We show that lattice dislocations of topological iron-based superconductors
such as FeTe1βxβSexβ will intrinsically trap non-Abelian Majorana
quasiparticles, in the absence of any external magnetic field. Our theory is
motivated by the recent experimental observations of normal-state topology and
surface magnetism that coexist with superconductivity in FeTe1βxβSexβ,
the combination of which naturally evokes an emergent second-order topological
superconductivity in a two-dimensional subsystem spanned by screw or edge
dislocations. This exemplifies a new embedded higher-order topological phase in
class D, where Majorana zero modes appear around the "corners" of a
low-dimensional embedded subsystem, instead of those of the full crystal. A
nested domain wall theory is developed to understand the origin of these defect
Majorana zero modes. When the surface magnetism is absent, we further find that
sΒ±β pairing symmetry itself is capable of inducing a different type of
class-DIII embedded higher-order topology with defect-bound Majorana Kramers
pairs. We also provide detailed discussions on the real-world material
candidates for our proposals, including FeTe1βxβSexβ, LiFeAs,
Ξ²-PdBi2β, and heterostructures of bismuth, etc. Our work establishes
lattice defects as a new venue to achieve high-temperature topological quantum
information processing.Comment: 12 pages, 5 figure