Complex topological configurations are fertile ground for exploring emergent phenomena and exotic phases in condensed-matter physics. For example, the recent discovery of polarization vortices and their associated complex-phase coexistence and response under applied electric fields in superlattices of (PbTiO3)n/(SrTiO3)n suggests the presence of a complex, multi-dimensional system capable of interesting physical responses, such as chirality, negative capacitance and large piezo-electric responses1–3. Here, by varying epitaxial constraints, we discover room-temperature polar-skyrmion bubbles in a lead titanate layer confined by strontium titanate layers, which are imaged by atomic-resolution scanning transmission electron microscopy. Phase-field modelling and second-principles calculations reveal that the polar-skyrmion bubbles have a skyrmion number of +1, and resonant soft-X-ray diffraction experiments show circular dichroism, confirming chirality. Such nanometre-scale polar-skyrmion bubbles are the electric analogues of magnetic skyrmions, and could contribute to the advancement of ferroelectrics towards functionalities incorporating emergent chirality and electrically controllable negative capacitance.Chiral polar-skyrmion bubbles are observed in superlattices of titanium-based perovskite oxides at room temperature.

Observation of room temperature polar skyrmions

Based on first-principles calculations and effective model analysis, all possible straight nodal-line (NL) phonons in symmorphic and nonsymmorphic space groups are uncovered. A classification of two-band $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ models at an arbitrary point on the NLs is carried out, and these NL phonons are found to locate along the high-symmetry lines of the Brillouin zone. According to our classification, there are two types of NL phonons. The first type is topologically nontrivial with a linear dispersion, while the second type is topologically trivial, exhibiting a quadratic dispersion. The second type hosts the highest order of NLs in phonon systems, and it is a promising platform for investigating topological phase transitions. All the minimum symmetries that guarantee the existence of straight NL phonons are uncovered, which can be used to distinguish the types of straight NLs. This paper not only classifies NL phonons but also provides guidance to search for topological NLs in bosonic systems.

Symmetry-enforced straight nodal-line phonons

Weyl materials, exhibiting topologically nontrivial touching points in band dispersion, are fascinating subjects of research, which have been extensively studied in electron-related systems. In this paper, by employing first-principles calculations of topological phonons in wurtzite-structured phases of $MX$ chalcogenides (where $M=\mathrm{Zn}$ and Cd and $X=\mathrm{O}$, S, Se, and Te), we demonstrate the existence of ideal type-II Weyl phonons in wurtzite ZnSe, a well-known II-VI semiconductor. There are in the ${\mathbf{q}}_{z}=0.0$ plane six pairs of Weyl points stemming from the inversion between the two optical branches. The nontrivial phonon surface states and surface arcs projected on the semifinite (0001) surfaces are investigated. Phonon surface arcs connecting each pair of Weyl points with opposite chirality, guaranteed to be $0.55\phantom{\rule{0.28em}{0ex}}{\AA{}}^{\ensuremath{-}1}$ and very long, are readily observable in experiment. The opposite chirality of Weyl points with quantized Berry curvature produces the Weyl phonon Hall effect. Our results propose a potential platform for future experimental study of type-II Weyl phonons in realistic materials.

First-principles prediction of ideal type-II Weyl phonons in wurtzite ZnSe

The topological phenomenon has been extensively studied in condensed matter physics and has attracted much attention in many different fields. Like electrons, phonons can also be studied using critical theorems and topology concepts, giving impetus to the birth of topological phonons. Among the topological phonons, the topological nodal line phonons in crystalline materials have emerged as a new area of rapid development in both experiment and theory. Researchers have been hunting for realistic materials with nodal line phonons for the last four years. To date, however, a timely review of recent advances in topological nodal line phonons, and especially their material realization, is still lacking. Considering the classification of the nodal line states, in this review, we will first review the identification of the materials hosting the nodal line phonons with different degeneracies, different types of dispersion, and different geometric shapes in theory. Moreover, we will review and discuss the reasons for the appearance of the nodal line phonons from the viewpoint of symmetry. Second, we will review the case where the nodal line appears in the projected surface phonon states instead of the bulk phonon states. Third, we will review the experimental material realization of nodal line phonons. Finally, we will present a summary, outlook, and additional notes. We believe that this review will contribute to a more advanced understanding of topological nodal line phonons in solid materials and will offer new perspectives on this rapidly expanding field.

Topological nodal line phonons: Recent advances in materials realization

Topological phases of matter have revolutionised the fundamental understanding of band theory and hold great promise for next-generation technologies such as low-power electronics or quantum computers. Single-gap topologies have been extensively explored, and a large number of materials have been theoretically proposed and experimentally observed. These ideas have recently been extended to multi-gap topologies with band nodes that carry non-Abelian charges, characterised by invariants that arise by the momentum space braiding of such nodes. However, the constraints placed by the Fermi-Dirac distribution to electronic systems have so far prevented the experimental observation of multi-gap topologies in real materials. Here, we show that multi-gap topologies and the accompanying phase transitions driven by braiding processes can be readily observed in the bosonic phonon spectra of known monolayer silicates. The associated braiding process can be controlled by means of an electric field and epitaxial strain, and involves, for the first time, more than three bands. Finally, we propose that the band inversion processes at the $\Gamma$ point can be tracked by following the evolution of the Raman spectrum, providing a clear signature for the experimental verification of the band inversion accompanied by the braiding process. 

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Phonons as a platform for non-Abelian braiding and its manifestation in layered silicates

Perovskite oxides exhibit a rich variety of structural phases hosting different physical phenomena that generate multiple technological applications. We find that topological phonons—nodal rings, nodal lines, and Weyl points—are ubiquitous in oxide perovskites in terms of structures (tetragonal, orthorhombic, and rhombohedral), compounds (BaTiO3, PbTiO3, and SrTiO3), and external conditions (photoexcitation, strain, and temperature). In particular, in the tetragonal phase of these compounds, all types of topological phonons can simultaneously emerge when stabilized by photoexcitation, whereas the tetragonal phase stabilized by thermal fluctuations only hosts a more limited set of topological phonon states. In addition, we find that the photoexcited carrier concentration can be used to tune the topological phonon states and induce topological transitions even without associated structural phase changes. Overall, we propose oxide perovskites as a versatile platform in which to study topological phonons and their manipulation with light.

Topological phonons in oxide perovskites controlled by light.

Perovskite oxides exhibit a rich variety of structural phases hosting different physical phenomena that generate multiple technological applications. We find that topological phonons, i.e., nodal rings, nodal lines, and Weyl points, are ubiquitous in oxide perovskites in terms of structures (tetragonal, orthorhombic, and rhombohedral), compounds (BaTiO3, PbTiO3, and SrTiO3), and external conditions (photoexcitation, strain, and temperature). In particular, in the tetragonal phase of these compounds, all types of topological phonons can simultaneously emerge when stabilized by photoexcitation, whereas the tetragonal phase stabilized by thermal fluctuations only hosts a more limited set of topological phonon states. Additionally, we find that the photoexcited carrier concentration can be used to tune the topological phonon states and induce topological transitions even without associated structural phase changes. Overall, we propose oxide perovskites as a versatile platform in which to study topological phonons and their manipulation with light.

Yuchen Hu

Papers

Topological phonons in oxide perovskites controlled by light.

Topological phonons in oxide perovskites controlled by light.