Nodal-line semimetals have band crossings that form closed loops in momentum space rather than discrete points. The topological invariant associated with these loops guarantees surface states: drumhead bands — flat or nearly flat bands that fill the interior of the projected nodal loop on the surface Brillouin zone. The flatness means a high density of states concentrated at the surface. Flat bands are unstable to interactions: any perturbation that opens a gap gains condensation energy proportional to the density of states, and a flat band has a divergent density of states.
Matsushima and Tsuchiura (arXiv 2602.22837, February 2026) show that when a nodal-loop semimetal develops superconductivity, the pairing is localized at the surface. Chiral p-wave order nucleates at the outermost layers and decays within a few layers into the bulk. The bulk remains normal or weakly paired. The superconductivity is a surface phenomenon, driven by the drumhead band's high density of states.
The analysis uses a minimal tight-binding model with a bulk nodal loop and open boundaries. In the normal state, the surface layer shows a sharp zero-energy peak in the density of states — the drumhead band. Interior layers show smooth, bulk-like spectra. When superconducting pairing channels are introduced, the chiral p-wave channel wins overwhelmingly. The d-wave order parameter is more than an order of magnitude smaller. The p-wave order is strongest at the surface and decays exponentially inward.
The drumhead band selects the pairing symmetry through its orbital structure. The flat band's states have specific momentum-space textures inherited from the topological character of the nodal loop. Chiral p-wave pairing — which has a specific angular momentum in the gap function — matches these textures better than d-wave. The pairing symmetry is not imposed; it's selected by the surface electronic structure.
When the p-wave gap opens, the drumhead's sharp zero-energy peak splits into two coherence peaks — the hallmark of a superconducting gap in tunneling spectroscopy. The surface has gone from a metallic flat band to a topological superconductor, with the gap protecting chiral edge modes that could host Majorana fermions.
The result suggests that surfaces of nodal-loop semimetals are natural platforms for topological superconductivity — no proximity effect, no heterostructure, no external engineering. The topology of the bulk band structure creates the surface states; the flat-band instability drives the pairing; the orbital texture selects the symmetry. The superconductor grows its own skin.