a Hofstadter butterfly-like band structure have been observed in a van der Waals system of monolayer graphene on top of a hexagonal boron nitrade surface.[@Hunt1303.6942]

The 1D effectively spinless superconductor, expected in 1D superconductor with strong spin-momentum coupling under magnetic field, is of the D symmetry class.[@PeriodicTable] Therefore its topology is classified by a $Z_2$ topological number. This suggests that the boundary between two topologically non-trivial 1D superconductors would not have a localized mode. Boundary phenomena between topologically equivalent or distinct phases, with Harper or Fibonacci potentials, have been experimentally studied using photonic quasicrystals.[@VerbinPRL2013]

In the scenario of Refs. the chemical potential needs to lie close to the band edge so that the band degeneracy is removed by the external magnetic field. However, the present authors have observed that, by a quasiperiodic lattice modulation with a fixed wavenumber, effectively single-band superconductor with end Majorana fermions is realized even when the chemical potential is closer to the center of the original cosine band, because energy separations are introduced within each of the Zeeman-split bands.[@Tezuka2012] We have also demonstrated that this physics is stable even in the presence of a Hubbard-like on-site interaction and/or a harmonic trapping potential. More recently, the effect 