Tunable moire spinons in magnetically encapsulated twisted van der Waals quantum spin liquids

Quantum spin-liquid van der Waals magnets such as ${\mathrm{TaS}}_2$, ${\mathrm{TaSe}}_2$, and ${\mathrm{RuCl}}_3$ provide a natural platform to explore new exotic phenomena associated with spinon physics, whose properties can be controlled by exchange proximity with ferromagnetic insulators such as ${\mathrm{CrBr}}_3$. Here we put forward a twisted van der Waals heterostructure based on a quantum spin-liquid bilayer encapsulated between ferromagnetic insulators. We demonstrate the emergence of spinon flat bands and topological spinon states in such heterostructure, where the emergence of a topological gap is driven by the twist. We further show that the spinon band structure can be controlled via exchange proximity effect to the ferromagnetic leads. We finally show how by combining small magnetic fields with tunneling spectroscopy, magnetically encapsulated heterostructures provide a way of characterizing the nature of the quantum spin-liquid state. Our results put forward twisted quantum spin-liquid bilayers as potential platforms for exotic moire spinon phenomena, demonstrating the versatility of magnetic van der Waals heterostructures.

Figure 1

(a) Sketch of a twisted bilayer Dirac QSL on a triangular lattice. (b) The moiré Brillouin zone of the twisted QSL. The dashed red and blue hexagons represent the Brillouin zone of the bottom and top layers. The red/blue circles (crosses) denote the location of the Dirac points in the original (folded) Brillouin zone (grey area). (c) Spinon band structure of the twisted Dirac QSL in the decoupled limit for $\theta ={22}^{\circ }$, showing the two sets of decoupled bands in the top (blue) and bottom (red) layers.

Figure 2

(a)–(c) Spinon band structure of the twisted Dirac QSL at different twisting angles $\theta =0.{81}^{\circ },0.{93}^{\circ },1.{20}^{\circ }$ [dashed lines in panel (d)], respectively. (d) Spinon DOS $\rho \left(\omega \right)$ of the twisted Dirac QSL near the flat band twisting angle $\theta =0.{93}^{\circ }$. (e) Spinon band structure of a twisted QSL nanoribbon at $\theta =3.5^{\circ }$.

Figure 3

(a) Sketch of the twisted bilayer Dirac QSL encapsulated by ferromagnets. (b) Spinon band structure of the twisted Dirac QSL at $\theta =0.{93}^{\circ }$ and interlayer spinon bias $J=0.1t$. (c),(d) Spinon DOS of the twisted bilayer Dirac QSL at (c) $\theta =0.{93}^{\circ }$ and (d) $\theta =1.{05}^{\circ }$ with different interlayer spinon bias $J$.

Figure 4

(a) Sketch of the experimental setup for probing QSL via inelastic spectroscopy. (b) Spinon DOS of the twisted QSL at $\theta =0.{93}^{\circ }$ and $J=0.1t$ under different $\alpha \left(B\right)$. (c) Spin structure factor $\mathcal{S}\left(\omega \right)$ with $\alpha =0$. (d) Change in spin structure factor $\mathrm{\Delta }\mathcal{S}(\omega ,\alpha )$ for different $\alpha$.

Figure 5

Spinon band structure of the twisted Dirac QSL at different twisting angles $\theta =1.{30}^{\circ },1.{12}^{\circ },0.{99}^{\circ },0.{93}^{\circ }$ [from (a) to (d)] with the same effective angle ${\theta }_{\text{eff}}$.

Figure 6

(a) Spinon DOS of the twisted QSL at $\theta =0.{93}^{\circ }$ and $J=0.05t$ under different $\alpha \left(B\right)$. (b) Change in spin structure factor $\mathrm{\Delta }\mathcal{S}(\omega ,\alpha )$ for different $\alpha$.