Tuning of resonances in the generalized random trimer model

The existence of nonscattered states in random systems composed of trimers in their generalized form and a second element is studied in the context of a tight-binding Hamiltonian. Many conditions for the existence of such states in this generalized random trimer model are obtained by introducing appropriate structural correlations between the host element and the trimer. This aspect of the correlated-disorder systems has not been studied before to our knowledge. The condition for tuning the positions of the two sets of nonscattered states is obtained. We further show that the two resonances of a single trimer in the host lattice can be merged at a single energy. For this case, when the resonance energy is inside the host band, the width of the nonscattered states is found to decay as ∼${\mathit{N}}^{\mathrm{-}1/4}$. $N— is the number of sites in the system. Experiments to observe the broadening of the width are proposed. In all other cases width is shown to decay as ∼${\mathit{N}}^{\mathrm{-}1/2}$.