| Summary: | 碩士 === 國立臺灣大學 === 物理研究所 === 101 === We consider spin and charge transport on a Sierpinski planar carpet; the interest here is its unique fractal geometry. Analyzing a fractal conductor as a combination of multiply connected quantum wires we observe the evolution of the transmission envelope in different generations of the fractal conductor. For a fractal conductor dominated by resonant modes the transmission is characterized by strong fluctuations and conducting gaps. We show that charge and spin transport have different responses 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.
Furthermore, we also discuss the percolation theory in spin transport. In the old percolation theory a metal can be turned into an insulator if its site ratio is lower than the percolation ratio. However, the percolation of charges and spin may be different. It means a charge insulator is possible to be a “spin conductor”. Our results are calculated numerically using the Keldysh Green function in the tight-binding framework.
Keywords: Spin, Quantum Transport, Fractal Structure, Landau-Keldysh Formalism, Non-Equilibrium Green Function, Spin Hall Effect
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