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# Nernst effect

In physics and chemistry, the Nernst Effect (also termed first Nernst-Ettingshausen effect, which is again frequently misspelled Nernst-Ettinghausen effect) is a thermoelectric (or thermomagnetic) phenomenon observed when a sample allowing electrical conduction is subjected to a magnetic field and a temperature gradient normal to each other. An electric field will be induced normal to both.

This effect is quantified by the Nernst coefficient |N|, which is defined to be

$|N|=\frac{E_Y/B_Z}{dT/dx}$

where EY is the y-component of the electric field that results from the magnetic field's z-component BZ and the temperature gradient dT / dx.

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 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.