Dynamic Cluster Quantum Monte Carlo Simulations of a Two-Dimensional Hubbard Model with Stripelike Charge-Density-Wave Modulations: Interplay between Inhomogeneities and the Superconducting State

Using dynamic cluster quantum Monte Carlo simulations, we study the superconducting behavior of a $1/8$ doped two-dimensional Hubbard model with imposed unidirectional stripelike charge-density-wave modulation. We find a significant increase of the pairing correlations and critical temperature relative to the homogeneous system when the modulation length scale is sufficiently large. With a separable form of the irreducible particle-particle vertex, we show that optimized superconductivity is obtained for a moderate modulation strength due to a delicate balance between the modulation enhanced pairing interaction, and a concomitant suppression of the bare particle-particle excitations by a modulation reduction of the quasiparticle weight.

Figure 1

Charge modulation potential $V(l_x)$ (bars) and resulting local occupation $⟨n⟩(l_x)$ (symbols connected by dashed lines) versus location $l_x$ along the long side in the $8\times 4$-site cluster. The system has translational invariance along $L_y$. Results are for a temperature $T=0.125$ and modulation wave vector (a) $Q=\pi /2$ and (b) $Q=\pi /4$. The dashed green or gray line indicates the average filling of $⟨n⟩=0.875$.

Figure 2

The leading ($d$-wave) eigenvalue of the particle-particle Bethe-Salpeter equation for the homogeneous and inhomogeneous systems with a modulation periodicity of 8 sites ($Q=\pi /4$) for different modulation strengths $V_0$. The stripe inhomogeneity significantly enhances the pairing correlations and $T_c$. The transition temperature $T_c$ as a function of modulation strength $V_0$ is shown in the inset.

Figure 3

The leading ($d$-wave) eigenvalue of the particle-particle Bethe-Salpeter equation for the homogeneous system ($V_0=0$) and the inhomogeneous systems (finite $V_0$) with a modulation periodicity of 4 sites ($Q=\pi /2$). The shorter length-scale inhomogeneity has no effect on the pairing correlations.

Figure 4

The pairing interaction $V_d(T)$ (a) defined in Eq. (4) and the bare $d$-wave pairing susceptibility $P_d^0(T)$ defined in Eq. (5) as a function of temperature for different modulation strength $V_0$ for the modulation with $Q=\pi /4$. The pairing interaction $V_d$ is enhanced by the charge modulation, while $P_d^0$ is reduced.