Dynamical method for studying localization-delocalization transition in two dimensional percolating systems |
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Authors: | M F Islam and H Nakanishi |
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Institution: | (1) Department of Physics, Purdue University, West Lafayette, IN 47907, USA |
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Abstract: | We study quantum percolation which is described by a tight-binding Hamiltonian containing only off-diagonal hopping terms
that are generally in quenched binary disorder (zero or one). In such a system, transmission of a quantum particle is determined
by the disorder and interference effects, leading to interesting sharp features in conductance as the energy, disorder, and
boundary conditions are varied. To aid understanding of this phenomenon, we develop a visualization method whereby the progression
of a wave packet entering the cluster through a lead on one side and exiting from another lead on the other side can be tracked
dynamically. Using this method, we investigate the localization-delocalization transition in a 2D system for various boundary
conditions. Our results indicate the existence of two different kinds of localized regimes, namely exponential and power law
localization, depending on the amount of disorder. Our study further suggests that there may be a delocalized state in the
2D quantum percolation system at very low disorder. These results are based on a finite size scaling analysis of the systems
of size up to 70 × 70 (containing 4900 sites) on the square lattice. |
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Keywords: | PACS" target="_blank">PACS 64 60 ah Percolation 05 60 Gg Quantum transport 72 15 Rn Localization effects |
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