Pseudospin Vortex Ring with a Nodal Line in Three Dimensions

TL;DR

This paper introduces a 3D topological semimetal model featuring a vortex ring nodal line with a pseudospin structure, revealing a new anomalous Hall effect and connecting vortex ring and Weyl point topologies.

Contribution

It presents a simple model of a topological semimetal with a vortex ring nodal line and analyzes its properties, including a transition to Weyl nodes and a novel Hall effect.

Findings

Vortex ring nodal line induces skyrmionic pseudospin patterns.

Model exhibits a maximal anomalous Hall effect.

Transition from vortex ring to Weyl nodes by tuning parameters.

Abstract

We present a model of a topological semimetal in three dimensions (3D) whose energy spectrum exhibits a nodal line acting as a vortex ring; this in turn is linked by a pseudospin structure akin to that of a smoke ring. Contrary to a Weyl point node spectrum, the vortex ring gives rise to skyrmionic pseudospin patterns in cuts on both sides of the nodal ring plane; this pattern covers the full Brillouin zone, thus leading to a new, `maximal', anomalous Hall effect in a 3D semimetal. Tuning a model parameter shrinks the vortex ring until it vanishes, giving way to a pair of Weyl nodes of opposite chirality. This establishes a connection between two distinct momentum-space topologies - that of a vortex ring (a circle of singularity) and a monopole-anti-monopole pair (two point singularities). We present the model both as a low-energy continuum and a two-band tight-binding lattice model. Its simplicity permits an analytical computation of its Landau level spectrum.