Embedded Topological Semimetals*

Topological semimetals, such as Dirac or Weyl semimetals, are gapless states of matter characterized by their nodal band structures and surface states. We consider layered (topologically trivial) insulating systems in D dimensions that are composed of coupled multi-layers of d-dimensional topological semimetals. Despite being nominal bulk insulators we show that crystal defects having co-dimension D-d can robustly harbor a lower dimensional topological semimetal embedded in a trivial insulating background. As an example we show that defect-bound topological semimetals can emerge in these trivial systems when stacking faults are introduced. We characterize the nature of these embedded semimetals by identifying the nodal structure of the bands and by computing the Berry phase characteristics across the Brillouin zone. 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.