Frustrated collisions and unconventional pairing on a quantum superlattice
Institute of Electronic Structure and Laser, FORTH - GR-71110 Heraklion, Crete, Greece, EU
2 Institut für Physik, Humboldt-Universität zu Berlin - D-12489 Berlin, Germany, EU
Accepted: 20 September 2010
We consider the problem of scattering and binding of two interacting spin-(1/2) fermions on a one-dimensional tight-binding superlattice with a period of twice the lattice spacing. We solve the problem analytically for all ranges of parameters of the system. We find that, for the non-trivial case of singlet states, both bound and scattering wave functions consist of a generalized Bethe ansatz augmented with an extra scattering product due to “asymptotic” degeneracy. If a Bloch band is doubly occupied, the extra wave can be a bound state in the continuum corresponding to a single-particle inter-band transition. In all other cases, it corresponds to a quasi-momentum changing, frustrated collision.
PACS: 05.30.Fk – Fermion systems and electron gas / 03.65.Nk – Scattering theory / 71.10.Pm – Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.)
© EPLA, 2010