Higher-order Weyl Semimetals

TL;DR

This paper explores higher-order Weyl semimetals, introducing a new type of Weyl node, and demonstrates how they can be realized, identified, and manipulated using models, measurements, and periodic driving techniques.

Contribution

It identifies a new second-order Weyl node, classifies various WSM phases, and proposes methods for their realization and detection, advancing the understanding of topological semimetals.

Findings

Discovery of second-order Weyl nodes with unique topological transitions

Identification of hybrid-order phases with coexisting surface and hinge states

Proposal of measurement techniques and driving methods to realize and detect HOWSMs

Abstract

We investigate higher-order Weyl semimetals (HOWSMs) having bulk Weyl nodes attached to both surface and hinge Fermi arcs. We identify a new type of Weyl node, that we dub a $2nd$ order Weyl node, that can be identified as a transition in momentum space in which both the Chern number and a higher order topological invariant change. As a proof of concept we use a model of stacked higher order quadrupole insulators to identify three types of WSM phases: $1st$-order, $2nd$-order, and hybrid-order. The model can also realize type-II and hybrid-tilt WSMs with various surface and hinge arcs. Moreover, we show that a measurement of charge density in the presence of magnetic flux can help identify some classes of $2nd$ order WSMs. Remarkably, we find that coupling a $2nd$-order Weyl phase with a conventional $1st$-order one can lead to a hybrid-order topological insulator having coexisting surface cones and flat hinge arcs that are independent and not attached to each other. Finally, we show that periodic driving can be utilized as a way for generating HOWSMs. Our results are relevant to metamaterials as well as various phases of Cd$_3$As$_2$, KMgBi, and rutile-structure PtO$_2$ that have been predicted to realize higher order Dirac semimetals.