Paired states of crystalline electrons in two dimensions

We show that in a perfect crystalline environment two electrons may pair to form a bound state. Such states form a band whose energy above the Bloch band center scales like the strength of the interaction. The pairs obey the dynamics of a composite particle. This is shown by considering an external electric field and verifying that there are Bloch oscillations corresponding to an object of charge 2e. If the strength of the interaction is comparable to the band width, or smaller, the Bloch and paired states bands may overlap, suggesting that in the ground state a bosonic fluid could be formed. The pair problem is equivalent to that of a single particle in a 4D lattice with a surface. The paired states correspond to surface states in such equivalent problem and decay exponentially as the particles move away from each other.