  We address the problem of boundary s-wave superconductivity on rectangular
honeycomb lattices: nanoflakes, armchair and zigzag nanotubes. We discuss how
the presence of edges and corners in these systems can significantly alter the
superconducting correlations at a macroscopic length scale, leading to either
nontrivial enhancement or suppression of the superconducting gap value near the
boundaries. This in turn results in different critical temperatures of the gap
closure at boundaries compared to the bulk gap. The effects are macroscopic but
strongly depend on the atomic-level structure of the boundaries.
