Competing higher order topological superconducting phases in triangular lattice magnet-superconductor hybrid systems

We demonstrate that a plethora of higher order topological phases emerge in magnet-superconductor hybrid (MSH) systems through the interplay of a stacked magnetic structure and an underlying triangular surface lattice; the latter being of great current experimental interest. Such lattices offer the ability to create three main types of edge terminations — called $x$-, $y$- and $y^{\prime }$-edges — of MSH islands that, in turn, give rise to a complex phase diagrams exhibiting various regions of higher order topological superconducting (HOTSC) phases. We identify the single adatom chain, as well as a pair of adjacent adatom chains (called a double-chain), as the basic building blocks for the emergence of HOTSC phases. Of particular interest are those HOTSC phases which arise from a competition between the topology of single- and double-chain blocks, which are absent for square lattices.