Two-Dimensional Antiferroelectricity in Nanostripe-Ordered ${\mathrm{In}}_2{\mathrm{Se}}_3$

Two-dimensional (2D) layered materials have been an exciting frontier for exploring emerging physics at reduced dimensionality, with a variety of exotic properties demonstrated at 2D limit. Here, we report the first experimental discovery of in-plane antiferroelectricity in a 2D material ${\beta }^{\prime }-{\mathrm{In}}_2{\mathrm{Se}}_3$, using optical and electron microscopy consolidated by first-principles calculations. Different from conventional 3D antiferroelectricity, antiferroelectricity in ${\beta }^{\prime }-{\mathrm{In}}_2{\mathrm{Se}}_3$ is confined within the 2D layer and generates the unusual nanostripe ordering: the individual nanostripes exhibit local ferroelectric polarization, whereas the neighboring nanostripes are antipolar with zero net polarization. Such a unique superstructure is underpinned by the intriguing competition between 2D ferroelectric and antiferroelectric ordering in ${\beta }^{\prime }-{\mathrm{In}}_2{\mathrm{Se}}_3$, which can be preserved down to single-layer thickness as predicted by calculation. Besides demonstrating 2D antiferroelectricity, our finding further resolves the true nature of the ${\beta }^{\prime }-{\mathrm{In}}_2{\mathrm{Se}}_3$ superstructure that has been under debate for over four decades.

Figure 1

(a) Plan-view ADF-STEM image of a ${\beta }^{\prime }-{\mathrm{In}}_2{\mathrm{Se}}_3$ flake. The bottom-left inset is a multislice-simulated image. (b) Models of the basic ${\beta }^{\prime }-{\mathrm{In}}_2{\mathrm{Se}}_3$ structure. (c) Atomic displacement map derived from (a) with respect to the reference lattice. The yellow (green) arrows are for bright (dark) columns. Displacement of only half of the dark columns is shown, with the other half being similar (see Fig. S4 in SM [30]). (d) Relative displacement map of bright columns with respect to the centers of the surrounding six dark columns. (e) Displacement profiles of bright and dark columns vertically averaged from (c). (f) Relative displacement profile of bright columns vertically averaged from (d). Error bars indicate $\pm 1\mathrm{s}.\mathrm{d}$.

Figure 2

Polarization mapping using EMPAD-based 4D STEM. Centers of mass (a) $⟨p_y⟩$ and (b) $⟨p_x⟩$ measured from CBED patterns. (c), (d) Vertically averaged $⟨p_y⟩$ profile from (a) and $⟨p_x⟩$ profile from (b). Error bars indicate $\pm 1\mathrm{s}.\mathrm{d}$.

Figure 3

(a) Polarized-light image of a ${\beta }^{\prime }-{\mathrm{In}}_2{\mathrm{Se}}_3$ flake, with the polarization directions labeled. (b) ADF STEM image of 120° twin domains in ${\beta }^{\prime }-{\mathrm{In}}_2{\mathrm{Se}}_3$, showing the switching of nanostripe direction across a coherent domain boundary. (c) SHG intensity of ${\beta }^{\prime }-{\mathrm{In}}_2{\mathrm{Se}}_3$ showing no detectable response, in contrast to the strong SHG signal from ferroelectric $\alpha -{\mathrm{In}}_2{\mathrm{Se}}_3$. (d) Thermal variation of lattice spacings measured from electron diffraction during in situ heating.

Figure 4

(a) Phonon dispersion of parent bulk 2H $\beta -{\mathrm{In}}_2{\mathrm{Se}}_3$ showing structural instabilities associated with the soft modes of the lowest branch (red solid line) along the $\mathrm{\Gamma }-M$ direction. The black dot indicates the soft mode generating the antiferroelectric ${\beta }^{\prime }$ phase. (b) Calculated antiferroelectric ${\beta }^{\prime }$ and (c) ferroelectric $\mathrm{FE}\beta$ structure for bulk ${\mathrm{In}}_2{\mathrm{Se}}_3$. (d) Calculated antiferroelectric ${\beta }^{\prime }$ and (e) ferroelectric $\mathrm{FE}\beta$ structure for single-quintuple-layer ${\mathrm{In}}_2{\mathrm{Se}}_3$. The $\mathrm{FE}\beta$ structure is remarkably similar to the local structure within the ${\beta }^{\prime }-{\mathrm{In}}_2{\mathrm{Se}}_3$ nanostripes, as indicated by the black unit-cell frames. (f) Relative displacement profile of bright columns measured from the simulated ADF STEM image based on the calculated structure in (b), compared to the experimental profile. (g) Polarization profiles across nanostripes of bulk and single-quintuple-layer ${\beta }^{\prime }-{\mathrm{In}}_2{\mathrm{Se}}_3$, calculated from the structure in (b) and (d). The dashed lines indicate the calculated polarization of bulk and single-quintuple-layer $\mathrm{FE}\beta$ phase for comparison.