Topology and ferroelectricity in group-V monolayers
Rehman Mutee Ur1, Hua Chenqiang1, 2, Lu Yunhao1, 2, ‡
       

(a) Top view of α phase group-V elemental ML. The unit cell is indicated with black dashed rectangle lines. (b) Free energy contour for α-As ML versus the buckling heights (hU, hL). The phases A, A′, and B are marked. (c) Side views of the two energy-degenerate distorted noncentrosymmetric structures (A and A′ phases) and undistorted centrosymmetric structure (phase B). The height differences between upper (red) and lower (blue) atomic layers are marked as hU and hL, respectively. (d) Side view of α-Bi ML in antiferroelectric (AFE) configuration. The atomic sites shifted up and down are colored in red and green, respectively. (e) Free energy contour of Bi MLs versus buckling heights (h(R), h(G)). For Bi, besides the FE phases A and A′, there also exist metastable AFE phases C and C′.[43]