Fig. 1. (Color online) (a) Schematic depiction of how the ferroelastic-antiferroelectric is induced from antiferroelectricity and ferroelasticity, in which the red and blue arrows indicate the FE polarization for each sector of the system. (b) Building the 2D AFE structures (cation X = Zn, Cd; anion Y = S, Se, Te, P2/c symmetry) with the wz monolayer (Pca2₁ symmetry) as building blocks. Here, the wz monolayer is exfoliated from the wz bulk thick layer with (110) crystallographic plane, which can bond spontaneously with another one when stacked vertically due to the inherent self-healable nature. (c) The average interlayer force (per bond in unit cell) and formation energy as a function of the slab thickness h in the 2D AFE ZnSe, 2L MoS₂ and 2L black phosphorene, respectively.

Fig. 2. (Color online) (a) Feasible phase transition channels for the 2D AFE structure. The triangle in either AFE-1/2/3/4 structure can transform into tetrahedra with the phase transition into CS₁C2/m structure, which further changes into CS₂P4/nmm structure due to the interlayer slipping for tetrahedra (a/4 or b/4 along the lattice direction). The continuing movement of the tetrahedra would make the structure restore the AFE phase through the C2/m structure, forming the AFE phase changing channel with π (inversed) or π/2 rotated triangle configurations. Here, the blue and red arrows denote the polarization direction within each layer of the AFE-n structure, as accentuated by the congruent hues presenting in the corresponding triangles. (b), (c) Phase changing barrier for the 2D AFE structures, where the ∆E₁ and ∆E₂ depict the barrier heights for the AFE-m,n → CS₁ and CS₁ → CS₂ phase changing process.

Fig. 3. (Color online) (a) Crystal structure for 2D AFE ZnSe with boxed α-sector and β-sector for hidden spin projection. (b) The first Brillouin zone of the 2D AFE structure, where the high symmetry k points (Γ, X, Y, and S) are indicated. (c) Band structure (HSE06 + SOC) for 2D AFE ZnSe. (d) 3D spin texture near the VBM region highlighted in (c), in which the red and blue arrows indicate the spin polarization contributed by α- and β-sector and the magnitude of spin vectors depend on the strength of SOC and spin splitting. Corresponding 2D diagram of the spin polarizations of α-sector (e), (f) and β-sector (g), (h) and the color scheme indicates the out-of-plane spin component, the shade of color bar represents the magnitude of the hidden spin polarization. (i) Switchable spin texture projected to the k space for the 2D AFE ZnSe around VBM, which is expected by tuning the in-plane AFE polarization.

Fig. 4. (Color online) (a) Top view for ZnSe AFE structure, in which we denote the projections of triangle and tetrahedra along b-axis by ∆d₁ and ∆d₂, respectively. (b) Variation of the ∆d₁ and ∆d₂ with strain along lattice a. (c) PDOS for the ZnX (X = S, Se, Te), indicating the localized/dispersive cation s/anion p state. (d) Anisotropic in-plane s-p_x/y and out-of-plane s-p_z orbital interactions in ZnX. (e) In-plane NPR response for 2D AFE ZnSe, which can be flipped through the AFE transition. (f) Statistical NPR values for the 2D AFE structures, among which three members have NPR exceeding −0.450.