Thermal Hall effect

In solid-state physics, the thermal Hall effect, also known as the Righi–Leduc effect, named after independent co-discoverers Augusto Righi and Sylvestre Anatole Leduc,^[1] is the thermal analog of the Hall effect. Given a thermal gradient across a solid, this effect describes the appearance of an orthogonal temperature gradient when a magnetic field is applied.

For conductors, a significant portion of the thermal current is carried by the electrons. In particular, the Righi–Leduc effect describes the heat flow resulting from a perpendicular temperature gradient and vice versa. The Maggi–Righi–Leduc effect describes changes in thermal conductivity when placing a conductor in a magnetic field.^{[citation needed]}

A thermal Hall effect has also been measured in a paramagnetic insulators, called the "phonon Hall effect".^[2] In this case, there are no charged currents in the solid, so the magnetic field cannot exert a Lorentz force. Phonon thermal Hall effect have been measured in various class of non-magnetic insulating solids,^[3][4][5][6] but the exact mechanism giving rise to this phenomenon is largely unknown. An analogous thermal Hall effect for neutral particles exists in polyatomic gases, known as the Senftleben–Beenakker effect.

Measurements of the thermal Hall conductivity are used to distinguish between the electronic and lattice contributions to thermal conductivity. These measurements are especially useful when studying superconductors.^[7]

Description

Given a conductor or semiconductor with a temperature difference in the x-direction and a magnetic field B perpendicular to it in the z-direction, then a temperature difference can occur in the transverse y-direction,

${\displaystyle {\frac {\partial T}{\partial y}}=R_{\mathrm {TH} }B{\frac {\partial T}{\partial x}}}$

The Righi–Leduc effect is a thermal analogue of the Hall effect. With the Hall effect, an externally applied electrical voltage causes an electrical current to flow. The mobile charge carriers (usually electrons) are transversely deflected by the magnetic field due to the Lorentz force. In the Righi–Leduc effect, the temperature difference causes the mobile charge carriers to flow from the warmer end to the cooler end. Here, too, the Lorentz force causes a transverse deflection. Since the electrons transport heat, one side is heated more than the other.

The thermal Hall coefficient ${\displaystyle R_{\mathrm {TH} }}$ (sometimes also called the Righi–Leduc coefficient) depends on the material and has units of tesla⁻¹. It is related to the Hall coefficient ${\displaystyle R_{\mathrm {H} }}$ by the electrical conductivity ${\displaystyle \sigma }$, as

${\displaystyle R_{\rm {TH}}=\sigma R_{\rm {H}}}$.

See also

• Hall effect

References

1. Lalena, John N.; Cleary, David A. (2010). Principles of Inorganic Materials Design (2nd ed.). John Wiley and Sons. p. 272. ISBN 978-0-470-40403-4. Retrieved 2011-04-25.
2. Strohm, Cornelius; Rikken, Geert L. J. A.; Wyder, Peter (October 7, 2005). "Phenomenological Evidence for the Phonon Hall Effect". Physical Review Letters. 95 (15): 155901. Bibcode:2005PhRvL..95o5901S. doi:10.1103/PhysRevLett.95.155901. PMID 16241740.
3. Li, Xiaokang; Fauqué, Benoît; Zhu, Zengwei; Behnia, Kamran (2020). "Phonon thermal Hall effect in strontium titanate". Physical Review Letters. 124 (10). APS: 105901. arXiv:1909.06552. Bibcode:2020PhRvL.124j5901L. doi:10.1103/PhysRevLett.124.105901. PMID 32216396.
4. Sharma, Rohit; Bagchi, Mahasweta; Wang, Yongjian; Ando, Yoichi; Lorenz, Thomas (2024). "Phonon thermal Hall effect in charge-compensated topological insulators". Physical Review B. 109 (10). APS: 104304. arXiv:2401.03064. Bibcode:2024PhRvB.109j4304S. doi:10.1103/PhysRevB.109.104304.
5. Sharma, Rohit; Valldor, Martin; Lorenz, Thomas (2024). "Phonon thermal Hall effect in nonmagnetic Y₂Ti₂O₇". Physical Review B. 110 (10). APS: L100301. arXiv:2407.12535. doi:10.1103/PhysRevB.110.L100301.
6. Li, Xiaokang; Machida, Yo; Subedi, Alaska; Zhu, Zengwei; Li, Liang; Behnia, Kamran (2023). "The phonon thermal Hall angle in black phosphorus". Nature Communications. 14 (1). Nature Publishing Group UK London: 1027. arXiv:2301.00603. Bibcode:2023NatCo..14.1027L. doi:10.1038/s41467-023-36750-3. PMC 9950068. PMID 36823192.
7. Grissonnanche, G (July 17, 2019). "Giant thermal Hall conductivity in the pseudogap phase of cuprate superconductors". Nature. 571 (7765): 376–380. arXiv:1901.03104. Bibcode:2019Natur.571..376G. doi:10.1038/s41586-019-1375-0. PMID 31316196. S2CID 197542068.