Dependence of critical level statistics on the sample shape

Details Dependence of critical level statistics on the sample shape Dependence of critical level statistics on the sample shape

1998-04-29

arxiv.org/abs/cond-mat/9804312v1

J. Phys.: Condens. Matter 10 (1998) L431-L435

Physics

Condensed Matter

Disordered Systems and Neural Networks

5 pages LaTeX, 3 ps-figures included. submitted to Journ. of Physics Condensed Matter

Scientific paper

10.1088/0953-8984/10/25/003

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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