# Topological semimetals with double-helix nodal link

## TL;DR

This paper introduces a novel topological semimetal featuring linked double-helix nodal loops with nontrivial topology, stabilized by symmetry breaking, and discusses potential realization in cold atom systems.

## Contribution

A new class of topological nodal line semimetals with linked double-helix structures supported by a specific symmetry-breaking mechanism.

## Key findings

- Nodal lines form a double-helix and Hopf link structure.
- Nodal lines carry a $$ Berry flux, indicating nontrivial topology.
- Surface flat bands are observed, enclosed by the nodal lines' projection.

## Abstract

Topological nodal line semimetals are characterized by the crossing of the conduction and valence bands along one or more closed loops in the Brillouin zone. Usually, these loops are either isolated or touch each other at some highly symmetric points. Here, we introduce a new kind of nodal line semimetal, that contains a pair of linked nodal loops. A concrete two-band model was constructed, which supports a pair of nodal lines with a double-helix structure, which can be further twisted into a Hopf link because of the periodicity of the Brillouin zone. The nodal lines are stabilized by the combined spatial inversion $\mathcal{P}$ and time reversal $\mathcal{T}$ symmetry; the individual $\mathcal{P}$ and $\mathcal{T}$ symmetries must be broken. The band exhibits nontrivial topology that each nodal loop carries a $\pi$ Berry flux. Surface flat bands emerge at the open boundary and are exactly encircled by the projection of the nodal lines on the surface Brillouin zone. The experimental implementation of our model using cold atoms in optical lattices is discussed.