On the topological character of three-dimensional Nexus triple point degeneracies

TL;DR

This paper explores the topological properties of Nexus triple point degeneracies in three-dimensional band structures, providing a homological classification based on wavefunction geometry and analyticity.

Contribution

It introduces a topological characterization framework for Nexus fermions, extending beyond traditional Dirac/Weyl semimetals, using homological methods and wavefunction analysis.

Findings

Homological classification of Nexus triple points

Wavefunction geometry and analyticity analysis

Topological characterization framework for Nexus fermions

Abstract

Recently a generic class of three-dimensional band structures was identified that host two-fold line degeneracies meeting at three-fold or triple point degeneracies, which resist the usual topological characterization of isolated point degeneracies as in Dirac/Weyl semimetals. For these so-called ``Nexus" fermions which lie beyond Dirac/Weyl fermions, we lay out several concepts to characterize the wavefunction geometry and spell out its topology. Our approach is based on an understanding of the analyticity properties of Nexus wavefunctions building on a two-dimensional analogue studied recently by us. We use this to write down a homological classification of various Nexus triple point degeneracies in three dimensions.