Dimer impurity effect on the 1D density of states

We study the effect of a dimer impurity on the local density of states (LDOS) associated with 1D tight binding Hamiltonian. Theoretical analysis is carried out by studying the resulting three-term recursion relation corresponding to the tridiagonal representation of the system Hamiltonian. We found a closed form expression for the perturbed LDOS in terms of the unperturbed one with a pre-factor that carries information on both location and potential strength of the dimer impurity.