# Weyl-link semimetals

## TL;DR

This paper introduces Weyl-link semimetals, a new topological phase with linked nodal rings, and demonstrates their properties through a two-band model and linking number detection methods.

## Contribution

It presents the concept of Weyl-link semimetals, constructs a specific model with linked nodal lines, and links topological invariants to physical observables.

## Key findings

- Linked nodal rings characterized by linking number.
- Chern-Simons 3-form depends on linking number.
- Zero-energy Landau levels reveal nodal line linking.

## Abstract

A family of topological semimetallic phases where twofold degenerate gapless points form linked rings is introduced. We refer to this phase as Weyl-link semimetals. A concrete two-band model with two linked nodal lines is constructed. We demonstrate that the Chern-Simons 3-form depends on the linking number of rings in a generic two-band model. In addition, we show the emergence of zero-energy modes in the Landau level spectrum can reveal the location of nodal lines, providing a method of probing their linking number.