Topological semimetals, such as Dirac, Weyl, or line-node semimetals, are gapless states of matter characterized by their nodal band structures and surface states. In this work, we consider layered (topologically trivial) insulating systems in $D$ dimensions that are composed of coupled multilayers of $d$-dimensional topological semimetals. Despite being nominal bulk insulators, we show that crystal defects having codimension $(D-d)$ can harbor robust lower-dimensional topological semimetals embedded in a trivial insulating background. As an example we show that defect-bound topological semimetals can be localized on stacking faults and partial dislocations. Finally, we propose how an embedded topological Dirac semimetal can be identified in experiment by introducing a magnetic field and resolving the relativistic massless Dirac Landau level spectrum at low energies in an otherwise gapped system.

• Received 6 September 2021
• Accepted 28 March 2022

DOI:https://doi.org/10.1103/PhysRevB.105.184105