Magnetic quadrupole moment in higher order topological semimetals

One characteristic feature of conventional two dimensional Dirac semimetals is the bulk orbital magnetic dipole moment (MDM), which is proportional to the energy separation of the bulk nodes, and manifests as boundary circulating currents. In this presentation, we instead consider the magnetic quadrupole moment (MQM) in the three dimensional higher order topological semimetals (HOTS). In contrast to all semimetals considered previously, the bulk energy bands of a HOTS could be gapped, and its surfaces form one (or half of a) two dimensional Dirac semimetal with surface Dirac nodes. By adding perturbations, an energy difference can be created between pairs of surface nodes. We show analytically and numerically that the nodal energy difference generates a bulk MQM and is associated with circulating hinge currents. We discuss possible experiments in solid state systems as well as in metamaterials to verify our predictions.