Finite-size scaling of multifractal wave functions: The metal-insulator transition in two-dimensional symplectic systems

Abstract

A finite-size scaling analysis of wave functions near the metal-insulator transition (MIT) point has been developed, and applied to the MIT in a two-dimensional disordered electron system in the presence of spin-orbit interaction. The present method has the following advantages: (i) Quantities characterizing the critical behavior, such as the critical disorder ${W}_{c}$ or the localization exponent $\ensuremath{\nu},$ are multiply calculated from independent scaling analyses of spatial parts with different intensities in wave functions. (ii) These quantities and the multifractality of the critical wave function are determined simultaneously. (iii) It is not necessary to treat many samples with different sizes. (iv) Much computing time is saved, and the scaling analysis can be done up to very large sizes. Using this method, we obtained ${W}_{c}=5.86\ifmmode\pm\else\textpm\fi{}0.04$ and $\ensuremath{\nu}=2.41\ifmmode\pm\else\textpm\fi{}0.24$ for a model of a two-dimensional symplectic system.