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Spectral changes in layered $f$-electron systems induced by Kondo hole substitution in the boundary-layer

We investigate the effect of disorder on the dynamical spectrum of layered $f$-electron systems. With random dilution of $f$-sites in a single Kondo insulating layer, we explore the range and extent to which Kondo hole incoherence can penetrate into adjacent layers. We consider three cases of neighboring layers: band insulator, Kondo insulator and simple metal. The disorder-induced spectral weight transfer, used here for quantification of the proximity effect, decays algebraically with distance from the boundary layer. Further, we show that the spectral weight transfer is highly dependent on the frequency range considered as well as the presence of interactions in the clean adjacent layers. The changes in the low frequency spectrum are very similar when the adjacent layers are either metallic or Kondo insulating, and hence are independent of interactions. In stark contrast, a distinct picture emerges for the spectral weight transfers across large energy scales. The spectral weight transfer over all energy scales is much higher when the adjacent layers are non-interacting as compared to when they are strongly interacting Kondo insulators. Thus, over all scales, interactions screen the disorder effects significantly. We discuss the possibility of a crossover from non-Fermi liquid to Fermi liquid behavior upon increasing the ratio of clean to disordered layers in particle-hole asymmetric systems.