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Layer dependence of geometric, electronic and piezoelectric properties of SnSe

By means of first-principles calculations, we explore systematically the geometric, electronic and piezoelectric properties of multilayer SnSe. We find that these properties are layer-dependent, indicating that the interlayer interaction plays an important role. With increasing the number of SnSe layers from 1 to 6, we observe that the lattice constant decreases from 4.27 $\mathring{A}$ to 4.22 $\mathring{A}$ along zigzag direction, and increases from 4.41 $\mathring{A}$ to 4.51 $\mathring{A}$ along armchair direction close to the bulk limit (4.21 $\mathring{A}$ and 4.52 $\mathring{A}$, respectively); the band gap decreases from 1.45 eV to 1.08 eV, approaching the bulk gap 0.95 eV. Although the monolayer SnSe exhibits almost symmetric geometric and electronic structures along zigzag and armchair directions, bulk SnSe is obviously anisotropic, showing that the stacking of layers enhances the anisotropic character of SnSe. As bulk and even-layer SnSe have inversion centers, they cannot exhibit piezoelectric responses. However, we show that the odd-layer SnSe have piezoelectric coefficients much higher than those of the known piezoelectric materials, suggesting that the odd-layer SnSe is a good piezoelectric material.