Multi-Q spin-valley order in twisted WSe2

TL;DR

This work reveals a new multi-Q spin-valley magnetic order in twisted WSe$_2$ at $\nu=1$, emerging from a continuous transition out of the $120^{\circ}$ spin-valley AFM as interaction strength and displacement field are varied. Using two continuum models (LO and HO) and self-consistent Hartree-Fock plus TDHF, the authors identify two distinct multi-Q phases—coplanar and non-coplanar—that are stabilized for experimentally relevant parameters and that exhibit spin-texture modulations with four ordering wave vectors: $\boldsymbol{\kappa}_\pm$ and the three moiré $M$-points. The transition is marked by a softening of spin fluctuations near the $M$-points and results in an enlarged unit cell by a factor of four; the topology of the bands remains nontrivial, though the non-coplanar state is consistent with zero Chern number. The findings suggest that soft spin fluctuations near the $M$-points could facilitate superconductivity observed near $\nu=1$ and small displacement fields, providing a robust scenario across different continuum-model implementations. Overall, the work expands the landscape of correlated phases in moiré TMDs and highlights the potential connection between multi-Q magnetism and superconductivity in twisted WSe$_2$.

Abstract

We report on a study of the interacting phase diagram of $3.65^\circ$-twisted WSe$_2$ at moiré hole filling $ν=1$, in which we find previously-overlooked types of magnetism. Specifically, in part of the phase diagram we obtain a magnetic order parameter which modulates in space with four different non-zero wave vectors, corresponding to the three $M$-points and one $K$-point of the moiré Brillouin zone. These multi-Q orders, which can be coplanar or non-coplanar, are continuous deformations of the $120^\circ$ spin-valley anti-ferromagnet (AFM), where the unit cell has expanded by a factor of four. Interestingly, we find that the multi-Q states are stabilized for experimentally relevant values of interaction strength and displacement field, and are accompanied by a softening of the spin fluctuations near the $M$-points of the moiré

Figures (8)

• Figure 1: Numerical results for HO model obtained on a $24\times 24$ moiré lattice. (a) Spin-valley U(1) order parameter $O_{\text{IVC}}$, (b) $\mathcal{T}'$ time-reversal order parameter $O_{\mathcal{T}'}$, (c) order parameter $O_{T'}$ for the generalized translation symmetry $T'_{{\mathbf{a}}_i}$. (d) Mean-field bandgap. (e-f) TDHF Goldstone mode dispersion relation $\omega_{\mathbf{q}}$ along ${\mathbf{q}}=(q_x,q_y=0)$, both for fixed $E$ as a function of $\epsilon$ (e), and for fixed $\epsilon$ as a function of $E$ (f).
• Figure 2: (a-d) Non-coplanar multi-Q spin texture in the top and bottom layers at $\epsilon = 25$. (a) In-plane magnetic order in the top layer, described by $|M_{xy}^t({\mathbf{r}})|$ (color) and $\theta_t({\mathbf{r}})$ (arrows). (b) $M_z^t({\mathbf{r}})$, the out-of-plane component of magnetic order in the top layer. (c) In-plane magnetic order in the bottom layer, described by $|M_{xy}^b({\mathbf{r}}))|$ (color) and $\theta_b({\mathbf{r}})$ (arrows). (d) $M_z^b({\mathbf{r}})$, the out-of-plane component of magnetic order in bottom layer. (e-h) Same as (a-d), but for $\epsilon=32$.
• Figure 3: In-plane spin texture for the coplanar multi-Q state at $\epsilon=40$ in (a) top layer and (b) bottom layer. Color represents $|M_{xy}^l({\mathbf{r}})|$, and arrows represent $\theta_l({\mathbf{r}})$.
• Figure 4: Band structure comparison at $\theta = 3.65^{\circ}$.
• Figure 5: (a - b) Bandwidth of the topmost band $W_1$ and minimum energy distances between neighboring bands $\Delta_{ij}({\mathbf{k}}) = E_i({\mathbf{k}})- E_j({\mathbf{k}})$ for the LO and HO model respectively. (c - d) Chern number $C_i$ of the topmost $i$-th band for the LO and HO model respectively.