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 $\nu$ 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.

14 pages with 6 colour figures, proceedings of the symposium 'Physics at the Nanoscale' at University of Manitoba, Winnipeg, Canada, April 2018 in honour of Prof. Tapash Chakraborty

References in corpus (8)

• Anderson Transitions
• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Localization of ultrasound in a three-dimensional elastic network
• Exact relations between multifractal exponents at the Anderson transition
• Critical parameters from generalised multifractal analysis at the Anderson transition
• Multifractal analysis with the probability density function at the three-dimensional Anderson transition
• Multifractal analysis of the metal-insulator transition in the 3D Anderson model I: Symmetry relation under typical averaging
• Multifractal finite-size scaling at the Anderson transition in the unitary symmetry class