Dynamical Systems, Topology and Conductivity in Normal Metals in strong magnetic fields

TL;DR

This paper provides a comprehensive description of conductivity regimes in normal metals under strong magnetic fields, introducing new topological characteristics based on dynamical systems on Fermi surfaces.

Contribution

It introduces new observable topological characteristics of conductivity and applies dynamical systems theory to analyze electron motion in magnetic fields in metals.

Findings

Introduction of integer-valued topological conductivity characteristics

Complete description of asymptotic conductivity regimes

Application of dynamical systems on Fermi surfaces

Abstract

We represent here the full description of all asymptotic regimes of conductivity behavior in the so-called "Geometric Strong Magnetic Field limit" in the 3D single crystal normal metals with topologically complicated Fermi surfaces. In particular, new observable integer-valued characteristics of conductivity of the topological origin were introduced by the present authors few years ago; they are based on the Topological Resonance found by the present authors and play the basic role in the total picture. Our investigation is based on the study of dynamical systems on Fermi surfaces for the semi-classical motion of electron in magnetic field realized by the Moscow topological group.