Bloch classification surface for three-band systems

TL;DR

This paper introduces a universal classification surface for three-band Hamiltonian systems, extending the concept of the Bloch surface used for two-band systems, enabling topological state classification in more complex quantum systems.

Contribution

The authors develop a generalized Bloch classification surface applicable to a broad class of three-band systems, expanding topological analysis tools beyond two-band models.

Findings

Identified specific classification surfaces for different three-band systems

Demonstrated the universality of the generalized Bloch surface

Provided a comprehensive study of three-band Hamiltonian topologies

Abstract

Topologically protected states can be found in physical systems, that show singularities in some energy contour diagram. These singularities can be characterized by winding numbers, defined on a classification surface, which maps physical state parameters. We have found a classification surface, which applies for three-band hamiltonian systems in the same way than standard Bloch surface does for two-band ones. This generalized Bloch surface is universal in the sense that it classifies a very large class of three-band systems, which we have exhaustively studied, finding specific classification surfaces, applying for each one.