Magnon-Mediated Superconductivity in the Infinite-$U$ Triangular Lattice

Abstract

We demonstrate that the infinite-$U$ triangular-lattice Hubbard model supports a superconducting state built from tightly bound Cooper pairs composed of two holes and one magnon ($2h1m$). Building on the seminal prediction of repulsively bound $2h1m$ states, we show that next-nearest-neighbor hopping $t_{2}$ coherently mixes symmetry-related configurations, stabilizing an $s$-wave bound state with substantial binding energy and a light effective mass. Large-scale DMRG calculations at finite doping identify a magnetization plateau corresponding to a gas of such bound states and quasi--long--range superconducting order with power-law $2h1m$ pair correlations. Our results establish a magnon-mediated superconducting mechanism driven by kinetic frustration, with immediate detectable signatures for moiré Hubbard materials and ultracold-atom simulators.

Figures (4)

• Figure 1: Ground-state wave function from $12\times12$ ED for $t_1=1,t_2=0.3$ with the two hole positions fixed at: (a) a NN bond; (b) a NNN bond; (c) the maximal separation allowed by periodic boundary conditions.
• Figure 2: The state map of the six NN and six NNN hole pairs (located at the blue markers) surrounding a fixed magnon at the center (red marker) reveals that the pairing manifold intrinsically possesses $s$–wave symmetry. Moreover, the next–nearest–neighbor hopping $t_{2}$ enables transitions between symmetry–related NN configurations as well as between symmetry–related NNN configurations, while the nearest–neighbor hopping $t_{1}$ connects a NN pair to a NNN pair.
• Figure 3: Magnetization $M$ as a function of magnetic field $h$ on four-leg cylinders at low temperature $k_BT=0.03t_1$: (a) for several number of hole dopings up to $n_{hole}=8$ at fixed length $L_x=24$, and (b) for system lengths up to $L_x=48$ at fixed doping $\delta=1/12$. In both cases, a finite field window $0.5t_1 < h < t_1$ is observed in which the system is stabilized in the multi-$2h1m$ bound-state regime.
• Figure 4: NN and NNN pair--pair correlations $\Phi(r)$ plotted on double-logarithmic scales in (a) and (b) for the $N=6\times32,\ \delta=1/12$ (bond dimension $m=15000$) and $N=4\times32,\ \delta=1/8$ (bond dimension $m=12000$) cylinders, respectively. In both cases, $\Phi(r)$ follows a power-law decay, $\Phi(r)\sim r^{-K_{\mathrm{sc}}}$. In contrast, the $2h$-only pair correlations $\Phi_{2h}(r)$, shown on a semi-logarithmic scale in (c), decay exponentially, $\Phi_{2h}(r)\sim e^{-r/\xi_{\mathrm{sc}}}$. The transverse spin--spin correlation $F(r)$, plotted on a semi-logarithmic scale in (d), also exhibits exponential decay, $F(r)\sim e^{-r/\xi_{\mathrm{s}}}$.