Nernst effect

In physics and chemistry, the Nernst effect (also termed first Nernst–Ettingshausen effect, after Walther Nernst and Albert von Ettingshausen) is a thermoelectric (or thermomagnetic) phenomenon observed when a sample allowing electrical conduction is subjected to a magnetic field and a temperature gradient normal (perpendicular) to each other. An electric field will be induced normal to both.

This effect is quantified by the Nernst coefficient ${\displaystyle \nu }$, which is defined to be

${\displaystyle \nu ={\frac {E_{y}}{B_{z}}}{\frac {1}{\partial _{x}T}}}$

where ${\displaystyle E_{y}}$ is the y-component of the electric field that results from the magnetic field's z-component ${\displaystyle B_{z}}$ and the x-component of the temperature gradient ${\displaystyle \partial _{x}T}$.

The reverse process is known as the Ettingshausen effect and also as the second Nernst–Ettingshausen effect.

Physical picture

Mobile energy carriers (for example conduction-band electrons in a semiconductor) will move along temperature gradients due to statistics^{[dubious ]} and the relationship between temperature and kinetic energy. If there is a magnetic field transversal to the temperature gradient and the carriers are electrically charged, they experience a force perpendicular to their direction of motion (also the direction of the temperature gradient) and to the magnetic field. Thus, a perpendicular electric field is induced.

Sample types

Semiconductors exhibit the Nernst effect. This has been studied in the 1950s by Krylova, Mochan and many others. In metals however, it is almost non-existent. It appears in the vortex phase of type-II superconductors due to vortex motion. This has been studied by Huebener et al. High-temperature superconductors exhibit the Nernst effect both in the superconducting and in the pseudogap phase, as was first found by Xu et al. Heavy-Fermion superconductors can show a strong Nernst signal which is likely not due to the vortices, as was found by Bel et al.

See also

• Spin Nernst effect
• Seebeck effect
• Peltier effect
• Hall effect
• Righi–Leduc effect

Journal articles

• Bel, R.; Behnia, K.; Nakajima, Y.; Izawa, K.; Matsuda, Y.; Shishido, H.; Settai, R.; Onuki, Y. (2004). "Giant Nernst Effect in CeCoIn₅". Physical Review Letters. 92 (21): 217002. arXiv:cond-mat/0311473. Bibcode:2004PhRvL..92u7002B. doi:10.1103/PhysRevLett.92.217002. PMID 15245310. S2CID 119337785.
• Huebener, R. P.; Seher, A. (10 May 1969). "Nernst Effect and Flux Flow in Superconductors. I. Niobium". Physical Review. 181 (2): 701–709. doi:10.1103/PhysRev.181.701.
• Huebener, R. P.; Seher, A. (10 May 1969). "Nernst Effect and Flux Flow in Superconductors. II. Lead Films". Physical Review. 181 (2): 710–716. doi:10.1103/PhysRev.181.710.
• Krylova, T. V.; Mochan, I. V. (1955). "Investigation of the Nernst Effect of Germanium". J. Tech. Phys. (USSR). 25: 2119.
• Rowe, V. A.; Huebener, R. P. (10 September 1969). "Nernst Effect and Flux Flow in Superconductors. III. Films of Tin and Indium". Physical Review. 185 (2): 666–671. doi:10.1103/PhysRev.185.666.
• Xu, Z. A.; Ong, N. P.; Wang, Y.; Kakeshita, T.; Uchida, S. (2000). "Vortex-like excitations and the onset of superconducting phase fluctuation in underdoped La_2−xSr_xCuO₄". Nature. 406 (6795): 486–488. Bibcode:2000Natur.406..486X. doi:10.1038/35020016. PMID 10952303. S2CID 205007888.