Phase coherence in tight-binding models with nonrandom long-range hopping

The density of states, even for a perfectly ordered tight-binding model, can exhibit a tail-like feature at the top of the band, provided the hopping integral falls off in space slowly enough. We apply the coherent potential approximation to study the eigenstates of a tight-binding Hamiltonian with uncorrelated diagonal disorder and long-range hopping, falling off as a power mu of the intersite distance. For a certain interval of hopping-range exponent mu, we show that the phase-coherence length is infinite for the outermost state of the tail, irrespectively of the strength of disorder. Such an anomalous feature can be explained by the smallness of the phase-space volume for the disorder scattering from this state. As an application of the theory, we mention that ballistic regime can be realized for Frenkel excitons in two-dimensional molecular aggregates, affecting to a large extent the optical response and energy transport