater than in classical semiconductors.
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This, in turn, affects phonon scattering on other phonons and reduces thermal conductivity.40 Wrapping up, Heremans called for more work on topological insulators and hybridized magnon-phonon systems and for advancing technologies such as solidstate refrigeration; waste heat scavenging; and thermal diodes, switches, and regulators. He recommended a 2013 paper by Martin Maldovan, then of MIT and the Georgia Institute of Technology, discussing acoustic and thermal cloaking, hypersonic phononic crystals, and more.41 Circling back to unidirectional heat propagation with which he began his talk, Heremans highlighted a 2014 paper proposing possible phonon modes capable of one-way propagation and cited the edge modes from Lucile Savary's work as potentially capable of providing such unidirectionality, if they could be isolated.42 40 H
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They used alu minum, which has no spin-Hall effect, to prove that the effect they observed was related to the spin signal coming from InSb. Another participant asked Heremans why the drag in the paramagnetic regime depends on carrier density whereas the Néel temperature does not.
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