A flat band is a significant platform for investigating a series of novel quantum phase in the condensed matter physics. However, its realization highlights the fundamental challenge and it has only been discovered in a small number of systems. In this work, we propose a bend-sliding atomic model to design the flat bands by mechanical bending in two-dimensional materials. We reveal that the bending can cause intersublayer sliding within a monolayer, thereby inducing changes in the interatomic distances and bonding. Especially, atomic reconstruction and changes in orbital occupation can significantly weaken the electron hopping, leading to the emergence of flat bands. Through the first-principles calculations, we use the two-dimensional materials $\mathrm{CuIn}{\mathrm{P}}_2{\mathrm{S}}_6$ and ${\mathrm{CuCrP}}_2{\mathrm{S}}_6$ as examples to verify the feasibility of the bend-sliding model. We find that when the degree of bending exceeds a critical value, the local atomic reconstruction occurs with the formation of new Cu-S chemical bonds. This changes the orbital occupation of top valence bands from the $P_y$ to $P_z$ orbital of S atoms and thus significantly weakens electron hopping between adjacent Cu-S configuration units, accompanied by the emergence of flat bands. Furthermore, according to Stoner's theory, we successfully induce magnetism in nonmagnetic $\mathrm{CuIn}{\mathrm{P}}_2{\mathrm{S}}_6$ through hole doping in flat bands. Our study indicates that the bend-sliding model offers a different perspective for the design of flat bands in two-dimensional flexible materials.

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• Flat bands
• 1-dimensional systems
• Density functional calculations
• Tight-binding model