Splitting the hinge mode of higher-order topological insulators

We study the effect of the coupling of a helical mode in a two-dimensional topological insula-
tor without inversion symmetry — focusing at the surface of a higher order topological insulator
(HOTI) — to a proximate ferromagnet and to a proximate s-wave superconductor. We find that
in contrast to the helical modes of inversion symmetric systems, which are gapped by these cou-
plings, when inversion is broken the helical modes generically remain gapless and spatially split.
The ferromagnet turns the helical mode into a chiral mode that surrounds the magnetized region,
and the superconductor, when strong enough, turns that mode to two helical Majorana modes that
surround the superconducting region. The enclosed superconductor comprises a two dimensional,
time-reversal invariant, topological superconductor. We propose that this state can be measured in
electrical transport by an extension of previously proposed interferometry experiments.