Abstract: A method for controllably making catalysts with at least one metallic surface state, that includes: a) identifying all the topological insulators in the ICSD, b) calculating the Real Space Invariants of the valence bands for all these topological insulators in order to c) identify in all these topological insulators the Wyckoff Positions where the irreducible Wannier Charge Centers (WCCs) are localized, and then d) selecting as potentially catalytic active compound a topological insulator in which the position of WCCs is not occupied by any atom; e) synthesizing a crystal of the selected potentially catalytic active compound either so that it is grown in a predefined crystallographic direction (characterized by its Miller indices (h,k,l)) which exposes the metallic surface state; or cutting the crystal in a predefined crystallographic direction (characterized by its Miller indices (h,k,l)), so that the metallic surface state is exposed when ( ( { ( h , k , l ) · ( x - X j , y -

Abstract: A magnetic topological nanowire structure comprises a superconductor and a quasi-1D magnetic nanowire. The quasi-1D magnetic nanowire is coupled to or embedded in the superconductor to produce a self-contained interaction resulting in a spatially separated pair of Majorana fermions. The pair of Majorana fermions corresponds to the topological superconductor and each of the pair of the Majorana fermions are localized near a respective endpoint of the nanowire.

Abstract: A magnetic topological nanowire structure comprises a superconductor and a quasi-1D magnetic nanowire. The quasi-1D magnetic nanowire is coupled to or embedded in the superconductor to produce a self-contained interaction resulting in a spatially separated pair of Majorana fermions. The pair of Majorana fermions corresponds to the topological superconductor and each of the pair of the Majorana fermions are localized near a respective endpoint of the nanowire.