EFFECTS OF A NONLINEAR IMPURITY IN A DIATOMIC CHAIN

The problem of the existence of bound states outside the continuum of the bands due to the presence of a nonlinear impurity is studied withi n a two-band tight-binding model in one dimension. The nonlinear impur ity deviates from the ordinary sites by an on-site energy of the form (chi)(\psi(0)\(2))(beta/2), where \psi(0)\(2) is the probability of fi nding the particle at the impurity site, chi is referred to as the str ength and beta is the nonlinearity of the impurity. For beta > 2, ther e exist threshold values for chi below which there is no bound state. For 0 < beta less than or equal to 2, there is always one bound state above the upper band for chi > 0; and two bound states, one with energ y inside the band gap and another below the lower band, for (chi) < 0. For beta < 0, there is always a bound state above (below) the upper ( lower) band for chi > 0 (chi < 0). For \beta\ < 2/3 (beta < 0), there is always a state inside the gap; while for \beta\ > 2/3, there exists an upper bound for \chi\ above which no bound states are found inside the gap.