Bound state attraction threshold in the layered Hubbard model

M. Bąk

Rodrigo A. Fontenele, Natanael C. Costa, Thereza Paiva +1 more

The attractive Hubbard model has become a model readily realizable with ultracold atoms on optical lattices. However, the superconducting (superfluid) critical temperatures ${T}_{c}$'s are still somewhat smaller than the lowest temperatures achieved in experiments. Here, we consider two possible routes, generically called layering, to increase ${T}_{c}$: a bilayer and a simple cubic lattice, both with tunable hopping ${t}_{z}$ between attractive Hubbard planes. We have performed minus-sign--free determinant quantum Monte Carlo simulations to calculate response functions such as pairing correlation functions, uniform spin susceptibility, and double occupancy, through which we map out some physical properties. We have found that by a judicious choice of fillings and intensity of on-site attraction, a bilayer can exhibit ${T}_{c}$'s between 1.5 and 1.7 times those of the single layer; for the simple-cubic lattice the enhancement can be 30% larger than the maximum for the single layer. We also check the accuracy of both a BCS-like estimate for ${T}_{c}$ in the attractive Hubbard model as well as of an upper bound for ${T}_{c}$ based on the superfluid density.

Manuel Valiente, David Petrosyan

We present a complete derivation of two-particle states of the one-dimensional extended Hubbard model involving attractive or repulsive on-site and nearest-neighbour interactions. We find that this system possesses scattering resonances and two families of energy-dependent interaction-bound states which are not present in the Hubbard model with the on-site interaction alone.

Bumsoo Kyung

Gideon Wachtel, Assaf Bar-Yaacov, Dror Orgad

We study a model of a composite system constructed from a ``pairing layer'' of disconnected attractive-$U$ Hubbard sites that is coupled by single-particle tunneling, ${t}_{\ensuremath{\perp}}$, to a disordered metallic layer. For small interlayer tunneling the system is described by an effective long-range $XY$ phase model whose critical temperature, ${T}_{c}$, is essentially insensitive to the disorder and is exponentially suppressed by quantum fluctuations. ${T}_{c}$ reaches a maximum for intermediate values of ${t}_{\ensuremath{\perp}}$, which we calculate using a combination of mean-field, classical, and quantum Monte Carlo methods. The maximal ${T}_{c}$ scales as a fraction of the zero-temperature gap of the attractive sites when $U$ is smaller than the metallic bandwidth, and is bounded by the maximal ${T}_{c}$ of the two-dimensional attractive Hubbard model for large $U$. Our results indicate that a thin, rather than a thick, metallic coating is better suited for the enhancement of ${T}_{c}$ at the surface of a phase fluctuating superconductor.

T. Schneider, H. Beck, Dierk Bormann +3 more