Ferroelastically controlled ferrovalley states in stacked bilayer systems with inversion symmetry

Realizing and manipulating valley polarization is extremely important to valleytronics. Ferrovalley materials with spontaneous valley polarization are excellent candidates for this purpose. However, for intrinsic ferrovalley materials, ferromagnetism or ferroelectric polarization is usually required, limiting the development of valleytronics, as only systems without inversion symmetry are considered. In this paper, using both group theory analysis and band structure calculations, we demonstrate that valley polarization can exist in systems with both time and space inversion symmetry, and the ferroelastic effect can control the ferrovalley states. Choosing stacking bilayer systems as an example, we achieved valley polarization switching using the shear strain, which uncovers the link between ferrovalley and ferroelasticity. Our investigations not only provide a mechanical way to manipulate valley degree of freedom but also enrich the understanding of the coupling between different ferroic properties.

Figure 1

(a) Crystal structure and (b) orbital-resolved band structure of the GaBr monolayer. (c) Free energy contour for GaBr bilayer vs the displacement of the upper layer. The AA, V+, and V− states are marked. The fine band structure near the valley and the irreducible representation of the conduction band (CB) and valence band (VB) of (d) V+ and (e) V− states. (f) Linear polarization optical absorption of the GaBr monolayer, V+ state, and V− state.

Figure 2

(a) In the monolayer lattice (unit), $m$ and $n$ atoms are located at the (0.0, 0.0) and (0.5, 0.5) positions of the lattice, respectively. $\mathrm{B}{\mathrm{L}}_1$ and $\mathrm{B}{\mathrm{L}}_2$ are bilayer structures in which yellow (green) plane denotes the lower (upper) layer. (b)–(d) are band structures of unit, $\mathrm{B}{\mathrm{L}}_1$, and $\mathrm{B}{\mathrm{L}}_2$, respectively. Red (blue) arrows represent $x$($y$)-polarized light. The irreducible representations of the conduction band (CB) and valence band (VB) are marked in (b)–(d).

Figure 3

(a) GaBr bilayer energy vs shear strain $[\varepsilon =\mathrm{si}{\mathrm{n}}^{-1}\left(\sqrt{-\cos 2\alpha }\right)]$. The energy of the V− state is set as zero, and the structure of relaxation under strain is labeled. (b) The switching barriers under different shear strains calculated by the nudged elastic band method.