Mobile electron pairs on lattices in the UV Model

<div>We investigate the conditions under which the ground state of a low-density quasi-two-dimensional electron (or hole) system is a Bose-Einstein condensate of mobile dimers. Such a ground state would require an effective attraction between electrons but an effective repulsion between dimers to prevent clustering. A UV model is assumed; this is not specific to the pairing mechanism but can be obtained from a Fröhlich-Coulomb model by the Lang-Firsov transformation. We survey the parameter space for each lattice restricting the dimer Hilbert spaces to the low-energy sector since we are interested in low-lying states and low densities. Singlet dimers are mobile on a triangular lattice; in the simplest case the effective Hamiltonian for dimer hopping is that of a kagome lattice. However, a dimer condensate is never the ground state in the triangular lattice, as dimers will either cluster or dissociate. For a square lattice with nearest- and next-nearest-neighbour hopping we find a substantial region in which dimers form a ground state. These dimers turn out to be very light since they can propagate by a “crab-like” motion without requiring virtual transitions. For a perovskite layer we find a substantial region in which dimers, which are also light and mobile due to crab-like motion, form a ground state. Our findings indicate that the existence of stable small mobile bipolarons is very sensitive to the lattice structure.</div><div>We secondly identify circumstances under which triplet dimers are strictly localised by interference in certain one- and two-dimensional lattices. We find that strict localisation is possible for the square ladder and some two-dimensional bilayers. We thirdly investigate the electronic properties of Graphene. We identify the origin of Graphene’s Dirac points and subsequently identify Dirac points in other two- and three-dimensional lattices. We finally investigate the dynamics of electrons and dimers on various oneand two-dimensional lattices by the use of Green’s functions.</div>