Impurity states between two bands

Abstract

It is shown that an impurity state in a one-dimensional periodic potential can be associated uniquely with one of the bands between which its energy level lies. If the procedure of Kohn and Onffroy is then used to construct the generalized Wannier functions (GWF), equivalent to the scattering states and bound states associated with a given band, it is found that the GWF have the same exponential localization as the Wannier functions of the perfect crystal. This is true even though the impurity-state wave functions themselves may be longer ranged. In addition, the GWF approach the Wannier functions of the perfect crystal exponentially in the distance from the impurity site.