Signatures of superconducting pairing driven by electron-electron interactions in moiré WSe$_2$/WSe$_2$ homobilayer modelled by Hubbard Hamiltonian

TL;DR

This work shows that a spin-valley polarized Hubbard model on a triangular moiré lattice for WSe$_2$/WSe$_2$ can host superconductivity driven by electron-electron interactions. Using density matrix renormalization group calculations on a cylinder geometry, the authors analyze pair correlations $P_{\nu}^{\alpha\beta}(n)$ across hole doping $\delta$ and displacement field $D$, identifying a mixed singlet-triplet superconducting state with dominant $d_{xy}$ singlet and coexisting $p_y$ triplet orders. The superconducting signal is strongest in a narrow $D$-$\delta$ window that coincides with experimental observations, and the symmetries show sensitivity to cylinder width, indicating a bulk tendency toward a $C_3$-symmetric mixed order (e.g., $d_{xy}$ and $p_y$ with $d\pm id$/$p\pm ip$ components). The results support a correlation-driven mechanism for superconductivity in moiré TMDs and provide a concrete microscopic realization of mixed pairing on a spin-valley polarized triangular lattice. Overall, the study links experimental superconductivity in WSe$_2$/WSe$_2$ to an electronic mechanism within a minimal Hubbard framework, offering insights into the pairing symmetry and its dependence on displacement field and carrier density.

Abstract

Strong evidence of unconventional superconductivity has been very recently reported experimentally in twisted transition metal dichalcogenide bilayer and gathered a significant amount of interest. Here we consider the Hubbard model on a triangular lattice describing the hole-doped moiré superlattice emerging in WSe$_{2}$/WSe$_{2}$ twisted homobilayer in the moderately correlated regime. By applying the Density Matrix Renormalization Group, we diagonalize the spin-valley-polarized Hamiltonian and show signatures of coexisting singlet and triplet pairings in the range of hole dopings and displacement fields reported in the experiments. In this view, we show that the superconductivity in the WSe$_{2}$/WSe$_{2}$ twisted homobilayer is likely to be induced by electronic correlations and has a mixed-symmetry character. These predictions can shed light on the nature of the superconducting state observed in the twisted homobilayer of WSe$_{2}$/WSe$_{2}$. We also identify the emerging superconducting orders, which are $d_{xy}(d_{x^2-y^2} \pm id_{xy} )$ and $p_y(p_{x}\mp ip_{y})$ for the singlet and triplet channels in the cylinder of width three(four), respectively.

Figures (13)

• Figure 1: (a) The sign of phase hopping with respect to the direction $\mathbf{R}_i$ and spin $\sigma=\{\uparrow,\downarrow\}$; (b) Spin-split bare-band for hopping at $D=0.4$ V/nm; (c) The cylinder of size $L_1\times L_2$ (red area) considered in DMRG calculations, shaded parts are replicas of simulated sample and symbol periodic boundary conditions applied along $\mathbf{R}_1$ direction.
• Figure 2: The decays of singlet (a) and triplet (b) pairing correlation functions at $D=0.4$V/nm obtained for the hole doping in the vicinity of half-filled band. Symbols refer to the obtained data from DMRG. The solid lines are maxima of fits obtained for $n\in[16,40)$ and further extrapolated beyond $L_1$ (marked as vertical dashed lines). In the insets the zoom of range for which the fitting procedure have been carried out is shown indicating high quality of power-law decaying fits.
• Figure 3: The decays of singlet (a) and triplet (b) pairing correlaton functions at $\delta\approx0.96$ collected for $D\in[0.25,0.55]$ V/nm. The lines and symbols meaning is the same as in Fig.\ref{['fig:4.0-decays']}.
• Figure 4: The interpolated maps representing phase diagram of pairing. That is maximal value of $P^{1,1}_{fit,\nu}(r=32|\mathbf{R_0}|)$ for the selected ranges of doping and displacement fields for singlet (a) and triplet (b) channels. The yellow dotted lines denote region for which superconductivity has been detected in experiment performed by Guo et al. Guo2025.
• Figure 5: The power-law decay exponent $K_s$ at $D=0.4$ V/nm for the considered dopings as of function of $1/M$. The lines are linear fits and in the inset virtually exact exponents, that is $K_s(M\rightarrow\infty)$ are shown. Presented data refer to the singlet pairing since for the triplet channel we obtain nearly identical outcome, note, that estimated errors are smaller than symbol size.