Recently, the Machida-Shibata states, which are surface states with an unusual weak coupling to a superconducting bulk, have been realized in Ag-corrals on Ag islands on superconducting Nb [1]. These time reversal invariant in-gap states, which represent the elemental form of a proximity gapped electronic state, form a new building block for in-gap topological electronic matter in symmetry class DIII. Intriguingly, symmetry class DIII has rigorously been shown not to exhibit topologically nontrivial phases in the proximity-coupling setup. By considering a small intra-corral electron interaction, we circumvent the no go theorem and theoretically demonstrate the hybridization of Machida-Shibata states to topologically nontrivial chains with pairs of Majorana modes at their ends, which are protected from mutual scattering by time-reversal symmetry [2].
Special emphasis is given on symmetry classification and the spectral peculiarities of this phase, which host vast regions of momenta with flat dispersion.

[1] https://www.nature.com/articles/s41586-023-06312-0
[2] https://arxiv.org/abs/2504.08674