Enhanced superconductivity via layer differentiation in trilayer Hubbard model

TL;DR

The paper addresses why multilayer cuprates achieve high $T_c$ by studying a single-orbital trilayer Hubbard model with layer-differentiated densities. Using large-scale DCA-CT-AUX with $N_c=24$, it resolves layer-resolved pseudogap and superconductivity under controlled density imbalances characterized by $\delta_I$, $\delta_O$, and $\delta_{avg}$. Key findings show that the IL can host $d$-wave superconductivity and that $T_c$ can exceed the single-layer value, with imbalanced doping ($\delta_I<\delta_O$) generally boosting SC; OLs can participate in SC when $\delta_I>\delta_O$. Antiferromagnetic spin fluctuations play a central role, as evidenced by the relation between the spin susceptibility $\chi_s$ and the leading $d$-wave Bethe-Salpeter eigenvalue $\lambda_d$, constraining mechanisms for high $T_c$ in multilayer cuprates and suggesting layer-differentiation as a route to enhanced superconductivity.

Abstract

Motivated by the highest superconducting transition temperature ($T_c$) in multilayer cuprates,we investigated the trilayer Hubbard model by adopting the large-scale dynamical cluster quantum Monte Carlo simulations. Focusing on the systems with hole dopings within the two outer layers (OL) higher than the inner layer (IL), which is believed to be relevant to the realistic multilayer cuprates, our exploration discovered that the IL and OL manifest strong differentiation in a wide range of hole doping combinations. Specifically, the OLs remain metallic while the IL shows a distinct transition from the pseudogap to superconducting state. More importantly, the highest $T_c$ of the composite trilayer system can be largely enhanced compared to the single layer model and the imbalanced hole dopings between IL and OL are generically beneficial for global SC. We further provide strong numerical evidence on the possibility of $d$-wave superconductivity solely hosted in the IL. Our investigation provides new insight into the origin of highest $T_c$ in multilayer cuprates.

Figures (7)

• Figure 1: Schematic diagram of the trilayer Hubbard model labeled with various hoppings and on-site interaction $U$. The site energy $e_I \neq0$ controls the density distribution.
• Figure 2: Layer and momentum differentiation between IL (upper) and OL (lower) at $\delta_{avg}=0.1$. (a) and (d): Temperature evolution of the extrapolated imaginary zero-frequency -Im$G(\textbf{K}, i\omega_n=0)$ obtained from a linear extrapolation of the first two Matsubara frequencies; (b) and (e): The spectral function $A(\textbf{K},\omega)$ at $T/t=0.06$; (c) and (f): The imaginary part of self-energy Im$\Sigma(\textbf{K},i\omega_n)$ at $T/t=0.06$. The solid and dashed line or open symbols indicate the anti-nodal $\textbf{K}=(\pi,0)$ and nodal $\textbf{K}=(\frac{\pi}{2},\frac{\pi}{2})$ directions respectively.
• Figure 3:
• Figure 4: Evolution of $T_c$ on the hole doping $\delta_I$ of IL for two fixed $\delta_{avg}=0.1, 0.15$. The more realistic density distribution $\delta_I<\delta_O$ is indicated by solid line; while the dashed line denotes the $\delta_I>\delta_O$ regime. The $T_c$ of single layer model is shown as comparison.
• Figure 5: The leading $d$-wave eigenvectors $\Phi_d(\mathbf{K},\pi T)$ of the OL (left) and IL (right) at $T/t=0.06$ and $\delta_{avg}=0.1$. The dots denote the finite $\mathbf{K}$ points sampling the Brillouin zone via our DCA simulation. The density distributions are $(\delta_I,\delta_O)=(0.06,0.12),(0.08,0.11)$, and $(0.1,0.1)$ in upper, middle, and lower rows respectively, which corresponds to the decreasing $T_c$ segment (orange solid line) in Fig. \ref{['Tc']}. When $\delta_I<\delta_O$, the IL is fully responsible for the $d$-wave SC.