Charge doping effect on sliding ferroelectricity by first-principles calculations (2024)

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  Figure 1

  Polarization in $\mathit{AB}$ stacked bilayer BN. (a) Top view illustration of the atomic arrangement for bilayer BN. To distinguish between the top and bottom layers, the atoms in the bottom layer are represented by larger radius. Nitrogen and boron atoms are shown in silver and green, respectively. (b) The side view of the differential charge density diagram. The yellow and cyan areas indicate the regions that gained and lost electrons, respectively. (c) The plane-averaged difference charge density in the $z$-axis direction. The two vertical lines in the diagram show where the two individual monolayers are located.

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  Figure 2

  Electrostatic doping in bilayer BN. The differential charge density diagram of (a) electron and (b) hole doping obtained by subtracting the charge density of the undoped system from that of the doped system. The plane-averaged differential charge density profile at difference (c) electrons and (d) holes doping concentrations in the $z$-axis direction; the doping concentrations are written in the labeling and different doping concentrations are indicated by different color lines. $\mathrm{\Delta }\rho \left(z\right)={\rho }_{\mathrm{doped}}\left(z\right)-{\rho }_{\mathrm{undoped}}\left(z\right)$, where ${\rho }_{\mathrm{doped}}\left(z\right)$ and ${\rho }_{\mathrm{undoped}}\left(z\right)$ are the planar average charge density for doped and undoped systems. The extent of the decrease in the top and bottom layer charge difference (black) and electrostatic potential difference (red) with (e) electron and (f) hole doping concentration.

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  Figure 3

  Band structures in bilayer BN. The band structures of (a) $\mathit{AB}$-stacked bilayer BN. The illustrations on the left and right sides of the diagram are the partial charge density in the CBM and VBM, respectively. The projected band structures of (b) top and (c) bottom layer. Shades of color indicate the strength of the contribution of the top (red)/bottom (blue) layer.

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  Figure 4

  (a) Bilayer sliding ferroelectric structure model with the red rectangles representing the top layer and the blue rectangles representing the bottom layer. The bilayer structure possesses an upward builtin electric field. (b) Band model near the Fermi level in the bilayer structure. The red and blue colors represent the bands of the top and bottom layers, respectively. The electron model represents the electron filling situation in the top and bottom layers when doping electrons.

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  Figure 5

  Polarization in bilayer $1T$′-$\mathrm{WT}{\mathrm{e}}_2$. (a) The side view of the differential charge density. The blue and orange spheres represent W and Te atoms, respectively. The yellow and cyan areas indicate the regions that gained and lost electrons, respectively. (b) The plane-averaged differential charge density between bilayer $\mathrm{WT}{\mathrm{e}}_2$ and two independent monolayers. $\mathrm{\Delta }\rho \left(z\right)={\rho }_{\mathrm{WT}{\mathrm{e}}_2}\left(z\right)-{\rho }_{\mathrm{top}}\left(z\right)-{\rho }_{\mathrm{bottom}}\left(z\right)$, where ${\rho }_{\mathrm{WT}{\mathrm{e}}_2}\left(z\right),{\rho }_{\mathrm{top}}\left(z\right),$ and ${\rho }_{\mathrm{bottom}}\left(z\right)$ are the charge densities of the bilayer $\mathrm{WT}{\mathrm{e}}_2$.

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  Figure 6

  Band structures of bilayer $1T$′-$\mathrm{WT}{\mathrm{e}}_2$. (a)–(c) The total band structure, the projected band structure on the top layer, and the projected band structure on the bottom layer, respectively. In the projected band structures, the shading of colors indicates the strength of the contribution of electrons from the top (red)/bottom (blue) layer.

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  Figure 7

  Electrostatic doping of bilayer $1T$′-$\mathrm{WT}{\mathrm{e}}_2$. The differential charge density diagram of (a) electron and (b) hole doping obtained by subtracting the charge density of the undoped system from that of the doped system. The plane-averaged differential charge density profile at difference (c) electron and (d) hole doping concentrations in the $z$-axis direction; the doping concentrations are written in the labeling and different doping concentrations are indicated by different color lines. $\mathrm{\Delta }\rho ={\rho }_{\mathrm{doped}}\left(z\right)-{\rho }_{\mathrm{undoped}}\left(z\right)$, where ${\rho }_{\mathrm{doped}}\left(z\right)$ and ${\rho }_{\mathrm{undoped}}\left(z\right)$ are the planar average charge density for doped and undoped systems. The extent of the decrease in the top and bottom layer charge difference (black) and electrostatic potential difference (red) with (e) electron and (f) hole doping concentration.

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