Strong enhancement of d-wave superconductivity in an extended checkerboard Hubbard ladder

TL;DR

This paper investigates how nearest-neighbor attraction $V$ and hopping inhomogeneity affect $d$-wave superconductivity in the extended checkerboard Hubbard model on a two-leg ladder using density-matrix renormalization group methods. The study finds that $V$ enhances superconducting correlations in both homogeneous ($t' = t$) and inhomogeneous ($t' < t$) regimes, with the critical attraction $|V_c|$ dramatically reduced by inhomogeneity. In the extremely inhomogeneous limit, superconductivity emerges concomitantly with hole-pair formation on plaquettes and exhibits $C_4$-symmetric pairing, consistent with a two-dimensional checkerboard lattice. Overall, the results demonstrate that combining strong correlations, NN attraction, and inhomogeneity robustly stabilizes $d$-wave superconductivity, offering insight into cuprate-like pairing mechanisms in strongly correlated, inhomogeneous systems.

Abstract

By employing the density-matrix renormalization group method, we study an extended checkerboard Hubbard model on the two-leg ladder, which includes an intraplaquette nearest-neighbour attraction V. The simulated results show that V plays a significant role in enhancing the d-wave superconductivity when the electron density is close to half-filling. In the homogeneous case t'=t (t and t' are the intraplaquette and interplaquette hopping integrals), large critical |Vc| is required to induce the superconducting ground state. With decreasing t', |Vc| is substantially diminished and the pair state has a nearly C4 symmetry. In the extremely inhomogeneous case t'<0.2t, the system transits to the d-wave superconducting phase at V\sim-0.3t and V\sim-0.4t for U=8t and U=12t, respectively, accompanying with a shift of spin and single-particle excitations from gapless to gapped type.

Figures (7)

• Figure 1: A sketch diagram of the checkerboard Hubbard model on the two-leg ladder. $t$ and $t'$ represent NN hoppings within and between plaquettes, respectively. $U$ denotes the on-site repulsion. $V$ stands for the intraplaqutte NN interaction.
• Figure 2: The SC correlation, charge density profile, spin correlation, and single-particle correlation for various intraplaquette NN attractions $V$ in the homogeneous case. (a) shows the singlet pairing correlation function $\Phi_{\rm{rr}}$. The dash-dotted and solid lines show two fitted curves of $\Phi_{\rm{rr}}$ at $V = -0.8$ and $V = -1.2$, respectively. (b) displays the real-space density profile. (c) and (d) show the single-particle and spin correlations. The data at $V = -0.8$ and $V = -1.2$ are well fitted by $B_{\alpha}(x-x_0)^{-K_{\alpha}}$ and $A_{\alpha}e^{-\frac{x-x_0}{\xi_{\alpha}}}$ respectively, as shown by the dotted and solid lines.
• Figure 3: Correlation functions and charge density profile at various intraplaquette NN attractions in the inhomogeneous case of $t'=0.4$. (a), (c) and (d) show the SC, single-particle and spin correlations, and (b) shows the charge density profile. The algebraical fitting curves for $\Phi_{\rm{rr}}$ at $V=-0.6$ and $V=-0.8$ are plotted in dash-dotted and solid lines, and the corresponding $K_{sc}$ values are given in (a). $G_c$ and $G_z$ at $V=0.0$ and $V=-0.6$ are well fitted by $B_{\alpha}(x-x_0)^{K_{\alpha}}$ and $A_{\alpha}e^{-\frac{x-x_0}{\xi_\alpha}}$, and the corresponding fitting parameters $K_{\alpha}$ and $\xi_{\alpha}$ are given in (c) and (d).
• Figure 4: Correlation functions and charge density profile at various intraplaquette NN attractions in the inhomogeneous case of $t'=0.1$. (a), (c) and (d) show the SC, single-particle and spin correlations, and (b) shows the charge density profile. The algebraical fitting curves for $\Phi_{\rm{rr}}$ at $V=-0.3$ and $V=-0.4$ are plotted in dash-dotted and solid lines, and the corresponding $K_{sc}$ values are given in (a). In (c) and (d), the dash-dotted lines represent algebraic fittings at $V=0.0$, while the solid lines represent power-law fittings at $V=-0.3$.
• Figure 5: Correlation functions at different interplaquette hopping integrals $t' = 1, 0.4, 0.2, 0.1, 0.05$ and various $V$. (a) and (b) show the effect of $t'$ on the SC correlation at $V=0.0$ and $V=-0.4$, respectively. (c) and (d) show the effect of $t'$ on the correlation functions of single-particle and spin at $V=-0.4$. In (c) and (d), the dash-dotted lines represent algebraic fittings at $t'=1.0$, while the solid lines represent power-law fittings at $t'=0.2$.