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We demonstrate how the non-trivial interplay between spin-orbit coupling andnodeless $s$-wave superconductivity can drive a fully gapped two-bandtopological insulator into a time-reversal invariant gapless topologicalsuperconductor supporting symmetry-protected Majorana flat bands. Wecharacterize topological phase diagrams by a ${\mathbb Z}_2 \times{\mathbbZ}_2$ partial Berry-phase invariant, and show that, despite the trivial crystalgeometry, no unique bulk-boundary correspondence exists. We trace this behaviorto the anisotropic quasiparticle bulk gap closing, linear vs. quadratic, andargue that this provides a unifying principle for gapless topologicalsuperconductivity. Experimental implications for tunneling conductancemeasurements are addressed, relevant for lead chalcogenide materials.

Majorana Flat Bands in s-Wave Gapless Topological Superconductors