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• W2317962360 abstract "Percolation has been studied extensively and a number of applications have been proposed due to its simplicity. One of its most interesting applications in solid state physics is the metal-insulator transition. Since the quantum phase transition is defined at absolute zero of temperature, the classical percolation picture is insufficient and the quantum effects should be taken into account. Thus localization due to the quantum interference effect becomes very important. In the classical percolation, we consider conducting and insulating elements. We define the portion of the conducting part to be p. With the increase of the conducting part, the current begins to flow once the conducting part percolates throughout the system, and the system becomes metallic. This metal-insulator transition occurs at the percolation threshold p = pc. However, in the quantum percolation (QP), even if there is already an infinite cluster, the wave function may be localized and the system remains to be in the insulating regime. With further increase of p, the localized wave function becomes delocalized at the quantum percolation threshold, p = pq(≥ pc). The MITs of non-interacting electron systems with randomness are often described as the Anderson transition (AT). If the QP belongs to the universality class of AT, our understandings of the QP are deepened, and it has been discussed whether the QP belongs to the universality classes of the AT or not. The most direct way is to estimate precisely the critical exponent of the QP and compare it with that for the AT. However, the exponent for the QP is at variance. For example, the critical exponent ν for the divergence of correlation and localization lengths ranges from 0.38 to 2.1. Using the finite size scaling of the energy level statistics, 16) we have recently studied the three dimensional (3D) bond percolation problems and estimated ν and pq. We have studied the effect of breaking the time reversal symmetry, 18) which is very important for the AT. The decrease of pq by breaking the time reversal symmetry and the values of ν are consistent with the conjecture that the QP is the AT. In this paper, we give further support of this conjecture by showing that the localization-delocalization transition occurs in 2D systems in the presence of time reversal but in the absence of the spin-rotational symmetry. This is consistent with the 2D Anderson transition that" @default.
• W2317962360 created "2016-06-24" @default.
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• W2317962360 date "2003-01-03" @default.
• W2317962360 modified "2023-10-16" @default.
• W2317962360 title "Quantum Percolation and the Anderson Transition" @default.
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• W2317962360 doi "https://doi.org/10.1143/jpsjs.72sa.141" @default.
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