# The complexity classes of angular diagrams of the metal conductivity in strong magnetic fields

## TL;DR

This paper classifies the complexity of angular diagrams of metal conductivity in strong magnetic fields, highlighting the role of Fermi surface structure and Hall conductivity in understanding diagram complexity.

## Contribution

It introduces a classification of angular conductivity diagrams based on their complexity and relates this to the Fermi surface structure of metals.

## Key findings

- Angular diagrams can be divided into a finite number of complexity classes.
- Diagrams with maximal complexity are associated with complex Fermi surfaces.
- Hall conductivity significantly influences the structure of complex diagrams.

## Abstract

We consider angular diagrams describing the dependence of the magnetic conductivity of metals on the direction of the magnetic field in rather strong fields. As it can be shown, all angular conductivity diagrams can be divided into a finite number of classes with different complexity. The greatest interest among such diagrams is represented by diagrams with the maximal complexity, which can occur for metals with rather complicated Fermi surfaces. In describing the structure of complex diagrams, in addition to the description of the conductivity itself, the description of the Hall conductivity for different directions of the magnetic field plays very important role. For the evaluation of the complexity of angular diagrams of the conductivity of metals, it is convenient also to compare such diagrams with the full mathematical diagrams that are defined (formally) for the entire dispersion relation.