Theory of Topological Superconductivity and Antiferromagnetic Correlated Insulators in Twisted Bilayer WSe$_2$

TL;DR

This work develops a topology-aware three-band tight-binding model for 3.65° twisted bilayer WSe2 by Wannierizing the low-energy continuum model, then analyzes onsite Hubbard repulsion and short-range attraction with a self-consistent mean-field treatment. The resulting phase diagram at filling $\nu=-1$ features a topological inter-valley superconductor with Chern number $C=\pm 2$ in the presence of small displacement fields, and a correlated insulator with $120^\circ$ antiferromagnetic order at larger displacement fields, in qualitative agreement with experiments. The study integrates RPA-inspired justification for the attractive term, maps interaction parameters from Wannier functions, and highlights the role of nontrivial band topology in stabilizing superconductivity in moiré TMDs, suggesting tangible experimental probes to detect edge modes and phase structure. Overall, the work provides a unified framework linking topology, magnetism, and superconductivity in twisted WSe2 and motivates further theoretical and experimental exploration of topological superconductivity in moiré materials.

Abstract

Since the very recent discovery of unconventional superconductivity in twisted WSe$_2$ homobilayers at filling $ν=-1$, considerable interest has arisen in revealing its mechanism. In this paper, we developed a three-band tight-binding model with non-trivial band topology by direct Wannierization of the low-energy continuum model. Incorporating both onsite Hubbard repulsion and next-nearest-neighbor attraction, we then performed a mean-field analysis of the microscopic model and obtained a phase diagram qualitatively consistent with the experiment results. For zero or weak displacement field, the ground state is a Chern number $C=\pm 2$ topological superconductor in the Altland-Zirnbauer A-class (breaking time-reversal but preserving total $S_z$ symmetry) with inter-valley pairing dominant in $d_{xy}\pm id_{x^2-y^2}$-wave (mixing with a subdominant $p_x\mp i p_y$-wave) component. For a relatively strong displacement field, the ground state is a correlated insulator with the $120^\circ$ antiferromagnetic order. Our results provide new insights into the nature of the twisted WSe$_2$ systems and suggest the need for further theoretical and experimental explorations.

Figures (12)

• Figure 1: Construction of the three-band tight-binding model from the continuum model by Wannierization. (a) Mini Brillouin zone formed by a small twist angle $\theta$ between two layers. (b) Density distribution of Wannier functions on two layers, with unit cell shown as dashed line. (c) Comparison of the band structure between continuum model (dashed line) and tight binding model (solid line), where colors representing sublattice components.
• Figure 2: Evolution of Fermi surfaces and density of states as a function of displacement field. (a) Fermi surfaces of free Hamiltonian at different displacement fields, with colors indicating the sublattice components, and thickness representing the DOS. The spin of the Fermi surfaces are labeled as solid arrows. When $\mathcal{V}_z=0$ meV, where spin up and down Fermi surfaces coincide, only spin down Fermi surface is shown. The approximate nesting wave vector $\bm{Q}$ between spin up and down Fermi surfaces are illustrated as dashed arrow. (b) The Fermi surface DOS of A, B, C sublattices as a function of displacement field $\mathcal{V}_z$.
• Figure 3: Illustration of the possible superconducting and antiferromagnetic order parameters. (a) The NNN SC order parameters $\Delta_{AA}$ and $\Delta_{BB}$, where the A, B, C sites are labeled as red, green, blue dots. (b) The pairing form factor of $s$-wave, $f$-wave, $p+ip$-wave, and $d-id$-wave on NNN bonds, with the irreducible representation labeled. (c) $120^{\circ}$ AFM pattern on a certain type of sublattice with wave vector $\pm Q$. (d) The folded Brillouin zone induced by the AFM order.
• Figure 4: Mean-field analysis and phase diagrams of $3.65^\circ$ tWSe$_2$. (a) The energy gain per hole of the ordered phases compared to the symmetric phase. (b) SC orders for $V_2=10$ meV on one specific NNN bond $\delta_0$ under the gauge described in the main text. The sign of order parameters correspond to the sign of real (imaginary) part of singlet (triplet) pairings. (c) The AFM mean-field charge gap at filling factor $\tilde{\nu}=-3$ in the folded Brillouin zone. (d) Magnitude of the AFM orders on A, B, C sublattices. (e, f) The phase diagrams for $V_2=10$ meV and $V_2=12.5$ meV respectively, indicating that under mean-field framework, the SC to AFM-I transition can either have an intermediate AFM-M phase or occur directly.
• Figure S1: Illustration of the representative hopping bonds up to $5$th-nearest-neighbor.