Suppression of spectral gap and flat bands on a cuprate superconductor side-surface

Side surfaces of cuprate superconductors are expected to display a suppressed d-wave order parameter and zero-energy topological flat bands with a large density of states, making them susceptible to symmetry broken orders. Yet such surfaces have never been investigated with momentum-resolved, surface-sensitive probes, because high-temperature superconductors rarely cleave along them. Using focused-ion-beam milling to define a controlled breaking point, we expose pristine (110) side surfaces of overdoped La_2-xSr_xCuO₄ (x = 0.22) suitable for angle-resolved photoemission. We do not resolve an opening or closing of a superconducting spectral gap within our energy resolution ( ~ 4 meV), in agreement with theoretical predictions. Surprisingly, the expected zero-energy flat band peak is also suppressed, despite the high topographic quality of the surface. Self-consistent Bogoliubov-de Gennes calculations show that the measured geometric roughness of the cleaved surface is too weak to eliminate these modes. The calculations further demonstrate that bulk inhomogeneities characteristic of high-temperature superconductors, modelled as moderate Anderson-type disorder, can broaden the flat-band states beyond detectability. Our results provide the first momentum-resolved view of the electronic structure on a cuprate side surface and identify disorder as a plausible mechanism obscuring the spectroscopic signatures of the predicted flat-band states.