Layertronics is an emerging field that effectively controls various physical behaviors of two-dimensional (2D) materials and their artificial stacks. While most prior works focused on modulating the interlayer interaction and layer-dependent properties, here we investigate layer-dependent disorder (either Anderson type or magnetic exchange field) effects, which could naturally occur in realistic 2D layered materials. We show that disorder could effectively toggle the spatial symmetry statistically. While the spatially homogeneous disorder tends to enhance the spatial symmetry, layer-dependent disorder is spatially inhomogeneous and could reduce such symmetry in a statistical manner, especially breaking the intact centrosymmetry $\mathcal{P}$. We further characterize such a $\mathcal{P}$ breaking by the emergence of shift current, an intrinsic bulk photovoltaic effect arising from the position mismatch between the valence and conduction band centers under linearly polarized light irradiation. This is rooted from momentum space shift and is illustrated by tight-binding model simulations and first-principles calculations on the $\mathcal{P}$-symmetric bilayer transition metal dichalcogenide (for on-site energy disorder) and trilayer antiferromagnetic ${\mathrm{CrI}}_3$ (for magnetic exchange disorder) as exemplary platforms. The layer-dependent disorder is permissible experimentally, especially under the substrate effect. This work expands the scope of layertronics and clarifies the symmetry control of layer-disorder effect.

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• Photocurrent
• 2-dimensional systems
• Layered crystals
• Density functional calculations
• Tight-binding model