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Motivated by the observation and prediction of clustering behavior forimpurities substituted into the host lattice of a real material, and thedramatic impact this can have on electronic properties, we develop a simpleapproach to describe such an effect via the electron self-energy. We employ adisorder averaged T-matrix expansion taken to second order, which we modify toinclude a clustering probability parameter. This approach circumvents the needfor specific cluster probability distributions, simplifying greatly theanalysis of clustered impurities. To gain analytical insights, we study anearest-neighbor square lattice tight-binding Hamiltonian with clusteredimpurity substitutions to investigate clustering of off-diagonal hoppingimpurities. We find that our T-matrix approach is in excellent agreement withexact numerical results from a tight-binding computation performed with theKWANT package. We observe a variety of interesting impurity clustering-inducedeffects in the self-energy such as the suppression of quasi-particle lifetimesat certain momenta and an increase in localization, as indicated by the inverseparticipation ratio. The KWANT results are reproduced in our modified T-matrixapproach. In addition, our method allows for a full analytical treatment ofclustering effects which can aid in physical insight.

Impact of clustering of substitutional impurities on quasiparticle lifetimes and localization