Impact of clustering of substitutional impurities on quasiparticle lifetimes and localization

Motivated by the observation and prediction of clustering behavior for impurities substituted into the host lattice of a real material and the dramatic impact this can have on electronic properties, we develop a simple approach to describe such an effect via the electron self-energy. We employ a disorder-averaged Formula Presented-matrix expansion taken to second order, which we modify to include a clustering probability parameter. This approach circumvents the need for specific cluster probability distributions, simplifying greatly the analysis of clustered impurities. To gain analytical insights, we study a nearest-neighbor square lattice tight-binding Hamiltonian with clustered impurity substitutions to investigate clustering of off-diagonal hopping impurities. We find that our Formula Presented-matrix approach is in excellent agreement with exact numerical results from a tight-binding computation performed with the kwant package. We observe a variety of interesting impurity clustering-induced effects in the self-energy such as the suppression of quasiparticle lifetimes at certain momenta and an increase in localization, as indicated by the inverse participation ratio. The kwant results are reproduced in our modified Formula Presented-matrix approach. In addition, our method allows for a full analytical treatment of clustering effects which can aid in physical insight.