Fluctuations of Hamiltonian eigenfunctions, measured by the inverse participation ratio (IPR), turn out to characterize topological-band insulator transitions occurring in 2D Dirac materials like silicene, which is isostructural with graphene but with a strong spin-orbit interaction. Using monotonic properties of the IPR, as a function of a perpendicular electric field (which provides a tunable band gap), we define topological-like quantum numbers that take different values in the topological-insulator and band-insulator phases.
@article{arxiv.1610.03696,
title = {Inverse participation ratio and localization in topological insulator phase transitions},
author = {M. Calixto and E. Romera},
journal= {arXiv preprint arXiv:1610.03696},
year = {2016}
}