Global topology of Weyl semimetals and Fermi arcs

TL;DR

This paper develops a comprehensive topological classification for Weyl semimetals across any dimension, accounting for complex linked Weyl surfaces and their surface Fermi arcs, advancing understanding of their global topological properties.

Contribution

It introduces a unified topological classification scheme for Weyl semimetals that includes linked Weyl surfaces and refines existing 3D models with a mathematically rigorous approach.

Findings

Derived a generalized charge cancellation condition for Weyl surfaces.

Analyzed the bulk-boundary correspondence and its duality transformation.

Clarified the impact of Weyl point movements on topological invariants.

Abstract

We provide a manifestly topological classification scheme for generalised Weyl semimetals, in any spatial dimension and with arbitrary Weyl surfaces which may be non-trivially linked. The classification naturally incorporates that of Chern insulators. Our analysis refines, in a mathematically precise sense, some well-known 3D constructions to account for subtle but important global aspects of the topology of semimetals. Using a fundamental locality principle, we derive a generalized charge cancellation condition for the Weyl surface components. We analyse the bulk-boundary correspondence under a duality transformation, which reveals explicitly the topological nature of the resulting surface Fermi arcs. We also analyse the effect of moving Weyl points on the bulk and boundary topological semimetal invariants.