[Paper Review] Enhanced Interlayer Coupling and Excitons in Twin-Stacked Two-Dimensional Magnetic CrSBr Bilayers

Sijia Ke, Yusuf Shaidu+1 more|arXiv (Cornell University)|Jan 18, 2026

2D Materials and Applications0 citations

TL;DR

The paper uses first-principles methods to show that twisting CrSBr bilayers yields nonmonotonic interlayer electronic coupling that peaks at twin-stacking, and that this coupling modulates excitons with strong polarization dependence. GW-BSE reveals nearly degenerate lowest excitons with layer-specific polarization, influenced by spin alignment.

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.

Motivation & Objective

• Investigate how relative twist angle between CrSBr layers affects interlayer electronic coupling and magnetic configuration.
• Determine how twist-induced coupling modulates electronic structure and optical excitations in CrSBr bilayers.
• Elucidate the role of Br p orbitals and spin orientation in controlling interlayer interactions.

Proposed method

• Perform DFT calculations with PBE functional and D3 dispersion to obtain electronic structures of untwisted and twisted CrSBr bilayers.
• Relax twisted bilayers using a machine-learned interatomic potential calibrated to DFT results to handle large moiré cells.
• Compute quasiparticle energies with G0W0 and solve the Bethe-Salpeter equation (BSE) for excitons, including noncollinear magnetism and spin-orbit coupling.
• Analyze interlayer coupling via valence band maximum splitting (VBS) as a proxy for interlayer electronic hopping.
• Model Br p_y - p_y orbital overlaps to correlate orbital registry with coupling strength.

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 spl

Experimental results

Research questions

• RQ1 How does twist angle modulate interlayer electronic coupling in CrSBr bilayers?
• RQ2 What is the relationship between Br p_y orbital overlap, spin alignment, and interlayer coupling?
• RQ3 How does twin-stacking influence excitonic states and their polarization in CrSBr bilayers?
• RQ4 How do magnetic configurations (FM, AFM, or noncollinear) affect exciton mixing and dipole polarization in twisted CrSBr?

Key findings

• Interlayer coupling is nonlinear and nonmonotonic with twist angle, with a pronounced maximum at the twin-stacking angle Θ_twin = 2 arctan(b/a).
• VBS scales with Br p_y - p_y overlaps times cos(Omega_S/2), linking orbital registry and interlayer spin angle to coupling strength.
• Twist-enabled mixing of intralayer excitons yields two lowest bright excitons that are nearly degenerate with a small residual splitting and polarization maxima aligned with each layer’s easy axis (b-axis).
• Exciton binding energies are 0.73 eV in untwisted interlayer AFM and ~0.60 eV in twin-stacked bilayers, with reduced interlayer hybridization in the twisted case.
• Noncollinear spin configurations allow interlayer coupling even when untwisted AFM coupling would suppress it, and the polarization of excitons reflects the interlayer spin alignment.
• The layer-resolved k-space analysis shows limited regions of interlayer hybridization in the twisted case, in contrast to broader hybridization in untwisted FM CrSBr.

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 multip