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    {
      "highlights": [
        "Recognizing the coupling between ferroelectricity and chirality in optically active ferroelectrics opens a route for manipulating chirality via ferroelectricity under an external electric field, enabling control over chirality-dependent quantum states. Here, we report the experimental demonstration of the coupling between ferroelectricity and phonon chirality in the molecular ferroelectric triglycine sulfate. By electrically switching the crystal chirality, we achieve reversible and device-compatible control of phonon chirality, as revealed by in situ time-resolved magneto-optical Kerr effect measurements. The Kerr rotation reverses with electric-field switching, while phonon chirality vanishes in the paraelectric phase and is tunable in the racemic ferroelectric state. Furthermore, density functional theory calculations and circularly polarized Raman spectroscopy further corroborate the opposite circular phonon motions. These results establish an electrically addressable coupling pathway linking ferroelectricity, structural chirality, chiral phonons, and spin, opening a route toward chiral-phonon-enabled spin and phonon control technologies based on ferroelectric materials.\n...\nChiral phonons\n...\nmoiré superlatt\n...\nFerroelectric materials exhibit switchable spontaneous polarization and broken inversion symmetry, providing an ideal platform for exploring symmetry-governed quantum phenomena such as chiral phonons 22, 23, 24, 25, 26, 27, 28, 29, 30, 31. Recent studies have revealed a potential coupling between ferroelectricity and chirality in optically active ferroelectrics 32, where electric polarization and structural chirality can be coupled for crystals in five out of ten ferroelectricity active polar point groups. This coupling enables the electrical control of chirality, providing a means to modulate a wide range of chirality-related properties, including optical rotation, circular dichroism, circularly polarized luminescence, asymmetric synthesis/catalysis, and chirality-induced spin selectivity 32, 33, 34. In this work, we further demonstrate that electric-field–induced switching of crystal chirality enables direct control of phonon chirality via ferroelectricity, thereby extending the functional scope of ferroelectrics beyond conventional polarization switching toward spin–lattice–chirality interactions.\n...\nSeveral theoretical studies have predicted that ferroelectricity could provide an effective route to manipulate chiral phonons 13, 35, 36, 37, yet experimental realization has remained elusive due to practical challenges. Building on the intrinsic coupling between ferroelectricity and chirality discussed above, here we present the experimental demonstration of in situ control of phonon chirality in a molecular ferroelectric crystal, triglycine sulfate (TGS) 32. By electrically switching the crystal chirality via an external electric field, we directly observe reversible modulation of phonon chirality using TR-MOKE measurements. Our results establish a sequential coupling pathway in which ferroelectricity controls structural chirality, chirality activates chiral phonons under heat flow, and chiral phonons transfer angular momentum to electronic spins, thereby enabling electrical control of spin (Fig. 1a). Such electrical manipulation of spin via chiral phonons opens opportunities for chiral-phonon-driven spintronic and phononic devices.\n...\nFerroelectricity depends on the presence of polarity, since it inherently breaks inversion symmetry. Among the 10 polar point groups that allow ferroelectricity, 5 are chiral that provide the potential to switch chirality and chiral phonons by applying an external electric field. To investigate the coupling between ferroelectricity and chiral phonons, we study a classic molecular ferroelectric compound, TGS. TGS is composed of one neutral glycine molecule with a dihedral angle, two protonated glycine cations that are coplanar, and one sulfate anion. It crystallizes in the space group, P 2 1, where structural chirality and ferroelectric polarization are intrinsically coupled, arising from the torsional distortion of the neutral, non-coplanar glycine molecule together with the cooperative polar displacement of the sulfate anions along the b axis. The electric field can induce a change in the O–C–C–N dihedral angle from positive (+19.68°) to negative (–19.19°) (Fig. 1b). The switchable polarity is demonstrated by polarization-electric field (P – E) loop measurements (Fig. 1b), while the chirality flip has been confirmed through single-crystal X-ray diffraction 32, where the P-TGS shows the opposite dihedral angle compared to the N-TGS. It is also confirmed by optical rotatory dispersion 38 and circular dichroism 39 measurements.\n...\nThe TGS crystal exhibits four distinct phases with different symmetry and chirality/polarity states during its phase transition process, which can be interconverted under specific external conditions (Fig. 1c) 39. These phase transitions provide three practical routes for phonon control: (i) temperature tuning across the ferroelectric–paraelectric transition, (ii) electric-field manipulation within the ferroelectric phase, and (iii) modulation of net chirality in different ferroelectric domains in the racemic phase. At elevated temperatures above 49 °C, TGS adopts a centrosymmetric, non-polar paraelectric phase (P 2 1/ m, Suppl. Table S1). Upon cooling under an applied electric field, it transforms into one of two ferroelectric phases with opposite polarization, homochirality, and optical activity, which are switchable by reversing the electric field direction. In contrast, if cooled without an external field, a racemic ferroelectric phase forms, consisting of an equal mixture of left- and right-handed chiral domains. These four states—non-polar paraelectric phase, left/right-handed ferroelectric phase, and racemic ferroelectric phase—are interrelated through temperature changes and electric-field-driven switching or depolarization processes (Fig. 1c).\n...\nWe demonstrate that chiral phonons in the ferroelectric crystal triglycine sulfate (TGS) can be reversibly switched by an external electric field, as evidenced by Kerr rotation signals detected at the Ag surface. By electrically switching the crystal chirality, the phonon chirality is correspondingly reversed, while the paraelectric phase completely suppresses chiral phonons. In the racemic ferroelectric state, the phonon chirality can be continuously tuned by varying the net crystal chirality within the laser spot, achieved by micrometer-scale translation of the sample position to probe different domain distributions. The reversal of phonon chirality is further corroborated by first-principles calculations and circularly polarized Raman spectroscopy, which reveal opposite collective molecular rotations in N- and P-TGS. Overall, this work establishes ferroelectricity as an effective control knob for activating and manipulating chiral phonons and their associated circular polarization, enabling electrical control of spin. By advancing chiral phonons from static observation to active electrical manipulation, our results open opportunities for chiral-phonon-based phononic and spintronic devices.\n...\nIn principle, the Kerr signal polarity can be switched by reversing the chirality of TGS under an applied electric field. However, complete chirality reversal is difficult to achieve within a short timescale in the ferroelectric phase, as observed in P– E loop measurements. This is due to the thermally driven and inherently slow nature of molecular reorientation or angular adjustments. To overcome this limitation, we employed a paraelectric-to-ferroelectric poling method, in which the crystal is heated into the paraelectric phase and subsequently cooled under a positive or negative electric field. This procedure enables full chirality switching and promotes the growth of large ferroelectric domains."
      ],
      "id": "https://www.nature.com/articles/s41467-026-73317-4",
      "image": "https://media.springernature.com/m685/springer-static/image/art%3A10.1038%2Fs41467-026-73317-4/MediaObjects/41467_2026_73317_Fig1_HTML.png",
      "publishedDate": "2026-05-29T00:00:00.000Z",
      "title": "Coupled ferroelectricity and phonon chirality | Nature Communications",
      "url": "https://www.nature.com/articles/s41467-026-73317-4"
    },
    {
      "author": "Hao Chen, Weikang Wu, Sun KangTai, Shengyuan A. Yang, Lifa Zhang",
      "entities": [
        {
          "id": "https://exa.ai/library/publication/bnnscj7n6cy",
          "properties": {
            "abstract": "Chiral phonons have attracted increasing attention, as they play important roles in many different systems and processes. However, a method to control phonon chirality by external fields is still lacking. Here, we propose that in displacement-type ferroelectric materials, an external electric field can reverse the chirality of chiral phonons via ferroelectric switching. Using first-principles calculations, we demonstrate this point in the well-known two-dimensional ferroelectric In2Se3. This reversal may lead to a number of electrically switchable phenomena, such as chiral phonon induced magnetization, the phonon Hall effect, and possible topological interface chiral phonon modes at ferroelectric domain boundaries. Our work offers a way to control chiral phonons, which could be useful for the design and application of thermal or information devices based on them.",
            "authors": [
              {
                "id": null,
                "name": "Hao Chen"
              },
              {
                "id": null,
                "name": "Weikang Wu"
              },
              {
                "id": null,
                "name": "Sun KangTai"
              },
              {
                "id": null,
                "name": "Shengyuan A. Yang"
              },
              {
                "id": null,
                "name": "Lifa Zhang"
              }
            ],
            "citationCount": 5,
            "date": "2024-02-26",
            "doi": "10.1063/5.0196731",
            "language": "en",
            "referenceCount": 38,
            "title": "Electrically controllable chiral phonons in ferroelectric materials",
            "type": "article",
            "year": 2024
          },
          "type": "publication",
          "version": 1
        }
      ],
      "highlights": [
        "# Electrically controllable chiral phonons in ferroelectric materials\n...\nChiral phonons have attracted increasing attention, as they play important roles in many different systems and processes. However, a method to control phonon chirality by external fields is still lacking. Here, we propose that in displacement-type ferroelectric materials, an external electric field can reverse the chirality of chiral phonons via ferroelectric switching. Using first-principles calculations, we demonstrate this point in the well-known two-dimensional ferroelectric In2Se3. This reversal may lead to a number of electrically switchable phenomena, such as chiral phonon induced magnetization, the phonon Hall effect, and possible topological interface chiral phonon modes at ferroelectric domain boundaries. Our work offers a way to control chiral phonons, which could be useful for the design and application of thermal or information devices based on them."
      ],
      "id": "https://exa.ai/library/publication/bnnscj7n6cy",
      "publishedDate": "2024-02-26T00:00:00.000Z",
      "title": "Electrically controllable chiral phonons in ferroelectric materials",
      "url": "https://doi.org/10.1063/5.0196731"
    },
    {
      "author": "Hiroki Ueda, Abhishek Nag, Carl P. Romao, Mirian García‐Fernández, Ke‐Jin Zhou, U. Staub",
      "entities": [
        {
          "id": "https://exa.ai/library/publication/1s4tb68ndjt",
          "properties": {
            "abstract": "Abstract Quasiparticles describe collective excitations in many-body systems, and their symmetry classification is of fundamental importance for physical processes such as excited states, transport phenomena, and phase transitions. Recent studies have introduced chirality as an additional degree of freedom in condensed matter physics, leading to a range of novel phenomena. Among these, chiral phonons are of special interest because they carry angular momentum and therefore intrinsically break time reversal symmetry, which non-trivially bridges the spin system with the lattice. Here, we directly prove the presence of chiral phonons in a prototypical polar LiNbO 3 crystal. Our demonstration of chiral phonons in a ferroelectric enables in-situ electrical control of momentum-dependent “magnetic” polarization with the reversible phonon handedness. This ferroic control of phonon chirality has substantial potential in the emerging field of chiral phononics, particularly along the associated control of its phonon angular momentum.",
            "authors": [
              {
                "id": null,
                "name": "Hiroki Ueda"
              },
              {
                "id": null,
                "name": "Abhishek Nag"
              },
              {
                "id": null,
                "name": "Carl P. Romao"
              },
              {
                "id": null,
                "name": "Mirian García‐Fernández"
              },
              {
                "id": null,
                "name": "Ke‐Jin Zhou"
              },
              {
                "id": null,
                "name": "U. Staub"
              }
            ],
            "citationCount": 7,
            "date": "2025-12-05",
            "doi": "10.1038/s41467-025-66911-5",
            "language": "en",
            "referenceCount": 33,
            "title": "Chiral phonons in polar LiNbO3",
            "type": "article",
            "year": 2025
          },
          "type": "publication",
          "version": 1
        }
      ],
      "highlights": [
        "Quasiparticles describe collective excitations in many-body systems, and their symmetry classification is of fundamental importance for physical processes such as excited states, transport phenomena, and phase transitions. Recent studies have introduced chirality as an additional degree of freedom in condensed matter physics, leading to a range of novel phenomena. Among these, chiral phonons are of special interest because they carry angular momentum and therefore intrinsically break time reversal symmetry, which non-trivially bridges the spin system with the lattice. Here, we directly prove the presence of chiral phonons in a prototypical polar LiNbO3 crystal. Our demonstration of chiral phonons in a ferroelectric enables in-situ electrical control of momentum-dependent \"magnetic\" polarization with the reversible phonon handedness. This ferroic control of phonon chirality has substantial potential in the emerging field of chiral phononics, particularly along the associated control of its phonon angular momentum.\n...\nHere, we demonstrate the presence of chiral phonons in the prototypical polar crystal LiNbO3 within a single ferroelectric domain by using resonant inelastic X-ray scattering (RIXS) with circular polarization. LiNbO3 was selected for this study for several reasons: (1) it is a wellestablished prototypical polar crystal, (2) high-quality single-domain crystals are commercially available, (3) ferroelectric domains can be controlled at the nanometer scale [32] , and (4) its phonon properties are directly relevant to technological applications, such as substrates for surface acoustic wave devices, thin-film growth, and piezoelectric devices. Angular momentum transfer between a circularly polarized X-ray photon and a chiral phonon needs to fulfill the selection rules of phonon excitation in the RIXS process, which results in a circular polarization contrast on a chiral phonon excitation peak. Density functional theory (DFT) calculations provide reliable phonon properties for LiNbO3 because it contains only a moderate number of non-magnetic light elements in the unit cell without significant electronic correlations. Therefore, combining RIXS experiments and DFT calculations yields an unambiguous and robust demonstration of chiral phonons in a polar (non-chiral) crystal and establishes a large and important class of materials for chiral phononics.\n...\n\n...\nIn conclusion, we have demonstrated the direct observation of chiral phonons in a polar crystal. Chiral phonons are a key ingredient of recently discovered exotic phenomena due to their phonon angular momentum [24] [25] [26] , magnetism mediating the spin-lattice coupling [23, 28, 43] , and non-trivial coupling with electrons [27] . Although LiNbO3 itself does not exhibit significant spin-lattice coupling, phonon angular momentum has been discussed in α-quartz [25] , where such coupling is also negligible. More importantly, our demonstration of chiral phonons in a polar crystal establishes their presence across a wide range of polar materials, including those where spin-lattice coupling is essential in emergent physics. Switching ferroelectric domains is straightforward in contrast to switching chiral domains. Such domain inversion allows us to switch angular momentum and therefore the spin-lattice coupling in-situ at general momentum points. This enables unique opportunities to explore physical properties based on controllable phonon chirality or its associated phonon angular momentum, and hence, opens the door for chiral phononics. Based on the bistability of ferroelectric domains and the developed technology for local switching thereof [31] , patterning chiral phononic devices in nanoscales will be possible. Another perspective is the possible phonon angular momentum switching at ultrafast timescales due to the ultrafast reversal of ferroelectric polarization [44] . The electrically controllable bistable states of phonon chirality or phonon angular momentum have significant potential to tailor emergent phenomena associated with chiral phonons.\n...\nThe authors demonstrate the existence of chiral phonons in a non-chiral ferroelectric material, opening the possibility for phonon chirality control through ferroic switching of the electric polarization."
      ],
      "id": "https://exa.ai/library/publication/1s4tb68ndjt",
      "publishedDate": "2025-12-05T00:00:00.000Z",
      "title": "Chiral phonons in polar LiNbO3",
      "url": "https://doi.org/10.1038/s41467-025-66911-5"
    },
    {
      "highlights": [
        "Chirality reveals symmetry breaking of the fundamental interaction of elementary particles. In condensed matter, for example, the chirality of electrons governs many unconventional transport phenomena such as the quantum Hall effect. Here we show that phonons can exhibit intrinsic chirality in monolayer tungsten diselenide. The broken inversion symmetry of the lattice lifts the degeneracy of clockwise and counterclockwise phonon modes at the corners of the Brillouin zone. We identified the phonons by the intervalley transfer of holes through hole-phonon interactions during the indirect infrared absorption, and we confirmed their chirality by the infrared circular dichroism arising from pseudoangular momentum conservation. The chiral phonons are important for electron-phonon coupling in solids, phonon-driven topological states, and energy-efficient information processing.\n...\nChirality is a fundamental property of an object not identical to its mirror image. For elementary and quasiparticles, it is an important quantum concept at the heart of modern physics. For example, the discovered handedness of neutrinos in electroweak interaction revolutionized our understanding of the universal parity conservation law. Chiral fermions with spin-momentum locking can emerge in solid-state systems such as the recently observed Weyl semimetals with inversion symmetry–breaking lattices (1). Electron chirality in graphene defined through pseudospin was found to cause distinctive transport properties such as unconventional Landau quantization and Klein tunneling (2, 3). Meanwhile, electrons in monolayer transition metal dichalcogenides with broken inversion symmetry display optical helicity, which opens the field of valleytronics (4). The outstanding question is whether bosonic collective excitations such as phonons can attain chirality. Recently, the intrinsic chirality of phonons without applied external magnetic fields in an atomic lattice was predicted theoretically at the corners of the Brillouin zone of an asymmetric two-dimensional (2D) hexagonal lattice (5). Because of the threefold rotational symmetry of the crystal and the momentum vectors, the vibrational plane wave is composed of unidirectional atomic circular rotation. Because the phonons in the same valley have distinct energy levels, the rotation is not the superposition of linear modes, in contrast to the circular motion in nonchiral cases (6). The hypothetical chiral phonons are potentially important for the control of intervalley scattering (7, 8), lattice modulation–driven electronic phase transitions (9, 10) and topological states (11), as well as information carriers that can be robust against decoherence for solid-state quantum information applications (12).\n...\nPAM l for each mode from the phase change after counterclockwise 120° rotation: Ĉ3(uk) = e−i(2π/3)luk, where uk is the function of atomic motion (fig. S6). Because LA(K) is always C3 symmetric, it has l = 0; in contrast, LO(K) gains negative phase after rotation (becomes ahead of time) and thus l = 1. The K phonons with different PAM are completely nondegenerate because of the mass difference between W and Se. The lifting of degeneracy guarantees that each mode has a distinctive selection rule for the electron-phonon and optical scattering (table S1). These features differentiate the intrinsically chiral phonons from any previously investigated phonons where circular atomic motion results from superposing linear polarized eigenmodes (6, 15, 16). Chirality in the absence of an external magnetic flux is also distinguished from the magnetic field–induced split of degenerate superposition modes (17). Finally, both the physical origin and properties of the atomic chiral phonons are fundamentally different from previous phononic\n...\nWe use an optical pump-probe technique to identify the chiral phonon by its scattering with holes (Fig. 1B and fig. S2). The linear momentum, PAM, and energy of the respective phonon modes are determined by characterizing all of the other particles involved in the intervalence band transition (IVBT) process (14). First, we inject holes at the K valley by a left–circularly polarized (LCP) optical pump pulse. The K valley–polarized hole relaxes to the valence band edge with initial linear momentum pi = −K. It can transit to the K′ point (pf = K) by emitting a K phonon (q = pi − pf = −2K = K), but the intermediate state is virtual because the spin-conserving state has much higher energy due to large spin-orbit coupling. We then send an IR pulse to satisfy the energy conservation and place the hole in the spin-split band at K′. Because the hole states have zero PAM, the PAM of the phonon must be equal to the spin angular momentum of the absorbed IR photon. Therefore, the LCP pulse controls the creation of only LO(K) phonons. Eventually, we recognize the final spin-split state in the opposite valley by the energy and right circular polarization of its radiative decay. The selection rule of phonon creation will be identical if the hole first absorbs an IR photon, transits to an intermediate state within the valley, and then emits a phonon, as long as the final state is the same. The phonon annihilation is negligible because the population is very low for all phonon modes at the K or K′ points at a base temperature of 82 K. The selection is also not affected by a small momentum distribution of the initial and final holes (14) due to finite thermal energy or the strong many-body interaction (21). This is because, like the optical valley-selectivity, the contrast of electron-phonon coupling strength remains large in the vicinity of K and K′, even if the PAM is only defined on these points.\n...\nThe PAM of valley phonons is determined by measuring the polarization selection of the absorbed IR photon, resulting from the chiral electron-phonon interaction. With LCP excitation, the intervalley transition of holes from the K valley can either absorb an LCP IR photon to produce LO phonons or absorb a right–circularly polarized (RCP) IR photon to produce TA/A1 phonons (Fig. 3A). We observe different IR absorption when the probe has the same polarization as the pump light (αsame) versus when it has the opposite polarization (αoppo). This IR circular dichroism (CD = αsame − αoppo) demonstrates that scattering cross sections of the two processes are not equal, owing to the difference of electron-phonon coupling strength. As shown in Fig. 3B, the CD at 82 K is always positive for valley-polarized holes. Because the holes have zero PAM regardless of valley index or spin-split bands, the angular momentum of the IR photon is transferred to either the spin or the phonon. The initial intravalley IVBT produces positive CD because the electronic spin flips from −1/2 in the spin-split band to +1/2 at the valence band edge at the K point. However, this contribution decays fast as a function of IR delay in accordance with Fig. 2B. Thus, the intervalley phonon-creating transition is the dominant source of positive CD for τ ≥ 0.8 ps. It indicates that the LO branch contributes most to the indirect IR absorption. For nonchiral systems, although photons with opposite circular polarization may interact with different particles, the probabilities are always equal. Therefore, the CD is the signature of intrinsic phonon chirality.\n...\nOur findings of chiral phonons are fundamentally important for potential experimental tests of quantum theories with chiral bosons (29) in the solid state. Our work also provides a possible route for controlling valley and spin through electron-phonon scattering and strong spin-phonon interactions (16). Furthermore, the lifting of degeneracy by chirality offers robust PAM information against decoherence and long-range perturbation and offers a new degree of freedom to the design and implementation of phononic circuitry (30) at the atomic scale without magnetic fields."
      ],
      "id": "https://www.science.org/doi/10.1126/science.aar2711",
      "image": "https://www.science.org/cms/asset/68026375-8668-4d09-8983-2b3d8f419b9c/359_579_f1.gif",
      "title": "Observation of chiral phonons | Science",
      "url": "https://www.science.org/doi/10.1126/science.aar2711"
    },
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      "highlights": [
        "Nonlinear optics reveal how the chirality of ferroelectric vortices can be deterministically controlled using an electric field.\n...\nPolar textures have attracted substantial attention in recent years as a promising analog to spin-based textures in ferromagnets. Here, using optical second-harmonic generation–based circular dichroism, we demonstrate deterministic and reversible control of chirality over mesoscale regions in ferroelectric vortices using an applied electric field. The microscopic origins of the chirality, the pathway during the switching, and the mechanism for electric field control are described theoretically via phase-field modeling and second-principles simulations, and experimentally by examination of the microscopic response of the vortices under an applied field. The emergence of chirality from the combination of nonchiral materials and subsequent control of the handedness with an electric field has far-reaching implications for new electronics based on chirality as a field-controllable order parameter.\n...\nOver the past several years, nontrivial topological dipolar textures have emerged as an area of great attention in condensed matter research ([*11*](#R11)–[*13*](#R13)), building from and complementing the ongoing revolution in topological spin-based textures such as chiral skyrmions and vortices ([*14*](#R14)–[*17*](#R17)). These dipolar textures have been mainly identified in epitaxial heterostructures in which exact electrostatic and elastic boundary conditions are imposed on a crystalline ferroelectric layer, such as PbTiO3([*13*](#R13),[*18*](#R18),[*19*](#R19)). Dipolar textures in ferroelectrics, such as polar vortices and skyrmions, have been extensively studied, and several interesting physical phenomena have been found, such as toroidal order and negative capacitance ([*20*](#R20)–[*22*](#R22)). Perhaps the most exotic and unexpected among them is the emergence of chirality (i.e., handedness) in polar vortices and skyrmions that arise from a sequence of achiral materials ([*20*](#R20),[*23*](#R23)). The existence of chiral behavior in these systems was demonstrated using resonant soft x-ray diffraction–based circular dichroism (RSXD-CD) measurements ([*20*](#R20),[*24*](#R24),[*25*](#R25)). However, the use of these synchrotron-based approaches, while scientifically sophisticated, can limit the pervasive impact of these chiral textures, particularly for possible applications in next-generation technologies. In parallel, strain engineering or electric field manipulation and control of chiral phases would be of fundamental and technological interest. This has been the subject of theoretical studies ([*26*](#R26)–[*28*](#R28)) but has remained elusive from the experimental point of view. A recent work addresses this problem, but the presence of random fields during the switching precludes a deterministic control of the vortex rotation reversal ([*29*](#R29)). With this as background, the present work introduces two main innovations: (i) the manipulation of the chirality in a controlled, deterministic, and reversible way in polar vortices over mesoscale regions using an electric field and (ii) the use of conventional optical techniques to probe chirality in these polar textures.\n...\nHaving established the equilibrium chiral domain structure, we next turn to their in situ manipulation during the SHG-CD measurements. A DC electric field was applied along the in-plane [001]*o*direction using lithographically patterned interdigitated electrodes (fig. S7, A and B). This pattern leads to linear electrostatic potentials, i.e., constant electric fields of opposite polarity for adjacent interdigitated regions (as indicated by the white arrows;[Fig. 4, A and B](#F4)). The direction of the DC field favors the [001]*o*component of the polarization in the same sense and, therefore, selects the direction of the buckling of the vortices. This offset of the vortex cores determines unequivocally the helicity, as shown in[Fig. 1 (E and F)](#F1), and is supported by the second-principles simulations in fig. S10. Therefore, the chirality can be deterministically controlled by the external field. An SHG-CD image taken with an applied field of ±50 kV/cm (±40 V across an 8-μm electrode spacing) within neighboring interdigitated regions is shown ([Fig. 4, A and B](#F4)). The applied electric field leads to the formation of large bands of uniform CD across the entire region between the interdigitated electrodes, with the sign of the CD response being the measure of the sign of the chirality. As expected, reversing the sign of the applied voltage switches the sign of the CD (chirality) in each region between the electrodes. The robustness of the switching is illustrated by the line profiles ([Fig. 4, C and D](#F4)), which correspond to SHG-CD along the white dashed lines ([Fig. 4, A and B](#F4)) for a sequence of opposite polarity fields. SHG-CD in these saturated regions is also larger in magnitude (by \\~50%) than that observed in the unmodified samples. This increased magnitude likely arises because of two factors. First, the average size of polar domains in the virgin sample is on the order or even smaller than the diffraction-limited imaging resolution of the SHG measurements, which leads to averaging over regions with positive and negative CD responses, consequently decreasing the magnitude of the resultant CD. Second, the application of an electric field induces larger offsets between the core of the vortices and, therefore, there is an enhancement of the helicity.\n...\nof the SHG-CD measurements ([Fig. 4E](#F4), blue data) reveals a CCW, hysteretic nature of the field dependence of the normalized SHG-CD (chirality) with a coercive field of \\~20 kV/cm and a nonvolatile remanent chiral state. This is a direct indication of the switchability of chirality by an electric field. Data illustrating reproducibility of the hysteresis effect are also presented in fig. S8 (A and B). To probe this further, we carried out polarization–electric field hysteresis measurements using the same interdigitated electrodes to probe the switching of the in-plane component of the switchable polarization ([Fig. 4E](#F4), red data). The raw data for this ferroelectric hysteresis loop measurement (fig. S9) show the existence of a linear dielectric component superimposed on the ferroelectric component. For the sake of simplicity, we have subtracted out the linear dielectric component ([Fig. 4E](#F4)). The overlap of the ferroelectric polarization hysteresis loops with the SHG-CD hysteresis establishes a direct correlation between the in-plane polarization (arising from the buckling pattern in the vortex arrays) and the consequent chiral behavior as discerned from the SHG-CD\n...\nIn summary, this work presents two broad implications. First, it has been shown that SHG-CD measurements using laboratory-based confocal optical measurements can be an effective probe of the chirality in these vortex arrays with a spatial resolution in the range of \\~300 nm. In turn, these studies show that the vortex arrays assemble into domains of opposite chirality, identified by the change in the sign of the CD. The coexistence of regions of opposite CD (i.e., chirality) points to an equilibrium between regions of opposite chirality and therefore to a pathway by which one region can be converted into the other with a thermodynamic field. Of greater importance is the observation that an electric field can switch the sign of the local chirality in a reversible, controlled, and deterministic fashion. To the best of our knowledge, this is one of but a few instances where the chirality of a material can be manipulated with thermodynamic fields other than the chemical field. This work also points to a host of possibilities including probing the dynamics of this chiral switching, the role of the chiral-domain boundary, and the microscopic structure of these domain boundaries."
      ],
      "id": "https://pmc.ncbi.nlm.nih.gov/articles/PMC8730600/",
      "title": "Electric field control of chirality",
      "url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC8730600/"
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