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

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.

💡 Research Summary

In this work, the authors combine atomic‑resolution scanning transmission electron microscopy (STEM), four‑dimensional STEM (4D‑STEM) with center‑of‑mass (CoM) analysis, multislice electron ptychography, and hybrid‑functional density‑functional theory (DFT) to elucidate the atomic and electronic structures of strongly charged domain walls (CDWs) in the van der Waals ferroelectric α‑In₂Se₃. Two types of CDWs are investigated: head‑to‑head (HH) and tail‑to‑tail (TT), both of which correspond to 180° in‑plane polarization reversal and therefore carry a large bound charge.

High‑angle annular dark‑field (ADF) STEM images reveal that every HH wall contains a single‑quintuple‑layer of the non‑polar β‑In₂Se₃ phase sandwiched between oppositely polarized α‑In₂Se₃ domains. This β layer is only ~1 nm thick, indicating an extremely localized depolarization region that screens the strong electric field at the wall. In contrast, TT walls appear atomically abrupt; no β layer is observed, and the two α domains meet directly, with only subtle contrast changes likely due to strain or defects. Both HH and TT walls exhibit an inter‑layer shear displacement (a 1/3 unit‑cell shift) that preserves the registry of the outer Se planes across the van der Waals gap. The authors find that such stacking shifts lower the formation energy of HH walls with a β layer by ~24 meV per formula unit, while the presence of the β layer itself reduces the energy by ~40 meV per formula unit. TT walls are intrinsically higher in energy (≈ 40 meV/formula unit) and are observed less frequently, consistent with the experimental statistics (7 HH vs. 3 TT walls in eight samples).

4D‑STEM CoM mapping of the (0001) and (000‑1) Bragg disks provides a rapid, large‑area visualization of the domain pattern. The CoM contrast clearly delineates the CDWs and shows that the walls are not perfectly planar but possess three‑dimensional curvature on the tens‑of‑nanometers scale. Multislice electron ptychography further confirms the three‑dimensional nature of the walls and offers sub‑nanometer resolution of the local polarization.

Hybrid HSE06 DFT calculations on bulk α‑In₂Se₃ and β‑In₂Se₃ reproduce the experimental band gaps (1.26 eV indirect for α, 0.91 eV indirect for β). Slab models containing HH or TT walls are constructed. For the lowest‑energy HH configuration (β layer + stacking shift), a new electronic state appears within the bulk band gap, localized on the β layer. Partial charge‑density analysis shows that this mid‑gap state is confined to a ~1 nm region, effectively forming a two‑dimensional electron gas (2DEG) at the wall. For the TT wall, DFT predicts states localized within the two innermost layers of the wall, indicating the possibility of a two‑dimensional hole gas (2DHG). Both walls therefore host conductive channels that are atomically thin and can be written, erased, or moved by external stimuli such as electric bias, light, or mechanical stress.

The combined experimental‑theoretical study demonstrates that strongly charged domain walls in α‑In₂Se₃ are intrinsically different from conventional ferroelectric walls: HH walls self‑stabilize by forming a non‑polar β interlayer, while TT walls remain abrupt but still support confined electronic states. The presence of robust, atomically thin conductive channels at these walls opens a pathway to domain‑wall‑based device concepts in van der Waals ferroelectrics, including non‑volatile memory elements, reconfigurable logic, and neuromorphic computing architectures where the walls themselves act as programmable 2D electronic pathways.