The second boundaries of Stability Zones and the angular diagrams of conductivity for metals having complicated Fermi surfaces

TL;DR

This paper explores the complex structure of stability zones in the angular diagrams of metals with complicated Fermi surfaces, revealing the existence of second boundaries and proposing a classification scheme for diagram complexity.

Contribution

It introduces the concept of second boundaries of Stability Zones and a theoretical scheme to classify angular diagrams as simple or complex in metals with arbitrary Fermi surfaces.

Findings

Any Stability Zone has a second boundary restricting a larger conductivity region.

A scheme to divide angular diagrams into 'simple' and 'complex' categories is proposed.

The relationship between diagram complexity and Hall conductivity behavior is discussed.

Abstract

We consider some general aspects of dependence of magneto-conductivity on a magnetic field in metals having complicated Fermi surfaces. As it is well known, a nontrivial behavior of conductivity in metals in strong magnetic fields is connected usually with appearance of non-closed quasiclassical electron trajectories on the Fermi surface in a magnetic field. The structure of the electron trajectories depends strongly on the direction of the magnetic field and usually the greatest interest is caused by open trajectories that are stable to small rotations of the direction of $\, {\bf B} $. The geometry of the corresponding Stability Zones on the angular diagram in the space of directions of $\, {\bf B} \, $ represents a very important characteristic of the electron spectrum in a metal linking the parameters of the spectrum to the experimental data. Here we will consider some very general features inherent in the angular diagrams of metals with Fermi surfaces of the most arbitrary form. In particular, we will show here that any Stability Zone actually has a second boundary, restricting a larger region with a certain behavior of conductivity. Besides that, we shall discuss here general questions of complexity of the angular diagrams for the conductivity and propose a theoretical scheme for dividing the angular diagrams into "simple" and "complex" diagrams. The proposed scheme will in fact also be closely related to behavior of the Hall conductivity in a metal in strong magnetic fields. In conclusion, we will also discuss the relationship of the questions under consideration to the general features of an (abstract) angular diagram describing the behavior of quasiclassical electron trajectories at all energy levels in the conduction band.