Thermal transport for probing quantum materials
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t = κe + κ ph + κother .
Introduction Quantum materials encompass a broad category of condensedmatter phases where emergent quantum phenomena play a decisive role in materials properties of interest,1 including conventional and unconventional superconductors,2–6 band topology such as quantum Hall families,7–15 topological insulators,16–18 topological semimetals,19–22 particularly Dirac and Weyl semimetals,23–26 frustrated magnetism and multiferroics,27–33 and graphene and low-dimensional van der Waals heterostructures.34–40 The manifestation of quantum effects usually requires low temperatures with suppressed thermal fluctuation. While electrical transport is often used to probe quantum phenomena, thermal transport seems to be less appreciated as it will unavoidably introduce some finite temperature effects. A natural question follows—why thermal transport in quantum materials? To address this question, it might be worthwhile to point out that although we can always perform thermal-transport measurements in a quantum material, it may not necessarily provide more information beyond electrical transport measurements. With this perspective in mind, we limit the scope of this article to where thermal transport can provide unique insights, with an emphasis on the emergent phenomena originating from the correlation effect and topology. The total thermal conductivity κ tot of a material can be written as the sum of contributions from electrons (κ e ), phonons (κ ph ) and other carriers (κ other )
(1)
For a large category of materials, the electronic contribution, κe , is related to electrical conductivity σ via the Wiedemann– Franz Law41 κe = L, σT
(2)
where T is the temperature, and the Lorenz number, 2
L≡
π2 kB −8 2 = 2.44 × 10 WΩ/K 3 e
is a universal constant in metals in which kB is Boltzmann constant and e is the elementary charge, but depends on carrier density in semiconductors. A large deviation of the Lorenz number from the universal value provides a clue to quantum transport, as is observed in the metal–insulator transition.42 At low temperatures, the phonon thermal conductivity, κph , can generally be well described by Debye’s model (i.e., κ ph ∝ T 3 for an isotropic material). For an electrically insulating material with κe = 0, the measurement of total thermal conductivity κ tot becomes suitable to probe other itinerant quasiparticles, κother, beyond the phonon contribution. As we will see, this is the case why thermal transport plays a crucial role in quantum spin liquids (QSLs). The previously discussed argument largely applies to longitudinal transport (Figure 1a). Transverse transport as
Mingda Li, Department of Nuclear Science and Engineering, Massachussetts Institute of Technology, USA; [email protected] Gang Chen, Department of Mechanical Engineering, Massachussetts Institute of Technology, USA; [email protected] doi:10.1557/mrs.2020.124
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• VOLUME 45 • MAY 2020 Uppsala • mrs.org/bulletin Downloaded MRS fromBULLETIN https://www.cambridge.org/core. Universitetsbibliotek, on 12 May 2020 a
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