Multifractality of ab initio wave functions in doped semiconductors
Abstract
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 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 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 critical multifractal spectrum at the MIT for Si:S.