Embedded topological semimetals

Topological semimetals, such as Dirac, Weyl, or line-node 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 composed coupled multi-layers $d$-dimensional topological semimetals. Despite being nominal bulk insulators, show crystal defects having co-dimension $(D-d)$ can harbor robust lower dimensional semimetals embedded a trivial background. As an example defect-bound be localized on stacking faults partial dislocations. Finally, propose how Dirac semimetal identified experiment introducing magnetic field resolving the relativistic massless Landau level spectrum at low energies otherwise gapped system.