Multifractality of ab initio wave functions in doped semiconductors

In Refs. [1,2] we have shown how a combination of modern linear-scaling DFT, together with a subsequent use of large, effective tight-binding Hamiltonians, allows to compute multifractal wave functions yielding the critical properties of the Anderson metal-insulator transition (MIT) in doped semiconductors. This combination allowed us to construct large and atomistically realistic samples of sulfur-doped silicon (Si:S). The critical properties of such systems and the existence of the MIT are well known, but experimentally determined values of the critical exponent $\nu$ close to the transition have remained different from those obtained by the standard tight-binding Anderson model. In Ref. [1], we found that this ``exponent puzzle'' can be resolved when using our novel \emph{ab initio} approach based on scaling of multifractal exponents in the realistic impurity band for Si:S. Here, after a short review of multifractality, we give details of the multifractal analysis as used in [1] and show the obtained \emph{critical} multifractal spectrum at the MIT for Si:S.