Topological Phenomena in Normal Metals

TL;DR

This paper explores how topological properties of complex Fermi surfaces in normal metals influence electrical conductivity in strong magnetic fields, revealing stable integral planes linked to electron orbits.

Contribution

It introduces a topological framework connecting Fermi surface geometry with observable conductivity phenomena in metals under magnetic fields.

Findings

Electrical conductivity reveals topological features of Fermi surfaces.

Stable integral planes correspond to non-closed electron orbits.

Topological analysis applies to complex Fermi surface geometries.

Abstract

This paper is devoted to topological phenomena in normal metals with rather complicated Fermi surface. The results of the article are based on the deep topological theorems concerning the geometry of non-compact plane sections of level surfaces of periodic function in 3-dimensional Euclidean space which are the quasi-classical electron orbits in the presence of homogeneous magnetic field. The main result is that the observation of electrical conductivity in strong magnetic fields can reveal such nontrivial topological characteristics of Fermi surface as integral planes, connected with conductivity tensor and locally stable under small rotations of magnetic field. This planes are connected with generic non-closed orbits on the Fermi surface. Some non-generic situations are also discussed.