Topological Quadrupolar Semimetals

TL;DR

This paper predicts new topological semimetals with bulk quadrupole moments, exploring their properties, types, and methods to calculate their quadrupole moments from energy and Wannier band nodes.

Contribution

It introduces several novel types of topological semimetals with quadrupole moments and details methods to compute their properties from spectral nodes.

Findings

Identification of three types of quadrupolar semimetals.

Methods to calculate quadrupole moments from bulk and surface nodes.

Demonstration of hinge states and surface polarization due to quadrupole moments.

Abstract

In this work we predict several new types of topological semimetals that exhibit a bulk quadrupole moment. These semimetals are modeled with a 3D extension of the 2D quadrupole topological insulator. One type of semimetal has bulk nodes and gapped, topological surfaces. A second type, which we may call a higher order topological semimetal, has a gapped bulk, but harbors a Dirac semimetal with an even number of nodes on one or more surfaces. The final type has a gapped bulk, but harbors half of a Dirac semimetal on multiple surfaces. Each of these semimetals gives rise to mid-gap hinge states and hinge charge, as well as surface polarization, which are all consequences of a bulk quadrupole moment. We show how the bulk quadrupole moments of these systems can be calculated from the momentum-locations of bulk or surface nodes in the energy spectrum. Finally, we illustrate that in some cases it is useful to examine nodes in the Wannier bands, instead of the energy bands, to extract the bulk quadrupole moment.