Hall effect

It is a characteristic of the material from which the conductor is made, since its value depends on the type, number, and properties of the charge carriers that constitute the current.

In the 1820s, André-Marie Ampère observed this underlying mechanism that led to the discovery of the Hall effect.

[3] However it was not until a solid mathematical basis for electromagnetism was systematized by James Clerk Maxwell's "On Physical Lines of Force" (published in 1861–1862) that details of the interaction between magnets and electric current could be understood.

[3] In 1879, he discovered this Hall effect while he was working on his doctoral degree at Johns Hopkins University in Baltimore, Maryland.

[4] Eighteen years before the electron was discovered, his measurements of the tiny effect produced in the apparatus he used were an experimental tour de force, published under the name "On a New Action of the Magnet on Electric Currents".

The effect becomes observable, in a perpendicular applied magnetic field, as a Hall voltage appearing on either side of a line connecting the current-contacts.

It exhibits apparent sign reversal in comparison to the "ordinary" effect occurring in the simply connected specimen.

First imagine the "ordinary" configuration, a simply connected (void-less) thin rectangular homogeneous element with current-contacts on the (external) boundary.

Current consists of the movement of many small charge carriers, typically electrons, holes, ions (see Electromigration) or all three.

[10] When such a magnetic field is absent, the charges follow approximately straight paths between collisions with impurities, phonons, etc.

However, when a magnetic field with a perpendicular component is applied, their paths between collisions are curved; thus, moving charges accumulate on one face of the material.

The result is an asymmetric distribution of charge density across the Hall element, arising from a force that is perpendicular to both the straight path and the applied magnetic field.

In some metals and semiconductors it appears "holes" are actually flowing because the direction of the voltage is opposite to the derivation below.

The vx term is the drift velocity of the current which is assumed at this point to be holes by convention.

In steady state, F = 0, so 0 = Ey − vxBz, where Ey is assigned in the direction of the y-axis, (and not with the arrow of the induced electric field ξy as in the image (pointing in the −y direction), which tells you where the field caused by the electrons is pointing).

And with the fingers (magnetic field) also being the same, interestingly the charge carrier gets deflected to the left in the diagram regardless of whether it is positive or negative.

Thus for the same current and magnetic field, the electric polarity of the Hall voltage is dependent on the internal nature of the conductor and is useful to elucidate its inner workings.

This property of the Hall effect offered the first real proof that electric currents in most metals are carried by moving electrons, not by protons.

It also showed that in some substances (especially p-type semiconductors), it is contrarily more appropriate to think of the current as positive "holes" moving rather than negative electrons.

Yet we observe the opposite polarity of Hall voltage, indicating positive charge carriers.

However, of course there are no actual positrons or other positive elementary particles carrying the charge in p-type semiconductors, hence the name "holes".

In the same way as the oversimplistic picture of light in glass as photons being absorbed and re-emitted to explain refraction breaks down upon closer scrutiny, this apparent contradiction too can only be resolved by the modern quantum mechanical theory of quasiparticles wherein the collective quantized motion of multiple particles can, in a real physical sense, be considered to be a particle in its own right (albeit not an elementary one).

[13] Unrelatedly, inhomogeneity in the conductive sample can result in a spurious sign of the Hall effect, even in ideal van der Pauw configuration of electrodes.

The simple formula for the Hall coefficient given above is usually a good explanation when conduction is dominated by a single charge carrier.

For large applied fields the simpler expression analogous to that for a single carrier type holds.

Although it is well known that magnetic fields play an important role in star formation, research models[17][18][19] indicate that Hall diffusion critically influences the dynamics of gravitational collapse that forms protostars.

It was predicted by Mikhail Dyakonov and V. I. Perel in 1971 and observed experimentally more than 30 years later, both in semiconductors and in metals, at cryogenic as well as at room temperatures.

The Hall parameter, β, in a plasma is the ratio between the electron gyrofrequency, Ωe, and the electron-heavy particle collision frequency, ν:

Nevertheless, when the Hall parameter is low, their motion between two encounters with heavy particles (neutral or ion) is almost linear.

Specifically, a set of Hall Effects has emerged based on excitons[24][25] and exciton-polaritons[26] n[check spelling] 2D materials and quantum wells.