Synthesizing Strong-Coupling Kohn-Luttinger Superconductivity in 2D Van der Waals materials

The Kohn-Luttinger (KL) mechanism of pairing, which describes superconductivity emergent from repulsive interactions, typically yields Cooper pairs at high angular-momentum ($\mathrm{\ell }>0$) and extremely low transition temperatures ($T_c$). Here, we reveal an inter-layer s-wave ($\mathrm{\ell }=0$) KL superconductivity with greatly elevated $T_c$ in a multi-layer Hubbard model, which prototypes stacked two-dimensional (2D) electrons in layered van der Waals materials. By employing determinant quantum Monte Carlo and dynamical mean-field theory simulations, we show that a strong pairing attraction $V^{\ast }$, without the mediation of collective modes, can emerge between inter-layer electrons in the system. As inter-layer repulsion $U$ increases, $V^{\ast }$ evolves from a conventional KL relation of $V^{\ast }\propto -U^2$, to a linear strong-coupling scaling of $V^{\ast }\propto -U$, resulting in enhanced superconductivity at large $U$. This strong-coupling KL pairing is robust against changes in lattice geometries and dimensionalities, and it can persist, in the presence of a large remnant Coulomb repulsion $U^{\ast }$ between pairing electrons. Using $\mathit{\text{ab}}\mathit{\text{initio}}$ calculations, we propose a few 2D layered van der Waals materials that can potentially realize and control this unconventional superconductivity.