Magnetic-field effects on localization in a fractal lattice

Magnetic-field effects on structure-induced localization in a fractal lattice are investigated by studying the usual tight-binding model on a Sierpinski gasket in the presence of a magnetic field. We find that a magnetic field can drastically change properties of states which are localized with high degeneracy in the absence of a magnetic field. In the presence of a magnetic field the degeneracies of those localized states are broken, and each of them becomes many extended states. Around these new extended state regions, the number of states whose localization length is larger than a certain value decreases with the logarithm of the localization length in a power-law fashion. The exponent of this power-law behavior does not depend on the strength of the magnetic field and the energy range chosen.