Atomically Sharp Walls

• Atomically sharp walls are sub-nanometer interfaces where order parameters change abruptly, localizing unique electronic, magnetic, and topological states.
• Advanced imaging techniques like STEM, STM, and PFM reveal wall widths as low as 0.5–1 nm, enabling detection of conductive ferroelectric walls and magnetic solitons.
• Theoretical models link wall formation to minimized gradient energy and discrete lattice effects, providing insights for engineering nanoscale electronic and quantum devices.

Atomically sharp walls are interfaces—typically domain walls, phase boundaries, or edges in crystals—across which an order parameter, atomic registry, or electronic property changes within the span of a single or a few atomic planes. Such walls constitute a fundamental length-scale limit of structural, electronic, or magnetic inhomogeneity in solids. They have been realized in a diverse range of systems, including ferroelectrics, antiferromagnets, correlated quantum materials, van der Waals heterostructures, and topological semimetals. Atomically sharp walls are characterized by a sub-nanometer width, often below 1–2 unit cells, and can host emergent electronic, magnetic, and topological states not found in the surrounding bulk.

1. Physical Realization and Microscopic Structure

Atomically sharp walls are experimentally realized in various systems, each with precise structural characterization:

• Ferroelectric domain walls: In GaV$_4$S$_8$, 109° ferroelectric walls exhibit a transition width $ξ ≲ 2$ nm, with polarization reversal occurring over 1–2 unit cells ($a ≈ 0.85$ nm) as determined by piezoresponse force microscopy (PFM) and conductive AFM (c-AFM) (Ghara et al., 2021). In BiFeO$_3$, high-resolution STEM combined with Bayesian inference yields a wall half-width $W ≈ 0.6 \pm 0.1$ nm (Nelson et al., 2020). Ultra-narrow, strongly charged 180° walls with thickness $<0.5$ unit cells are observed in ZrO$_2$ (Afroze et al., 25 Jul 2025).
• Antiferromagnetic and ferrimagnetic domain walls: CuMnAs displays Néel vector reversal in a single atomic layer, imaged via differential-phase-contrast STEM with $≤4$ Å width (Krizek et al., 2020). One-dimensional ferrimagnetic chains support atomically sharp 180° domain walls when the anisotropy:exchange ratio exceeds a critical threshold (Zeng et al., 2024).
• Magnetic solitons: In EuRhAl$_4$Si$_8$0, competition between RKKY exchange and uniaxial anisotropy yields domain walls of exactly one lattice constant width, interpreted as atomically sharp 1D solitons (Allen et al., 10 Feb 2026).
• Electronic and topological interfaces: Atomically sharp $_8$1–$_8$2 junctions in graphene can be synthesized via Cu monolayer-vacancy-island engineering, yielding potential steps as abrupt as a single graphene–Cu bond (≲1 nm) (Bai et al., 2017). MBE-grown FeSe films support nematic domain walls where both strain and nematic order change within ≤4 Å (Yuan et al., 2019). Atomically abrupt 1D interfaces in VSe$_8$3–NbSe$_8$4 lateral heterostructures are observed via STM, with interface widths <1 nm (Huang et al., 2024).

The atomic arrangements at such walls may reflect registry shifts, passivating reconstructions (e.g., closed zigzag edges in bilayer phosphorene (Lee et al., 2022)), or symmetry-enforced stacking changes (merohedral twins in Weyl semimetal CoSi (Mathur et al., 2022)). Tables below summarize characteristic length scales.

Material/System	Measured Wall Width	Method
GaV$_8$5S$_8$6 ferroelectric DW	$_8$7 nm ($_8$82 u.c.)	c-AFM/PFM
ZrO$_8$9 180° charged wall	$ξ ≲ 2$0 u.c., in-plane <1 nm$ξ ≲ 2$1	ABF-STEM
BiFeO$ξ ≲ 2$2 180° wall	$ξ ≲ 2$3 nm	STEM/Bayesian fit
CuMnAs AF wall	≤4 Å (=1 c-axis lattice)	DPC-STEM
EuRhAl$ξ ≲ 2$4Si$ξ ≲ 2$5 soliton wall	1 lattice spacing ($ξ ≲ 2$60.4 nm)	Atomistic MC
Graphene $ξ ≲ 2$7–$ξ ≲ 2$8 interface (Cu step)	≲1 nm	STM/STS
FeSe nematic wall	≲4 Å	STM
VSe$ξ ≲ 2$9–NbSe$a ≈ 0.85$0 lateral interface	<1 nm	STM/DFT
CoSi (001) merohedral twin boundary	1 atomic plane	HAADF-STEM

2. Theoretical Description: Models and Formation Mechanisms

Atomically sharp wall profiles typically arise when the gradient energy penalty for order parameter variation ($a ≈ 0.85$1) is small relative to bulk (e.g., Ginzburg–Landau–Devonshire models). For conventional ferroelectrics, the equilibrium wall width $a ≈ 0.85$2 is set by $a ≈ 0.85$3, with $a ≈ 0.85$4 the gradient term and $a ≈ 0.85$5 the inverse linear susceptibility. In BiFeO$a ≈ 0.85$6 and GaV$a ≈ 0.85$7S$a ≈ 0.85$8, using $a ≈ 0.85$9 J m$_3$0/C$_3$1 and $_3$2 J m/C$_3$3 gives $_3$4 nm (Ghara et al., 2021, Nelson et al., 2020).

In antiferromagnets and ferrimagnets, domain wall width $_3$5 follows $_3$6, where $_3$7 is nearest-neighbor exchange, $_3$8 uniaxial anisotropy, and $_3$9 the lattice constant. When $W ≈ 0.6 \pm 0.1$0 rises above a threshold ($W ≈ 0.6 \pm 0.1$1), $W ≈ 0.6 \pm 0.1$2, the atomic–scale (“sharp”) limit (Zeng et al., 2024, Krizek et al., 2020). Notably, in CuMnAs, relativistic DFT calculations reveal that abrupt walls can be energetically stabilized beyond the reach of classical Heisenberg models (Krizek et al., 2020).

For topological phase boundaries—e.g., in FeSe or CoSi—the wall sharpness is enforced by lattice registry or inversion-twinning, and the interface abruptly connects regions of distinct topological invariants, e.g., Z$W ≈ 0.6 \pm 0.1$3 or Chern number, over a single atomic plane (Yuan et al., 2019, Mathur et al., 2022).

3. Emergent Electronic, Magnetic, and Topological States

Atomically sharp walls serve as platforms for localized or confined states inaccessible in the bulk. Key examples:

• Conductive ferroelectric walls: In GaV$W ≈ 0.6 \pm 0.1$4S$W ≈ 0.6 \pm 0.1$5, alternating head-to-head (n-type) and tail-to-tail (p-type) segments act as quasi-2D electron and hole gases. Local carrier densities approach $W ≈ 0.6 \pm 0.1$6 cm$W ≈ 0.6 \pm 0.1$7, with per-segment conductance $W ≈ 0.6 \pm 0.1$8 up to $W ≈ 0.6 \pm 0.1$9 S/μm, while wall widths remain atomically confined (Ghara et al., 2021).
• Topological helical states: MBE-grown FeSe films exhibit Z$<0.5$0=1 across the wall, supporting edge channels separated by $<0.5$12 nm and bound zero modes at four–wall crossings (Yuan et al., 2019). Atomically sharp $<0.5$2–$<0.5$3 junctions in graphene function as potential barriers capable of confining massless Dirac fermions, forming quantum dots with quantized resonances $<0.5$4 for dot radius $<0.5$5 (Bai et al., 2017).
• Fermi arc localization: At the (001) (inversion-twin) plane of CoSi nanowires, internal Fermi arcs emerge, sharply distinct from external arcs and bulk states. They are confined to $<0.5$60.1 unit cell around the wall and manifest distinct local DOS peaks (Mathur et al., 2022).
• Spin-wave filtering and polarization: Atomically sharp antiferromagnetic walls act as spin-wave polarizers—transmitting only one circular polarization and reflecting the other—owing to sharp boundary conditions on the discrete spin chain (Faridi et al., 2022).
• Interband magnon scattering: In collinear ferrimagnets, atomically sharp walls enable magnon transmission without spin reversal—interband conversion replaces the chirality-flipping mechanism seen in wide walls of ferromagnets or antiferromagnets (Zeng et al., 2024).
• Magnetic solitons: In EuRhAl$<0.5$7Si$<0.5$8, solitonic walls act as quantized 1D topological excitations whose density can be field-tuned and read out in magnetization or transport (Allen et al., 10 Feb 2026).

4. Synthesis, Control, and Experimental Characterization

Atomically sharp walls are accessed by precise synthesis and characterization techniques:

• Imaging: Aberration-corrected STEM/HAADF-ABF, c-AFM, STM/STS, PFM, MFM, and XMLD-PEEM provide sub-Ångström spatial mapping of wall profiles and local order parameters (Lee et al., 2022, Krizek et al., 2020, Afroze et al., 25 Jul 2025, Yuan et al., 2019, Bai et al., 2017).
• Fabrication: Solution Monolayer Epitaxy (SoME) permits atomically sharp oxide interfaces with sub-unit-cell intermixing, utilizing self-limiting surface reactions (Ron et al., 2017). Lateral 2D heterostructures, e.g., VSe$<0.5$9–NbSe$_2$0, are produced by sequential molecular beam epitaxy with edge-selective nucleation, confirmed by atomic-resolution STM (Huang et al., 2024).
• Wall writing and erasure: In GaV$_2$1S$_2$2, electric and magnetic fields can create, move, or annihilate domain wall networks, effecting abrupt transitions in global conductance (Ghara et al., 2021). In ferroic oxides and noncollinear antiferroelectrics, tip-induced local poling can controllably manipulate atoms—moving charged walls, tuning piezoresponse, or creating reconfigurable boundary geometries (Ushakov et al., 2 Jul 2025).
• Spectroscopic mapping: Tunneling spectra in graphene and FeSe track quantum Hall edge states or topological edge modes, with sharp interfaces required for non-reconstructed behavior (Li et al., 2012, Yuan et al., 2019, Bai et al., 2017).

5. Device Implications and Functional Prospects

Atomically sharp walls are central to the engineering of electronic, spintronic, and quantum devices at the atomic limit:

• Nanoelectronic building blocks: In GaV$_2$3S$_2$4 and ultrathin ZrO$_2$5, walls can be configured as p/n segments, diodes, memory elements, or crossbar logic, with bit densities approaching $_2$6 bits/cm$_2$7 (Ghara et al., 2021, Afroze et al., 25 Jul 2025).
• Topological quantum computation: The absence of edge-state reconstruction at atomically sharp boundaries in graphene and FeSe is prerequisite for universal edge-bulk correspondence in quantum Hall and quantum spin Hall devices, as well as the formation of Majorana zero modes (Li et al., 2012, Yuan et al., 2019).
• Spintronic and magnonic components: In antiferromagnets and ferrimagnets, atomically sharp domain walls enable ultra-fast, field-insensitive switching and neuromorphic functionality, as well as atomic-scale magnonic filters or polarizers (Krizek et al., 2020, Faridi et al., 2022, Zeng et al., 2024).
• Correlated and topological states at engineered interfaces: Lateral walls in 2D heterostructures localize bands and Kondo resonances, acting as designer 1D wires for correlated electron phases or topological superconductivity (Huang et al., 2024).

6. Fundamental Impact and Theoretical Consequences

Atomically sharp walls challenge and extend established theoretical frameworks:

• Beyond continuum models: At atomic length scales, traditional micromagnetic and Ginzburg–Landau models fail; the physics is dominated by discrete lattice effects, strong electronic correlations, relativistic corrections, and quantum coherence (Krizek et al., 2020, Zeng et al., 2024).
• Lattice-induced phenomena: Interfacial hopping across sharply defined atomic steps in graphene yields "tilted Klein tunneling," with perfect transmission no longer at normal incidence—an effect inaccessible to $_2$8 or continuum Dirac models (Zhang et al., 2018).
• Energy scaling: Atomically sharp walls can, in select systems, be the lowest-energy defect class, due to quantum lowering of interface energy outside semiclassical expectations—as observed in CuMnAs and EuRhAl$_2$9Si$≤4$0 (Krizek et al., 2020, Allen et al., 10 Feb 2026).
• Topological boundary phenomena: Atomically sharp internal interfaces in topological materials (e.g., twin boundaries in Weyl semimetals) can host distinct Fermi arc states and local topological invariants isolated from external surface effects (Mathur et al., 2022).

The control of wall width to the atomic limit enables the realization of emergent states and functionalities impossible in the continuum or at larger scales, making atomically sharp walls a fundamental motif in nanoscale science and device physics.