On chaotic regimes of conductivity behavior in the tight-binding approximation

TL;DR

This paper explores the complex conductivity regimes in metals with tight-binding electron spectra under strong magnetic fields, estimating their likelihood and conditions for experimental observation.

Contribution

It provides a theoretical analysis of the probability and conditions for detecting chaotic conductivity regimes in metals, linking electron trajectory geometry to observable phenomena.

Findings

Estimated probability of chaotic regimes occurrence

Conditions for experimental detection identified

Theoretical framework for complex electron trajectories

Abstract

We investigate the probability of detecting the most nontrivial conductivity behavior regimes in metals whose electron spectrum is described by the tight-binding approximation. These regimes are associated with the emergence of highly complex electron trajectories on the Fermi surface and correspond to a nontrivial (scaling) behavior of the conductivity tensor in strong magnetic fields. The geometry of such trajectories, as well as the corresponding conductivity regimes, have been well studied theoretically; however, they have not yet been observed experimentally. The results of our study allow us, in particular, to estimate the probability of their occurrence and to indicate the conditions for their possible detection for a wide class of conductors.