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arXiv 0712.0449cond-mat.str-elcond-mat.mes-hall
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三维量子逾渗中的金属-绝缘体相变

Metal - Insulator Transition in 3D Quantum Percolation

Igor Travenec

摘要:

利用简单立方晶格上的量子位点渗流模型研究了金属-绝缘体相变.本文用转移矩阵法计算了能量分布的二元体系的输运性质--朗道电导.我们详细计算了无序(绝缘位点的比率)-能量平面中的迁移率边缘,我们发现极端临界无序有点接近经典的逾渗阈值,比以前报道的。我们计算了沿迁移率边缘的临界指数$ν$,发现它是常数,与三维Anderson模型的临界指数相等,从而确定了共同的普适类。可能的例外是导带的中心,在那里,单参数缩放不再有效,或者有限尺寸效应是巨大的。这种说法的原因之一是在特定能量下电导的算术平均和几何平均结果之间的差异。只有几何平均值才能在带中心产生零临界无序,这是理论预测的。

英文摘要:

We present the metal - insulator transition study of a quantum site percolation model on simple cubic lattice. Transfer matrix method is used to calculate transport properties - Landauer conductance - for the binary distribution of energies. We calculate the mobility edge in disorder (ratio of insulating sites) - energy plane in detail and we find the extremal critical disorder somewhat closer to the classical percolation threshold, than formerly reported. We calculate the critical exponent $ν$ along the mobility edge and find it constant and equal to the one of 3D Anderson model, confirming common universality class. Possible exception is the center of the conduction band, where either the single parameter scaling is not valid anymore, or finite size effects are immense. One of the reasons for such statement is the difference between results from arithmetic and geometric averaging of conductance at special energies. Only the geometric mean yields zero critical disorder in band center, which was theoretically predicted.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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