Gurzhi effect

The Gurzhi effect was theoretically predicted[1][2] by Radii Gurzhi in 1963, and it consists of decreasing of electric resistance

of a finite size conductor with increasing of its temperature

for some temperature interval).

Gurzhi effect usually being considered as the evidence of electron hydrodynamic transport[3][4][5][6][7][8] in conducting media.

The mechanism of Gurzhi effect is the following.

The value of the resistance of the conductor is inverse to the

{\displaystyle l_{lost}=\min\{l_{boundary},l_{V}\}}

— a mean free path corresponding to the momentum loss from the electrons+phonons system

is the average distance which electron pass between two consecutive interactions with a boundary, and

is a mean free path corresponding to other possibilities of momentum loss.

The electron reflection from the boundary is assumed to be diffusive.

When temperature is low we have ballistic transport with

{\displaystyle l_{lost}\approx l_{boundary}\approx d}

is a mean free path corresponding to effective normal electron-electron collisions (i.e. collisions without total electrons+phonons momentum loss).

For low temperatures phonon emitted by electron quickly interacts with another electron without loss of total electron+phonons momentum and

{\displaystyle l_{ee}\approx l_{ep}}

is a mean free path corresponding to the electron-phonon collisions.

Thus the resistance for lowest temperatures is a constant

The Gurzhi effect appears when the temperature is increased to have

In this regime the electron diffusive length between two consecutive interactions with the boundary can be considered as momentum loss free path:

{\displaystyle l_{lost}\approx l_{boundary}\approx d^{2}/l_{ee}}

, and the resistance is proportional to

, and thus we have a negative derivative

Therefore, Gurzhi effect can be observed when

Gurzhi effect corresponds to unusual situation when electrical resistance depends on a frequency of normal collisions.

As one can see this effect appears due to the presence of a boundaries with finite characteristic size

Later Gurzhi's group discovered a special role of electron hydrodynamics in a spin transport.

[9][10] In such a case magnetic inhomogeneity plays role of a "boundary" with spin-diffusion length[11] as a characteristic size instead of

This magnetic inhomogeneity stops electrons of the one spin component which becomes an effective scatterers for electrons of another spin component.

In this case magnetoresistance of a conductor depends on the frequency of normal electron-electron collisions as well as in the Gurzhi effect.