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

TL;DR

This work addresses how strong-coupling inter-layer KL superconductivity can emerge in stacked 2D van der Waals materials from purely repulsive inter-layer interactions. Using determinant quantum Monte Carlo and dynamical mean-field theory on a trilayer Hubbard model, the authors reveal a crossover from $V^* \propto -U^2$ at weak coupling to $V^* \propto -U$ at strong coupling, yielding elevated $T_c$ for inter-layer $s$-wave pairing that is robust to lattice geometry and persists under sizable remnant Coulomb repulsion $U^*$. They show that strong-coupling KL pairing can survive in realistic conditions and extend over a broad doping range, contrasting with magnetically mediated mechanisms in cuprates. Complementary ab initio calculations identify candidate 2D materials (e.g., Fe-doped phosphorene and NaCr$_2$Cl$_6$) with suitable bandwidths and interlayer interactions, suggesting experimental routes to realize and tune this unconventional superconductivity in van der Waals stacks. Overall, the study provides a viable pathway to engineer higher-$T_c$ superconductivity in layered 2D systems without invoking phonons or magnetic fluctuations, leveraging strong inter-layer repulsion and controlled dielectric environments.

Abstract

The Kohn-Luttinger (KL) mechanism of pairing, which describes superconductivity emergent from repulsive interactions, typically yields Cooper pairs at high angular-momentum ($\ell > 0$) and extremely low transition temperatures ($T_c$). Here, we reveal an inter-layer s-wave ($\ell=0$) 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 $V^{*}$, without the mediation of collective modes, can emerge between inter-layer electrons in the system. As inter-layer repulsion $U$ increases, $V^{*}$ evolves from a conventional KL relation of $V^{*} \propto -U^2$, to a linear strong-coupling scaling of $V^{*} \propto -U$, 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 $U^{*}$ between pairing electrons. Using \textit{ab initio} calculations, we propose a few 2D layered van der Waals materials that can potentially realize and control this unconventional superconductivity.

Figures (6)

• Figure 1: Illustration of the trilayer Hubbard model and KL electron pairing on 2D triangular lattice. (a): AAA-stacking trilayer triangular lattice with spinfull electrons($N_l =3$, $N_{\sigma}=2$). Within a unit cell, different Hubbard terms $U_{l \sigma,m \sigma^{'}}$ are depicted. Long-range interaction $U_{mq}(r)$ terms beyond a unit cell are not shown here. (b): One of the Kohn-Luttinger second order Feynman diagrams leading to inter-layer attraction between a pair of electrons residing on the top- and bottom- layer respectively, via the polorization of the middle-layer. (c): A cartoon showing the inter-layer pairing of two electrons (solid dots) in real-space (indicated by wavy line). Here hollow dots denote holes. For clarity, only one spin species is shown.
• Figure 2: Pairing susceptibilities $\chi$ and effective pairing attractions $V^{*}$ of the spinless trilayer Hubbard model on 2D triangular lattice from $6\times 6\times 3$ DQMC simulation. (a): Pairing sueptiblities $\chi_{l}$ for $\ell=s-$ wave as a function of temperature $T$ at $U=6,U^{*}=0,n_1 = n_2=n_3=n=0.5$. The bubble contributuion $\chi^{0}_{s}$ is shown in dashed line. (b): Effective pairing susceptiblities $\chi_{\mathrm{eff}} = \chi_{l} - \chi_{0,l}$ as a function of temperature $T$. For $p-$ and $d-$ wave, $\chi_{\mathrm{eff}} <0$ , denoting these pairing symmetries are disfavored by correlation effects. Other parameters are the same as in (a). (c): $\chi_s$ and $\chi_s^{0}$ as functions of $U^{\prime}$ at $U=6t,n=0.5, T=0.5t$. The critical $U^{\prime}_c$ where $\chi_s - \chi_s^{0} \approx 0$ is used to define the effective pairing attraction $V^{*} = -U^{\prime}_c$. (d): $V^*$ as a function of $U$ at $n=0.5, T=0.5t$. (e): $V^*$ as a function of electron density of the middle layer $n_2$ at $U=4, T=0.5$. Here $n_1$ and $n_3$ are fixed as $n_1=n_3=0.5$. (f): Inverse $s-$ wave pairing susceptibility as a function of temperature $T$. Here $U=6t, n=0.6$. $\chi^{-1} \rightarrow 0$ is indicated as where $T$ approaches superconducting transition temperature $T_c$. Here $U^* = 0$ for all plots.
• Figure 3: Superconducting transition temperature $T_c$ from DMFT calculations. (a)$T_c$ as a function of $U$ at $n_1=n_2=n_3= 0.6$ for a few different $U^*$. (b)$T_c$ as a function of $U^*$ at $U = 8t$ at $n=0.6$ (20% electron doping). (C) Same as (b) but at $n=0.7$ (40% electron doping). In (b) and (c) The values of $T_c$ at $U^* = U/2 = 4t$ is marked out by dashed lines.
• Figure 4: Phase diagrams showing superconducting instability (SC) and density wave (DW) instability. (a) Superconducting transition temperature $T_c$ as a function of electron density $n$ on the 2D triangular lattice at $U=6$. (b) Same as (a) but at $U=12$. (c) Density wave and superconducting transition temperatures as a function of electron density $n$ on the 3D cubic lattice at $U=10$. Here for all three cases $n_{1}=n_{2}=n_{3}=n$. The repulsion between layer- ( spin flavor-) 1 and layer- (spin flavor-) 3, $U_{13}=U^{'}=0.$
• Figure 5: Effective pairing attraction $V^{*}$ as a function long-range Coulomb repulsion $U_{nn}$ for spinless and spinfull models on 2d Triangular lattice at $U=4, U_o = 8, U^{\prime} =0, T=1.0$. $U_{nn}$ denotes repulsion between intra-layer nearest-neighbouring sites, $U_{nn} \equiv U_{ll} (|r|=1)$.