Topology of contact points in Lieb-kagom\'e model

TL;DR

This paper investigates the topological properties of contact points in the Lieb-kagomé model, revealing a classification surface that characterizes band structure singularities through winding numbers, with special focus on the Lieb case.

Contribution

It introduces a topological classification surface for the Lieb-kagomé model's eigenstates and analyzes its fundamental group to characterize band singularities.

Findings

Eigenstates parametrized by a 4D classification surface

Singularities characterized by four independent winding numbers

Lieb case has a unique classification surface with a single winding number

Abstract

We analyse Lieb-kagom\'e model, a three-band model with contact points showing particular examples of the merging of Dirac contact points. We prove that eigenstates can be parametrized in a classification surface, which is a hypersurface of a 4-dimension space. This classification surface is a powerful device giving topological properties of the energy band structure; the analysis of its fundamental group proves that all singularities of the band structure can be characterized by four independent winding (integer) numbers. Lieb case separates: its classification surface differs and there is only one winding number.