Publications

Abstract: Quasicrystalline order induces a fractal energy spectrum, yet its impact on topological protection remains an open fundamental question. Here, we demonstrate that the topological phase transitions characterised by the appearance of Majorana Bound States themselves have a fractal character. By extending this analysis to the full family of Sturmian words, we uncover Kitaev’s Butterfly — a spectral fractal analogous to Hofstadter’s butterfly, but fundamentally distinguished by a central superconducting gap. Within this framework, we identify Majorana’s Butterfly as a fractal topological phase diagram governed by the competition between quasicrystallinity and superconducting pairing. We show that this competition dictates a hierarchy of Majorana stability, where the survival of the topological phase against fractal fragmentation is determined by the relative strength of these competing energy scales.