Homochiral Polarization Textures

• Homochiral polarization textures are spatial regions exhibiting uniform handedness that result from inversion symmetry breaking and interactions like DMI and flexoelectric coupling.
• They are characterized using advanced techniques such as PFM, STEM, and electric field switching, enabling precise visualization and control of chiral domain structures.
• Their topological nature links real-space polarization fields with underlying band topology, paving the way for innovations in spintronics, ferroelectric devices, and chiral photonics.

Homochiral polarization textures refer to spatially extended regions in which a polarization field—be it electronic, ionic, molecular, magnetic, or optical—exhibits uniform handedness (chirality) at the nanoscale to mesoscale. Such textures frequently involve topologically nontrivial features (e.g., merons, skyrmions, or domain walls with fixed rotational sense) and can arise through the interplay of symmetry, band topology, interfacial engineering, strain, electronic structure, and electromagnetic fields. The term “homochiral” emphasizes a consistent chirality (rather than mere local twisting) across the domain. Below, the theoretical underpinnings, physical mechanisms, control strategies, and characterization of homochiral polarization textures are synthesized from recent research.

1. Fundamental Mechanisms and Definitions

Homochiral polarization textures emerge due to local or global inversion symmetry breaking, spin-orbit interactions, and the presence of energetic terms that favor twisting or curling of the polarization field with a fixed handedness. Canonical microscopic mechanisms include:

• Dzyaloshinskii-Moriya Interaction (DMI) and Flexoelectric Coupling: In ultrathin magnetic multilayer films, interfacial DMI ($$\mathbf{D} \cdot (\mathbf{S}_i \times \mathbf{S}_j)$$) stabilizes homochiral Néel walls and skyrmions by energetically favoring a single rotational sense of the spin (or polarization) vector across the wall (Fallon et al., 2019). In ferroelectric nanostructures, flexoelectric coupling ($$G_{\mathrm{flexo}} = -\int_V F_{ijkl} (\sigma_{ij} \partial_l P_k - P_k \partial_l \sigma_{ij}) \, d^3 r$$) acts as a Lifshitz invariant that twists the polarization, stabilizing structures such as "flexons"—chiral polarization vortices or merons resembling their magnetic analogues (Morozovska et al., 2021).
• Spin-Orbit and Band Topology Effects: In chiral crystals (e.g., Te, or artificial lattices), broken inversion and mirror symmetry enable spin-momentum locking or "hedgehog"-like radial spin textures with a chirality that is set by the lattice structure (Sakano et al., 2019). The polarization textures in such systems may inherit topological invariants such as the Chern number from the underlying band structure (Jankowski et al., 25 Apr 2024).
• Electrostatics, Strain, and Interfacial Chemistry: In oxide ferroelectrics (e.g., BiFeO$_3$) grown under anisotropic compressive strain and on electrodes with designed surface terminations, the competition between elastic, electrostatic, and chemical boundary conditions determines both the direction and the homochiral nature of the stable polarization texture (Gradauskaite et al., 28 Aug 2025). Surface reconstruction (e.g., spontaneous formation of a Bi$_2$O$_2$ layer for charge compensation) can locally stabilize otherwise unfavorable polarization directions, reinforcing homochirality.

2. Quantitative Modeling and Topological Characterization

Theoretical and computational descriptions of homochiral polarization textures use a variety of mathematical frameworks:

• Micromagnetic and Polarization Energy Functionals: For (anti)ferromagnets and ferroelectrics, the total free energy can be written as

$$F = F_{\text{elastic}} + F_{\text{electrostatic}} + F_{\text{gradient}} + F_{\text{DM}} + F_{\text{flexo}} + \dots$$

where $$F_{\text{DM}} = \mathbf{D} \cdot (\mathbf{P}_i \times \mathbf{P}_j)$$ is the DMI analogue in ferroelectrics, and $F_{\text{flexo}}$ is the Lifshitz invariant representing flexoelectricity (Morozovska et al., 2021, Gradauskaite et al., 28 Aug 2025).

• Topological Charge and Indices: The chiral (topological) nature of a polarization (or magnetization) texture is quantified by indices such as the skyrmion number or meron number,

$$n = \frac{1}{4\pi} \int_S \mathbf{p} \cdot \left( \frac{\partial \mathbf{p}}{\partial x} \times \frac{\partial \mathbf{p}}{\partial y} \right) dx\,dy,$$

where $\mathbf{p} = \mathbf{P}/|\mathbf{P}|$ is the unit polarization or spin vector (Morozovska et al., 2021, Yang et al., 2022).

• Semilocal Hybrid Polarizations (SHPs): For systems with nontrivial band topology (nonzero Chern number), gauge-invariant definitions of local polarization must account for the obstruction to exponentially localized Wannier functions. Here, SHPs based on hybrid Wannier charge centers (HWCCs) allow one to define local polarization that reflects both the real-space winding (e.g., merons, skyrmions) and the momentum-space (band) topology (Jankowski et al., 25 Apr 2024):

$$P_\beta^{(h)}(r_j, \xi) = -\frac{ef}{\Omega_0} \sum_n^\text{occ} \int_0^{x(r_j)} \frac{\partial \bar{w}_{n,\beta}^{(h)}(\xi)}{\partial x_\beta'} dx_\beta'$$

This expression is applicable for nontrivial bands as it remains well-defined even when full Wannier localization is forbidden.

3. Experimental Realization, Imaging, and Control

A combination of advanced experimental tools enables the direct visualization, measurement, and manipulation of homochiral polarization textures:

• Imaging Techniques:
  • Piezoresponse Force Microscopy (PFM): Both vertical and lateral PFM, along with sample rotation (vector PFM), allow mapping of both out-of-plane and in-plane polarization components at the nanoscale. This is critical for revealing multidomain and homochiral domain-wall configurations (Gradauskaite et al., 28 Aug 2025).
  • Scanning Transmission Electron Microscopy (STEM): Atomic-resolution mapping of cation displacements unveils the nucleation and stabilization of reconstructed (e.g., Bi$_2$O$_2$) layers over specific polarization variants, thereby directly linking interfacial chemistry to local polarization chirality.
  • Lorentz Transmission Electron Microscopy and Differential Phase Contrast (TEM/DPC): Enables quantitative identification of Bloch and Néel contributions in chiral magnetic hybrid walls, as well as determination of the topological indices (Fallon et al., 2019).
  • Second Harmonic Generation (SHG) Microscopy: SHG and SHG-interferometry enable observation of polar meron-like textures and their chirality at the optical scale (Yang et al., 2022).
• Control Strategies:
  • Electric Field Switching: In polar vortex arrays formed from otherwise non-chiral materials, chirality (helicity) can be deterministically and reversibly controlled by applied electric fields. The degree of chirality is quantified by the integrated helicity,

  $$\mathcal{H} = \int [ \mathbf{p}(\mathbf{r}) \cdot (\nabla \times \mathbf{p}(\mathbf{r})) ] \, d\mathbf{r}$$

  which switches sign upon reversal of the applied field (Behera et al., 2021). - Strain and Interfacial Engineering: The combination of large anisotropic compressive strain and charge compensation or engineered buffer layers (such as Aurivillius phases with Bi$_2$O$_2$ terminations) enables tuning between multidomain and uniform polarization states, and enforces deterministic rotation (i.e., homochiral domain wall textures) (Gradauskaite et al., 28 Aug 2025). - Chemical Doping: Chirality in polar textures can be biased externally via chiral dopants, which suppresses the statistical appearance of both chiralities and enforces a unique sense over large regions (Yang et al., 2022).

4. Topological Phase Transitions and Coupling to Band Topology

Recent theoretical advances have demonstrated that nontrivial real-space polarization textures—homochiral merons, skyrmions, and their analogues—can coexist and interplay with electronic band topology:

• Coexistence across Phase Transitions: In Chern insulators and moiré superlattices, as the system is tuned through topological phase transitions (e.g., by varying the Haldane mass parameter or external potential), the magnitude of local polarization may decrease sharply, but the topological winding number (defining the homochiral texture) is preserved (Jankowski et al., 25 Apr 2024). Thus, polar topology can coexist robustly with band topology.
• Implications for Edge States and Hall Conductivity: Modulation of the polarization texture by external potentials or stacking in twisted bilayer systems has been shown to generate domains with distinct Chern markers and to control local Hall conductivity, suggesting novel means of engineering edge currents or topological switching for device applications.

5. Applications, Implications, and Future Directions

Homochiral polarization textures hold significant potential for a wide range of technologies and fundamental physics insights:

• Chiral Domain Electronics and Spintronics: The deterministic control of domain-wall chirality and domain configuration enables the realization of domain-based memory, logic, or neuromorphic devices in oxide ferroelectrics and antiferromagnets. Homochiral antiferromagnetic textures avoid the skyrmion Hall effect, offering robust, deflection-free, high-velocity information carriers (Harrison et al., 2021, Gradauskaite et al., 28 Aug 2025).
• Relaxor Ferroelectric Functionality: In materials like PMN-PT, overlapping, swirling homochiral polarization textures set the nanoscale basis for dielectric relaxation, provide a mechanism for frequency-dependent permittivity, and mediate dynamic response to ac fields (Eremenko et al., 25 Feb 2025).
• Optical Manipulation and Chiral Photonics: Optical fields tailored to possess 4D topological polarization textures (4D skyrmions) can be generated using spatial light modulators and high-NA optics. Such engineered fields offer new paths for nonreciprocal light–matter interactions, chiral sensing, and information encoding (Marco et al., 2022).
• Topological Metamaterials and Bulk–Boundary Correspondence: A geometrically defined chiral polarization field, rigorously connected to the underlying frame topology, provides a robust predictor of zero-mode waveguides in disordered and amorphous systems, extending the reach of topological design to beyond-crystalline materials (Guzmán et al., 2020).

System Type	Chirality Mechanism	Key Control/Characterization
Magnetic/ferroelectric multilayers	Interfacial DMI, flexoelectric	STEM, TEM/DPC, micromagnetic modeling
Moiré/twisted bilayers, Chern insulators	Band topology, HWCCs, SHPs	Berry phase, local Chern marker, SHPs
Relaxor ferroelectrics	Compositional heterogeneity	RMC refinement, vector-field metrics
Liquid/soft-matter ferroelectric nematics	Elastic/polar coupling, chiral dopants	FCPM, SHG, mean-field modelling
Optical fields (plasmonic lattices, light beams)	Phase structuring, SLMs	Polarization-resolved imaging, SLM optics

6. Outlook

The recognition that homochiral polarization textures can be engineered and controlled by symmetry, band topology, strain, electrostatics, and field application opens broad prospects for hybrid devices that leverage their unique topology and chirality. Next-generation electronics, spintronics, and photonics may all leverage these textures for nonvolatile memory, neuromorphic computing, robust information transmission, and novel chiral sensing, underscoring the unifying importance of chirality and topology across condensed matter and materials physics.