Superconductivity in strongly correlated systems for local repulsive interactions

TL;DR

This paper investigates superconductivity in a two-dimensional Hubbard model with local repulsive interactions, comparing to the attractive case, using Green's functions within the Hubbard-I approximation. It reveals a kinetically driven pairing mechanism mediated by a non-local gap $\Delta_{nl}$, with a minimum repulsion $U_{min}$ necessary for pairing and a $T_c$ that saturates at strong coupling, accompanied by a dome-shaped $T_c(n_d)$ and potential first-order transitions. The attractive case, treated with local pairing only, shows $T_c$ increasing logarithmically with $1/U$ and saturating, while $\mu(T_c)$ does not vanish, indicating residual fermionic character and possible phase separation. These findings highlight how strong correlations and kinetic energy shape superconductivity in 2D Hubbard systems and offer insights into non-BCS pairing and the BCS–BEC crossover in strongly correlated materials.

Abstract

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.

Figures (7)

• Figure 1: Values of the parameters for which the dispersion relations of the quasi-particles are real, for $n_d = 0.5$ upper curve and $n_d = 1$. For values of $\Delta_{nl}$ above the lines superconductivity is unstable as evidenced by an imaginary part in the energy of the quasi-particle excitations.
• Figure 2: (a) Dispersions relations of $\omega_{2}(k)$ of the quasi-particles excitations for $U/\mu\rightarrow 1$ and $\Delta_{nl}>0$ and $\Delta_{nl}=0$. (b) It is shown for $k=0$ and finite $\Delta_{nl}$ the $U$ region with negative values of $B(k)$ that gives non-real $\omega_{1,2}(k)$ energies. For $\Delta_{nl}=0$ the condition in Eq. (\ref{['21']}) $U_{min}=\mu$ is shown. For all figures we used $\mu/E_{F}=1.0$ and $n_{d}=0.5$.
• Figure 3: The $T_{c}\times n_d$ phase diagram for an electron gas in two dimensions. For strong repulsive interactions the highest value of $T_c$ is observed around $n_d=0.5$
• Figure 4: $T_c$ and chemical potential ${\mu}(T_c)$ as function of $U$ in logarithmic scale for strong repulsive interaction. Notice that $U$ is normalized by the band width $D$ and $\mu_0=\mu(T_c,U/D=1)$.
• Figure 5: a) The ground state ($T=0$) phase diagram $U_c \times n_d$ for an electron gas in 2D with a constant density of states $\rho(\omega)=1/D$. The dashed line represents the first-order phase transition line. b) The non-local order parameter $\Delta_{nl}$ as a function of $n_d$ for several values of $U/D$. In this case, we observe both second-order and first-order phase transitions.