Analysis of localization-delocalization transitions in corner-sharing tetrahedral lattices

Abstract

We study the critical behavior of the Anderson localization-delocalization transition in corner-sharing tetrahedral lattices. We compare our results obtained by three different numerical methods namely the multifractal analysis, the Green resolvent method, and the energy-level statistics which yield the singularity strength, the decay length of the wave functions, and the (integrated) energy-level distribution, respectively. From these measures a finite-size scaling approach allows us to determine the critical parameters simultaneously. With particular emphasis we calculate the propagation of the statistical errors by a Monte-Carlo method. We find a high agreement between the results of all methods and we can estimate the highest critical disorder Wc = 14.474 (8) at energy Ec = − 4.0 and the critical exponent ν = 1.565 (11). Our results agree with a previous study by Fazileh et al. [F. Fazileh, X. Chen, R.J. Gooding, K. Tabunshchyk, Phys. Rev. B 73, 035124 (2006)] but improve accuracy significantly.