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In the context of recent experimental observations of an unexpectedly large thermal Hall conductivity, $\kappa_H$, in insulating $\mathrm{La_2CuO_4}$ (LCO) and $\mathrm{SrTiO_3}$ (STO), we theoretically explore conditions under which acoustic phonons can give rise to such a large $\kappa_H$.
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If Δ H ¯ ≠ 0 \overline{\Delta H}\not=0 in electron scattering (e.g. when disorders are mostly repulsive Ishizuka and Nagaosa 2017 ), then the leading Berry curvature induced skew scattering occurs at ( Δ H ) 3 ¯ ∼ 1 / ℓ 3 / 2 \overline{(\Delta H)^{3}}\sim 1/\ell^{3/2} , hence its contribution to σ H \sigma_{H} is 1 / ℓ 1 / 2 1/\ell^{1/2} smaller than σ L \sigma_{L}
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We have used the bulk value of χ ϵ 0 F \chi\epsilon_{0}F . Near the twin boundaries where the scatterings occur, the local value is likely different (probably enhanced) due to the localized dipoles and structures Zubko et al. 2007 ; Scott et al. 2012 ; Morozovska et al. 2012
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2012
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P. Zubko, G. Catalan, and A. K. Tagantsev, Annual Review of Materials Research 43
2013
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Between 10 − 20 K 10-20\mathrm{K} the phenomenon of Poiseuille flow Guyer and Krumhansl 1966a ; Guyer and Krumhansl 1966b is observed Martelli et al. 2018 , where κ L \kappa_{L} increases faster than T 3 T^{3} with T T . This is because the onset of phonon-phonon interactions decreases the true diffusion velocity compared to the ballistic phonon velocity, and hence increases the relaxation time. Similar increase is observed in κ H \kappa_{H} in the same temperature range Li et al. 2020 , in support of our interpretation of κ H \kappa_{H} as an extrinsic effect
2018
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G. Grissonnanche, A. Legros, S. Badoux, E. Lefrançois, V. Zatko, M. Lizaire, F. Laliberté, A. Gourgout, J.-S. Zhou, S. Pyon, et al. , Nature 571
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2020
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The measured values of κ H \kappa_{H} appear to vary by of order a factor of two for different samples, and even for the same sample if a thermal cycle is performed across the tetragonal transition temperature at 105 K 105\mathrm{K} . This is taken as evidence that κ H \kappa_{H} is due extrinsically to twin boundaries Li et al. 2020 , although why the dependence on thermal history is larger in κ H \kappa_{H} than in κ L \kappa_{L} remains unclear without a modeling of the scattering process
2020
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