Sliding ferroelectricity in bilayer honeycomb structures: A first-principles study

The sliding ferroelectricity is engineered by artificially stacking the nonpolar two-dimensional (2D) materials, which greatly broadens the 2D ferroelectrics from very few candidate materials to a large family of 2D materials. However, the electric polarizations are generally small due to the weak van der Waals interlayer interaction. The search for 2D sliding ferroelectrics with large polarization presents an ongoing challenge. Here we systematically investigate the sliding ferroelectricity in the bilayer honeycomb structures of $\mathrm{B}X$ $(X=\mathrm{P}, \mathrm{As}, \mathrm{Sb})$, $Y\mathrm{N}$ $(Y=\mathrm{Al}, \mathrm{Ga}, \mathrm{In})$, and $Z\mathrm{C}$ $(Z=\mathrm{Si}, \mathrm{Ge}, \mathrm{Sn})$ based on first-principles calculations. It is shown that the electric polarization decreases with the increase of the interlayer distance, and increases with the difference in electronegativity of the two constituent elements. Such dependence is further corroborated by a simple model. It is interesting to see that GeC can be an ideal sliding ferroelectric material with high polarization and energetically favorable polar stacking. Our results reveal the key factors in determining the electric polarization, which could facilitate the search and design of 2D sliding ferroelectrics with large out-of-plane polarization.

Figure 1

Schematic diagram of atomic structures of the stacked bilayer. (a) Top and side views of six general high-symmetry stacking configurations, where the orange dashed line indicates the mirror or inversion symmetry for those non-polar stacking configurations. (b) Side views of BP, GaN, and GeC in the AC stacking configuration. The black arrows indicate the directions of the out-of-plane electric polarization.

Figure 2

Sliding ferroelectricity of BP, GaN, and GeC. (a)–(c) Reversal out-of-plane electric polarization (red curve with dots) and corresponding energy barrier (black curve with triangles) between AC and AB stacking configurations. (d)–(f) Differential charge density with an isosurface value of $0.00025e/{\AA }^3$, where the yellow and cyan areas represent electron accumulation and depletion, respectively. (g)–(i) Layer-projected band structures, where the energy bands derived from upper and lower layer are highlighted in red and blue, respectively. The Fermi level of each system is shifted to energy zero in all the band structures.

Figure 3

Key factors underlying the magnitude of electric polarization. (a) Polarization as a function of the interlayer distance, where the black circles on the line refer to their equilibrium interlayer distances. (b) The slope of each material in (a) at its equilibrium interlayer distance versus the ratio of electronegativity of the two constituent elements, where the smooth solid line is used as a guide to the eye.

Figure 4

Polarization versus the ratio of electronegativity at the same interlayer distance (a) and the respective optimal interlayer distance (b). (c) Polarization versus the respective optimal interlayer distance. (d) Optimal interlayer distance versus the ratio of electronegativity. (e) Polarization versus the effective distance. (f) Polarization versus the ratio of electronegativity of the two constituent elements divided by the effective distance.

Figure 5

(a) Energy differences of the AA′ (AC′ for BP and BAs) stacking configuration with respect to the AC. (b) Strain dependence of the energy difference (blue line) and the magnitude of polarization (red line) on the strain for AC stacking configuration of GeC, where the blue dash-dot line indicates the position where the energy difference is zero.