Analytical approximations of dispersion laws and ultra-complex conductivity diagrams

Abstract

We study the probability of the emergence of ultra-complex conductivity diagrams in conductors that satisfy the tight-binding approximation and have the simple or body-centered cubic lattice. The presence of ultra-complex conductivity diagrams allows us to observe a number of highly nontrivial effects in strong magnetic fields, however, the probability of their emergence in a given substance is quite low. In the case of the simple or body-centered cubic lattice, the leading tight-binding approximation does not allow us to estimate this probability due to the peculiarities of the spectra in this situation. To estimate this probability, we use higher-order corrections to the leading approximation, which yield more accurate analytical expressions for the electron spectra.