Atomic and Electronic Structure of Strongly Charged Domain Walls in van der Waals α-In$_2$Se$_3$

TL;DR

This study investigates strongly charged in-plane domain walls in the 2D van der Waals ferroelectric $\alpha$-In$_2$Se$_3$, focusing on head-to-head (HH) and tail-to-tail (TT) walls as templates for emergent 2D electron/hole gases. It combines atomic-resolution STEM, 4D-STEM/CoM mapping, and multislice electron ptychography with first-principles DFT (including HSE06) to resolve the atomic structure, polarization textures, and electronic states at the walls. HH walls consistently harbor a single nonpolar $\beta$-In$_2$Se$_3$ layer and possess a localized midgap state within $\sim 1$ nm, while TT walls are atomically abrupt and show band bending that yields localized valence states near the interface. 4D-STEM and ptychography reveal three-dimensional, curved walls that migrate between layers, challenging the idealized $180^\circ$ picture, and DFT energetics show stacking shifts and the $\beta$ layer lower HH wall energy, highlighting the potential of charged domain walls in $\alpha$-In$_2$Se$_3$ for engineering nm-thick conducting channels in van der Waals ferroelectrics.

Abstract

Here, we use atomic resolution scanning transmission electron microscopy (STEM) and first principles calculations to study the atomic and electronic structure of strongly charged domain walls in $α$-In$_2$Se$_3$. STEM imaging and density functional theory (DFT) show that head-to-head (HH) domain walls contain a layer of nonpolar $β$-In$_2$Se$_3$, whereas tail-to-tail (TT) domain walls are atomically abrupt. We apply 4D STEM and multislice electron ptychography to map ferroelectric domains in 2D and 3D, showing that nearly $180^\circ$ domain walls exhibit complex, curved 3D structures that differ from ideal $180^\circ$ structures. Band structure calculations show localized conducting states within a $\sim$ 1 nm thick layer at both HH and TT domain walls, such as a midgap state at the $β$ layer of the HH domain wall. These properties make strongly charged domain walls in $α$-In$_2$Se$_3$ excellent candidates for realizing 2D electron or hole gases and domain wall engineering in van der Waals ferroelectrics.

Figures (6)

• Figure 1: Atomic structure and polarization of $\alpha$-In2Se3. (a) Schematic of ferroelectric $\alpha$- and nonpolar $\beta$-In2Se3, viewed along [$1\bar{1}00$]. A horizontal line through the top In2Se3 quintuple layers marks the centerline of the layer, highlighting the offset of the center Se ion in each polarization state. (b) Atomic resolution ADF-STEM image and corresponding polarization determined by center Se ion offset. (c) ADF-STEM image of ferroelectric domains around a kink, with arrows indicating polarization obtained from STEM imaging. Transverse domain walls (blue) form where polarization within individual layers changes at kinks in the In2Se3. The upper In2Se3 layers delaminate and undergo an odd number of kinks, creating a head-to-head domain wall (red).
• Figure 2: Atomic structure and polarization of strongly charged domain walls in $\alpha$-In2Se3. (a,b) ADF-STEM images of head-to-head DWs imaged along (a) $[1\bar{1}00]$ and (b) $[10\bar{1}0]$, with red and blue shading indicating local polarization direction. The head-to-head domain wall contains one layer of nonpolar $\beta$-In2Se3. (c,d) ADF-STEM images of tail-to-tail DWs imaged along (c) $[1\bar{1}00]$ and (d) $[10\bar{1}0]$. No nonpolar layer is visible in the TT DW. A/B/C lettering in (b,d) indicates stacking order. The HH and TT domain walls are each accompanied by in-plane shifts between quintuple layers, which preserve the relative local alignment between outer Se planes across the van der Waals gaps. (e) Schematic of 4D-STEM acquisition. A 2D array of diffraction patterns is collected as a function of position on the sample. (f) A representative PACBED pattern from the downwards polarized region of (h) with $(0001)$ and $(000\bar{1})$ Bragg disks marked, where intensity is greater in the $(000\bar{1})$ disk. (g) A representative PACBED pattern from the upwards polarized region of (h). Intensity is greater in the $(000\bar{1})$ disk. 1 mrad convergence angle at 300 kV is used for (f,g). (h) 4D-STEM polarization map from center of mass of intensity in (0001) disks. The domain wall is clearly visible in the CoM image, providing a rapid, large-area method to locate domain walls in In2Se3.
• Figure 3: Relative domain wall energies of head-to-head and tail-to-tail DW structures in (a) 3R and (b) 2H $\alpha$-In2Se3, both with and without a nonpolar $\beta$ layer. From left to right, the structures are: 1) HH with $\beta$ and no stacking shift (SS), 2) HH with $\beta$ and SS, 3) abrupt HH, 4) abrupt HH with SS, 5) TT with $\beta$, 6) TT with $\beta$ and SS, 7) abrupt TT, and 8) abrupt TT with SS. The lowest energy HH (but not TT) domain wall structures contain a $\beta$ layer. Both HH and TT DWs in 3R with $\beta$ are lower energy with a stacking shift, whereas DWs with and without stacking faults are similar in energy for the other DW configurations. These results are consistent with the structures observed in our experiments.
• Figure 4: Simulated electronic structure in bulk and interfaces in In2Se3 from Density Functional Theory (hybrid, HSE06 functional). Electronic band structures for (a) bulk $\alpha$-In2Se3 with a 1.26 eV indirect band gap and (b) bulk $\beta$-In2Se3 with a 0.91 eV indirect gap. (c) Electronic band structure of a 9 layer slab with head-to-head domain wall in $\alpha$-In2Se3. States colored red denote spatial localization within the $\beta$ layer of the head-to-head domain wall, obtained via partial charge density calculations. (d) Partial charge density map showing the gap-crossing HH-DW state at the M point (i.e. the conduction band minimum in (c)) with atomic positions superimposed. (e) Electronic band structure of an 8 layer slab with tail-to-tail domain wall. States colored red denote localization within the two innermost layers of the tail-to-tail domain wall. (f) Partial charge density map showing localization of the valence band maximum in (e) with atomic positions superimposed. These simulations show that the domain walls strongly modify the local electronic structure in ferroelectric In2Se3, producing mid-gap states localized within 1 nm of the DW interface.
• Figure 5: Multislice electron ptychography reconstruction of a nearly $180^\circ$In2Se3 domain wall with in-plane and out-of-plane components. (a) ADF-STEM image of a 3D domain wall, where polarization in some layers is unclear in projection. (b) 2D projection of ptychographic reconstruction of a nearby region to (a). Six atomic planes appear in the highlighted layer, indicating both up and down polarizations stacked in projection. Unlike perfectly oriented HH domain walls, no $\beta$ layer is evident. (c) Depth slices of the highlighted layer in (a), taken at depths of z=1 nm, 4 nm, and 10 nm. The polarization is uniformly downwards at z = 1 nm and upwards at z = 10 nm. The z = 4 nm image shows the polarization changing from up (red) to down (blue) across the image, with a central transitional region $\sim$1 nm thick and another transition beginning at the far left. (d) Polarization map of the layer in (b), orientated in the xz plane. Blue/red indicate polarization into/out of the xz plane and white represents regions where the polarization cannot be assigned. The domain wall migrates between layers and exhibits a complex, curved structure within layers. Pixel size in x corresponds to interatomic spacing (2.1 Å) and pixel size in z corresponding to reconstruction slice thickness (1 nm). The 1, 4, and 10 nm slice depths in (c) are indicated. (e) Stack of xz polarization maps for all 5 layers in (a). (f) 3D volume displaying polarization, with transparent upper domain. Although the polarization is oriented near a head-to-head configuration, the atomic structure domain wall structure is complex and curved in 3D and distinct from the HH structure.