Dependence of critical level statistics on the sample shape

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.

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

References in corpus (2)

• Asymptotics of Universal Probability of Neighboring Level Spacings at the Anderson Transition
• Spectral statistics of disordered metals in the presence of several Aharonov-Bohm fluxes

Cited by in corpus (11)

• Fluctuations of the inverse participation ratio at the Anderson transition
• Boundary conditions at the mobility edge
• How does geometry affect quantum gases?
• Anderson localization in optical lattices with correlated disorder
• Fermions on a torus knot
• Few-boson localization in a continuum with speckle disorder
• Influence of boundary conditions on level statistics and eigenstates at the metal insulator transition
• Real-space renormalization-group approach to the integer quantum Hall effect
• Origin of quantum shape effect
• Quantum gases on a torus
• Boundary hopping and the mobility edge in the Anderson model in three dimensions