Two-dimensional (2D) sheets typically have a high Föppl–von Kármán number, that is, their in-plane extent is much greater than thickness, and can be easily bent, much like a paper, making such deformation a novel feasible way to design distinct electronic phases. Through first-principles calculations, we reveal the formation of 1D polarization domains and 1D flat electronic bands by bending-undulation of a 2D bilayer semiconductor. For a 1D sinusoidal deformation of a hexagonal boron nitride ($h\mathrm{BN}$) bilayer as an example, we demonstrate how undulation induces nonuniform shear patterns, creating regions with unique local stacking and vertical polarization akin to sliding-induced ferroelectrics observed in twisted moiré systems. A particular sliding-induced polarization pattern also appears in double-wall BN nanotubes due to curvature differences between inner and outer tubes. Furthermore, undulation generates a shear-induced 1D moiré pattern that perturbs electronic states, confining them into 1D quantum well-like bands with kinetic energy quenched in modulation direction while dispersive in other directions (1D flat bands). This electronic confinement is attributed to modulated shear deformation potential resulting from tangential polarization due to the moiré pattern. Thus, the bending modulation and interlayer shear it causes offer an alternative avenue, termed “curvatronics”, to induce exotic phenomena in 2D bilayer materials.

Close

PrevNext

View figure in article

• Electronic structure
• Flat bands
• Strain
• Bilayer films
• Density functional calculations