Abstract
The Sierpinski gasket fractal has been studied in the presence of a magnetic field applied perpendicular to the plane of the fractal. The discretized Schr\"odinger equation for a single electron is solved using an exact real-space decimation technique. An infinite number of energy eigenvalues exist that give rise to perfectly extended eigenstates on this fractal. A prescription for their evaluation is proposed. Aharonov-Bohm oscillations in the transmission coefficient have been investigated in the case of this fractal lattice. The nature of oscillations for different electron energies and its dependence on the system size as well as on the boundary sites are discussed in detail.
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