Sierpi?ski Structure and Electronic Topology in Bi Thin Films on InSb(111)B Surfaces

Deposition of Bi on InSb(111)B reveals a striking Sierpi\ifmmode \acute{n}\else \'{n}\fi{}ski-triangle (ST)-like structure in thin films. Such fractal geometric topology is further shown to turn off the intrinsic electronic film. Relaxation huge misfit strain about 30% 40% between adlayer and substrate revealed drive ST-like island formation. A Frenkel-Kontrova model developed illustrate enhanced relief ST islands offsetting additional step energy cost. Besides sufficiently large tensile strain, forming structures also requires larger adlayer-substrate intra-adlayer elastic stiffnesses, weaker interatomic interactions.