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Effect of Phonon Focusing and Shear Waves on Drag Thermopower in Potassium Single-Crystal Nanostructures at Low Temperatures. Review 3

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Abstract

The effect of phonon focusing on electron–phonon drag and thermopower in nanostructures based on potassium single crystals at low temperatures is studied. The role of quasi-longitudinal and quasi-transverse phonons, as well as shear waves, in the drag thermopower of the nanostructures is considered. It is shown that, in the Knudsen flow regime of a phonon gas, the slow quasi-transverse t2 mode makes the dominant contribution to the drag thermopower of the nanostructures and, only in directions close to the focusing of longitudinal phonons (L-phonons), their contribution become comparable to the contribution of the t2 mode. The directions of heat flux in which the maximum and minimum values of drag thermopower are achieved in nanowires, films, and nanoplates based on potassium single crystals are determined. The study of the effect of focusing on the phonon propagation in potassium single crystals made it possible to calculate a number of new, unusual effects in the anisotropy of drag thermopower in potassium-based nanostructures. These effects are mainly due to the competition between the contributions of the t2 mode and L-phonons to the drag thermopower. Since the relaxation rate of L-phonons on electrons in potassium is 25 times higher than for the t2 mode, with an increase in the transverse dimensions of potassium nanostructures, the anisotropy of the drag thermopower in them, in contrast to the anisotropy of thermal conductivity in dielectric nanostructures, changes nonmonotonically. It first increases, reaching a maximum, then decreases, and vanishes when the dimensions become macroscopic (D ≥ 10–1 cm). One of the interesting effects calculated in this work is the orientational anisotropy of drag thermopower in potassium nanoplates. In two identical nanoplates with a rectangular cross section, the thermopower in the direction of the temperature gradient [011] for the orientation of the wide faces of the {100} plates turns out to be significantly greater than for the {110} orientation. With increasing plate width, the orientational anisotropy of thermopower increases to 37%. It is shown that the orientational anisotropy of the thermopower is due to the effect of focusing on the phonon propagation in the plates. The competition between the contributions of the t2 mode and L-phonons, which determine the maximum and minimum values, leads to a nonmonotonic dependence of the orientational anisotropy of the drag thermopower on the thickness of the nanoplate. It is shown that, for square potassium films with {100} and {111} orientations of planes, the drag thermopower is isotropic in the film plane, but, for the {110} orientation, it becomes ellipsoidal with its major axis in the [001] direction. A characteristic feature of drag thermopower in square films is orientation anisotropy. For the [011] directions of the temperature gradient, the drag thermopower in potassium films with the {100} orientations of planes turns out to be significantly greater than with the {110} orientations. It behaves nonmonotonically, reaching a maximum of 57% at a thickness D = 2.2 × 10–5 cm. It is obvious that the effects calculated in this work open up new prospects for experimental studies of electron–phonon drag in metal films.

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This work was carried out as part of the state assignment of the Ministry of Education and Science of Russia (topic “Function”, no. 122021000035-6).

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  1. Mikheev Institute of Metal Physics, Ural Branch, Russian Academy of Sciences, 620108, Ekaterinburg, Russia

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ADDITIONAL INFORMATION

This review is an English translation of Chapter 3 of the monograph: I.G. Kuleyev and I.I. Kuleyev, The Role of Quasi-Transverse Phonons and Elastic Anisotropy in Electrical Resistivity and Thermoelectric Effects in Alkali and Noble Metals (Ekaterinburg: UMTS UPI, 2023, p. 205. ISBN 978-5-8295-0882-1).

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Translated by E. Chernokozhin

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Kuleyev, I.I., Kuleyev, I.G. Effect of Phonon Focusing and Shear Waves on Drag Thermopower in Potassium Single-Crystal Nanostructures at Low Temperatures. Review 3. Phys. Metals Metallogr. 124 (Suppl 1), S60–S86 (2023). https://doi.org/10.1134/S0031918X23602160

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