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.