Abstract

Understanding how stacking controls the nonlinear optical response of two-dimensional materials is key to designing van der Waals heterostructures with tailored functionalities. Here, we establish a comprehensive symmetry-based framework mapping the structural configuration of MoS₂ bilayers across four point groups (D3h, D3d, C3v, and C₃) to their second-order susceptibility tensor χ(2). Using group-theory arguments benchmarked against first-principles calculations, we demonstrate how symmetry breaking controls the activation and suppression of individual tensor elements in these systems. We show that the emergence of the in-plane component χxxx in twisted configurations (C₃ group) induces a rigid azimuthal rotation of the second-harmonic generation polar lobes, which remains frequency-independent across the entire optical spectrum, locking to half of the structural twist angle. Our findings establish a direct, wavelength-independent optical route for twist-angle determination and provide a clear roadmap for engineering nonlinear optical responses in two-dimensional materials.

Abstract

Understanding how stacking controls the nonlinear optical response of two-dimensional materials is key to designing van der Waals heterostructures with tailored functionalities. Here, we establish a comprehensive symmetry-based framework mapping the structural configuration of MoS₂ bilayers across four point groups (D3h, D3d, C3v, and C₃) to their second-order susceptibility tensor χ(2). Using group-theory arguments benchmarked against first-principles calculations, we demonstrate how symmetry breaking controls the activation and suppression of individual tensor elements in these systems. We show that the emergence of the in-plane component χxxx in twisted configurations (C₃ group) induces a rigid azimuthal rotation of the second-harmonic generation polar lobes, which remains frequency-independent across the entire optical spectrum, locking to half of the structural twist angle. Our findings establish a direct, wavelength-independent optical route for twist-angle determination and provide a clear roadmap for engineering nonlinear optical responses in two-dimensional materials.

Abstract

Understanding how stacking controls the nonlinear optical response of two-dimensional materials is key to designing van der Waals heterostructures with tailored functionalities. Here, we establish a comprehensive symmetry-based framework mapping the structural configuration of MoS₂ bilayers across four point groups (D3h, D3d, C3v, and C₃) to their second-order susceptibility tensor χ(2). Using group-theory arguments benchmarked against first-principles calculations, we demonstrate how symmetry breaking controls the activation and suppression of individual tensor elements in these systems. We show that the emergence of the in-plane component χxxx in twisted configurations (C₃ group) induces a rigid azimuthal rotation of the second-harmonic generation polar lobes, which remains frequency-independent across the entire optical spectrum, locking to half of the structural twist angle. Our findings establish a direct, wavelength-independent optical route for twist-angle determination and provide a clear roadmap for engineering nonlinear optical responses in two-dimensional materials.

Abstract

Understanding how stacking controls the nonlinear optical response of two-dimensional materials is key to designing van der Waals heterostructures with tailored functionalities. Here, we establish a comprehensive symmetry-based framework mapping the structural configuration of MoS₂ bilayers across four point groups (D3h, D3d, C3v, and C₃) to their second-order susceptibility tensor χ(2). Using group-theory arguments benchmarked against first-principles calculations, we demonstrate how symmetry breaking controls the activation and suppression of individual tensor elements in these systems. We show that the emergence of the in-plane component χxxx in twisted configurations (C₃ group) induces a rigid azimuthal rotation of the second-harmonic generation polar lobes, which remains frequency-independent across the entire optical spectrum, locking to half of the structural twist angle. Our findings establish a direct, wavelength-independent optical route for twist-angle determination and provide a clear roadmap for engineering nonlinear optical responses in two-dimensional materials.