Dynamical Systems, Topology and Conductivity in Normal Metals

TL;DR

This paper explores the topological properties of electron trajectories in 3D normal metals under strong magnetic fields, revealing new integer-valued topological invariants that influence conductivity.

Contribution

It introduces a topological classification of electron trajectories on Fermi surfaces and identifies new observable topological invariants affecting conductivity in metals.

Findings

Discovery of new integer-valued topological invariants

Classification of asymptotic regimes for high magnetic fields

Topological analysis of electron dynamics on Fermi surfaces

Abstract

New observable integer-valued numbers of the topological origin were revealed by the present authors studying the conductivity theory of single crystal 3D normal metals in the reasonably strong magnetic field ($B \leq 10^{3} Tl$). Our investigation is based on the study of dynamical systems on Fermi surfaces for the motion of semi-classical electron in magnetic field. All possible asymptotic regimes are also found for $B \to \infty$ based on the topological classification of trajectories.