Abstract
We consider spin and charge transport in a Sierpinski planar carpet; the interest here is its unique geometry. We analyze the fractal conductor as a combination of multiply connected quantum wires, and we observe the evolution of the transmission envelope in different fractal generations. For a fractal conductor dominated by resonant modes the transmission is characterized by strong fluctuations and conduction gaps. We show that charge and spin transport have different responses both to the presence of defects and to applied bias. At a high bias, or in a high-order fractal generation, spin accumulation is separated from charge accumulation because the larger drift velocity needs a longer polarization length, and the sample may turn into an insulator by the action of the defects. Our results are calculated numerically using the Keldysh Green function within the tight-binding framework.
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