Boundary-Obstructed Topological High-Tc Superconductivity in Iron Pnictides

Nontrivial topology and unconventional pairing are two central guiding principles in the contemporary search for and analysis of superconducting materials and heterostructure compounds. It is quite rare that a single material compound possesses both non-trivial topological electronic band structure and unconventional pairing. In this work, we will describe an example of such system in iron-based superconductors. We propose to realize high-order topological superconductors, a new topological phase with the gapless modes located at the corner/hinge instead of the edge/surface, in the 112-family of iron pnictides, such as Ca_1-xLa_xFeAs₂ [1], with the great advantage of the Curie temperature above 40K. Our theory provides the microscopic physical mechanism and topological characterization of this topological phase. Our works not only provide a physical understanding of the existing experiments, but also opens a new arena for high-order topological superconductivity with stable corner/hinge Majorana modes in intrinsic superconductors with high Curie temperature.