Paired states of interacting electrons in a two dimensional lattice

We show that two tight binding electrons that repel may form a bounded pair in two dimensions. The paired states form a band with energies that scale like the strength of the interaction potential. By applying an electric field we show that the dynamics of such states is that of a composite particle of charge 2e. The system still sustains Bloch-like states, so that if the two bands overlap single and paired states might coexist allowing for a bosonic fluid component that, if condensed, would decrease the resistance at low temperatures. The presence of two bands allows for new oscillations whose experimental detection would permit a direct measurement of the interaction potential strength.