Relaxation time for magnetoresistance obtained from the band structure of a perfect cubic metal

Abstract

A well-known fact about the electrical resistance of a perfect crystal lattice is that this resistance is zero. The paper demonstrates that a different situation does apply for magnetoresistance: only a perfectly free-electron gas provides us with an infinite relaxation time and zero-magnetoresistance effect, but the presence of the crystal lattice makes the relaxation time equal to a finite quantity. The size of the product of the relaxation time for magnetoresistance and the electron gyration frequency is found to be a constant dependent on both the structure of electron states in a perfect lattice and the band filling. This property of constancy implies that the relaxation time is a quantity which becomes inversely proportional to the strength of the magnetic field applied to a crystal sample. Explicit calculations on the product of the relaxation time and the frequency of electron gyration are performed for the bands of the tightly bound s electrons in simple-cubic, body-centered-cubic, and face-centered-cubic lattices taken as examples.

Magnetoconductivity of planar crystalline systems and its semiclassical quantization

“…For a perfectly free-electron gas we have This result is valid solely for a perfectly free-electron case [21] making the behavior of parameter σ xy rather a special one. For, in the limit of contrary to an infinite value (5.2) obtained in a perfectly free-electron case [21] because for crystals τ…”

“…we obtain [21] ( ) and ω are the terms being constant in time; they depend solely on the band structure of a crystal and the size of the parameter 0 a defined in (2.1). A general property found from the calculations [31] is that…”

“…It should be noted that product τ Ω and ω calculated on the basis of the crystal band structure [21]. With the aid of the former calculations [21] we have:…”

“…This is not the case for magnetoresistance which does not vanish in a perfect lattice giving us a finite relaxation time also for an ideal crystal sample. Solely a perfect electron gas gives an infinite relaxation time for magnetoresistance [21]. In result, we have a situation which implies a different treatment of the relaxation time for magnetoresistance than that characteristic for electroresistance which is due to defects.…”

“…the lattice vibrations or those due to defects. Therefore, not the lattice vibrations but solely the very presence of a rigid perfect lattice can provide us with a finite relaxation time for magnetoresistance [21]. A consequence of such an approach is that a finite relaxation time in the presence of a crystal lattice multiplied by the frequency of electron gyration becomes a constant, dependent only on the crystal band structure and its filling by the electrons [21].…”