Enhanced Interlayer Coupling and Excitons in Twin-Stacked Two-Dimensional Magnetic CrSBr Bilayers

TL;DR

This work addresses how twist angle controls interlayer electronic coupling and excitonic properties in CrSBr bilayers, a rectangular-lattice 2D magnet. Using first-principles $DFT$ and many-body $G_0W_0$-BSE on twisted bilayers generated via a twist_layers workflow, supplemented by a machine-learning interatomic potential to relax large moiré cells, they map the coupling landscape. They find a highly nonlinear, nonmonotonic dependence with a pronounced maximum at the twin-stacking angle $\

Abstract

The degree of electronic coupling between individual layers in few-layer van der Waals heterostructures offers a route to engineer their magnetic, electronic, and optical functionalities. Using state-of-the-art first-principles calculations, we demonstrate that the electronic coupling between two monolayers of CrSBr, an anisotropic two-dimensional magnetic semiconductor, is highly nonlinear and nonmonotonic with respect to their relative twist angle, exhibiting a pronounced maximum at the twin-stacking configuration. The coupling strength scales with both the degree of overlap of Br orbitals adjacent to the van der Waals gap and the cosine of half of the interlayer spin angle. This enhanced interlayer electronic coupling gives rise to excitons delocalized across the two layers with a strong polarization dependence that reflects the details of the interlayer spin alignment. Our results reveal a sensitive interplay between twist angle, magnetism, and excitonic properties in twin-stacked CrSBr bilayers, and they establish twin stacking as an effective route to engineering interlayer coupling and optical response in anisotropic two-dimensional magnets with rectangular lattices.

Figures (4)

• Figure 1: a-d The atomic structure of untwisted (a, b), near twin-stacked angle (c, d). The magnetic easy axis of each layer is shown as an black arrow for near twin-stacked angle in d. The local magnet moments are represented as green arrows on Cr. e DFT-PBE calculated valence band maximum splitting (VBS, red diamond), used as a measure of the interlayer electronic coupling, shown in the left axis, and the multiple of Br $p_{y}$-$p_{y}$ overlap (defined in SI) and cosine of half angle between spins (180$\degree - \Theta$) across MLIP-relaxed CrSBr bilayers (black dot), shown in the right axis, both as a function of twist angle. Interlayer electronic coupling is orbital forbidden in the 90$\degree$-twisted structure.
• Figure 2: a Valence band maximum splitting (VBS) in untwisted (blue) and twin-stacked (orange) CrSBr bilayers as a function of the cosine of half the interlayer spin angle, where the twin-stacked VBS is increased by a factor of 10 for visibility. b VBS in several twisted CrSBr scales with the multiple of Br $p_{y}$-$p_{y}$ orbital overlap and cosine of half of the spin angle.
• Figure 3: a-b Top (a) and side (b) view of a representative twin-stacked CrSBr bilayer. The green and purple dashed rectangles in (a) indicate the primitive unit cells of each monolayer before relaxation, and notably the diagonal of these two rectangles overlap. c$G_{0}W_{0}$@PBE and PBE calculated band structure of the untwisted CrSBr bilayer, with the reciprocal space points shown in g. Layer $\alpha$ is the lower layer and layer $\beta$ is the upper layer, shown for example in (b). d, e The conduction (d) and valence (e) band structure in the twin-stacked CrSBr supercell shown in black curves. The green and purple points represent states of the monolayer primitive cell folded into the Brillouin zones of twin-stacked CrSBr. The chosen reciprocal space paths and their ends are shown in h. f The purple and green solid rectangles represent the Brillouin zones of the monolayer primitive unit cell, and the blue solid rectangle represents the Brillouin zone of the twin-stacked CrSBr bilayer supercell. g, h Layer contributions to the lowest conduction band states for untwisted (g) and the twin-stacked (h) CrSBr.
• Figure 4: a Polarization dependence of the lowest-lying exciton in the untwisted CrSBr bilayers. b Polarization dependences of the two lowest-lying excitons in a 36-atom twisted CrSBr bilayer. The purple and green dashed lines on the polar plots indicate the magnetic easy axis of the two layers. The light blue curves are computed from the interlayer FM case, the darker blue curves are associated with the $\Omega_{S} =\Theta^{twin}$ case, the red curves are from our calculations with $\Omega_{S} = 180 \degree - \Theta^{twin}$, and the orange curves are from the interlayer AFM case. c, d The sum of exciton coefficients associated with transitions from occupied valence $v$ to unoccupied conduction $c$ states at wavevector $k$ ($\sum_{v,c}|A^{S}_{vck}|^{2}$) in the untwisted (c) and the twin-stacked (d) structure for the lowest exciton. e-g Magnitude of the first exciton wavefunction in solid curves for the untwisted bilayer with interlayer AFM order (e), interlayer FM order (f), and the twin-stacked bilayer with canted magnetic configuration $\Omega_{S} = 180 \degree - \Theta^{twin} = 109.5 \degree$ (g) along z, normal to the bilayer with the hole position fixed in the upper and lower layer, respectively, shown in the dashed lines of color corresponding to the plotted wavefunction. (Green curves represent the lower layer and purple curves represent the upper layer.) A side view of the untwisted and twin-stacked CrSBr atomic structure is shown, aligned with z coordinates for reference.