Dependence of critical level statistics on the sample shape

H. Potempa; L. Schweitzer

doi:10.1088/0953-8984/10/25/003

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Dependence of critical level statistics on the sample shape

H. Potempa·L. Schweitzer

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Abstract

The level-spacing distribution of consecutive energy eigenvalues is calculated numerically at the metal insulator transition for 3d systems with different cuboid shapes. It is found that the scale independent critical $P_c(s)$ changes as a function of the aspect ratio of the samples while the critical disorder $W_c/V=16.4$ remains the same. We use our data to test whether an expression for the small-$s$ behaviour of the level statistics proposed by Kravtsov and Mirlin for the metallic regime is applicable also at the critical point. For this reason, a shape dependent dimensionless critical conductance $g_c$ has been extracted from the small-$s$ behaviour of the critical level statistics. Our result for a cubic sample, $g_c=0.112\pm 0.005$, is in good agreement with a value obtained previously from calculations using the Kubo-formula.

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BibTeX RIS

H. Potempa, L. Schweitzer. 1998-04-29. Dependence of critical level statistics on the sample shape. https://doi.org/10.1088/0953-8984%2F10%2F25%2F003

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