Fig. 3

Layer and subband index dependence of the biaxial strain effect. a Averaged shift rates of E₁₁, E₂₂, and E₃₃ peaks as a function of layer number in 2–10L BP. The solid curves are fitted to the data using the tight-binding model shown in the text. The error bar is defined from the data spread of multiple samples. For each layer, at least three samples were measured. b DFT calculated shift rates for 1L, 2L, 3L, and 8L BP induced by in-plane biaxial strain. c Illustration of two in-plane hoping parameters (\(t_{{\mathrm{||}}}^1\) and \(t_{{\mathrm{||}}}^2\)) and one out-of-plane hopping parameter (t_⊥) in a 2L BP. d is the height of an individual layer and D is the gap between two layers. When biaxial in-plane tensile stain is applied, the average distance between two layers (D + d) decreases due to Poisson effect, while the gap (D) increases accompanied by a stronger decrease of d (see Supplementary Fig. 9). d Schematic illustration of the band structure evolution of a bilayer BP under tensile and compressive strain. The orange dashed curves are the bands for a monolayer BP. The change of subband splittings causes the shift rate of E₂₂ smaller than that of E₁₁. Layered materials governed by van der Waals (vdW) interactions offer opportunities for interlayer tuning of the materials’ properties. Here, the authors demonstrate that in-plane tensile strain can effectively tune the vdW interactions of few-layered black phosphorus and weaken its interlayer coupling even though the sample shrinks in the vertical direction