Superconductivity in strongly correlated systems for local repulsive interactions

The understanding of the mechanisms responsible for superconductivity in strongly correlated systems is an interesting and important subject in condensed matter physics. Several theoretical proposals were considered for these systems. The Coulomb interaction between electrons allow a new approach to study this problem. In this paper, we use a usual Hubbard model with a local repulsive interaction to describe a 2D system. The system of equations are solved using the Green’s functions method, within a Hubbard-I mean field approximation, which allows to treat the strong interaction limit. We consider both cases of attractive and repulsive interactions and obtain the zero temperature phase diagram of the model. Our results show, in the repulsive case, the existence of a superconducting ground state mediated by the kinetic electronic energy and described by a non-local order parameter. A minimum value of the repulsive interaction $U_{min}$ is required to create a pairing state. At finite temperatures, for strong interactions, the critical temperature $T_c$ shows a saturation similar to the Bose-Einstein condensation observed for strong attractive interactions.

💡 Research Summary

The authors investigate superconductivity in a two‑dimensional Hubbard model with a purely local repulsive interaction U, using the Green’s‑function formalism combined with the Hubbard‑I mean‑field approximation. This approach allows them to treat the strong‑coupling limit analytically while keeping the essential correlation effects. Two order parameters are introduced: a local gap Δ, associated with on‑site Cooper pairs ⟨d†i↑ d†i↓⟩, and a non‑local gap Δₙₗ, describing inter‑site pairing ⟨d†i↑ d†j↓⟩ (i≠j). Within the Hubbard‑I scheme the higher‑order propagators are decoupled, leading to closed equations for the normal and anomalous Green’s functions. The resulting quasiparticle spectrum consists of two branches ω₁,₂(k)=A(k)±B(k), where A(k)=ξ_k²+U²+ξ_k U n_d/2 and B(k)=√