Pseudomagnetic suppression of non-Hermitian skin effect.

It has recently been shown that the non-Hermitian skin effect can be suppressed by magnetic fields. In this work, using a two-dimensional tight-binding lattice, we demonstrate that a pseudomagnetic field can also lead to the suppression of the non-Hermitian skin effect. With an increasing pseudomagnetic field, the skin modes are found to be pushed into the bulk, accompanied by the reduction of skin topological area and the restoration of Landau level energies. Our results provide a time-reversal invariant route to localization control and could be useful in various classical wave devices that are able to host the non-Hermitian skin effect but inert to magnetic fields.

Multiple Brillouin Zone Winding of Topological Chiral Edge States for Slow Light Applications.

Photonic Chern insulators are known for their topological chiral edge states (CESs), whose absolute existence is determined by the bulk band topology, but concrete dispersion can be engineered to exhibit various properties. For example, the previous theory suggested that the edge dispersion can wind many times around the Brillouin zone to slow down light, which can potentially overcome fundamental limitations in conventional slow-light devices: narrow bandwidth and keen sensitivity to fabrication imperfection. Here, we report the first experimental demonstration of this idea, achieved by coupling CESs with resonance-induced nearly flat bands. We show that the backscattering-immune hybridized CESs are significantly slowed down over a relatively broad bandwidth. Our work thus paves an avenue to broadband topological slow-light devices.

Localization of Chiral Edge States by the Non-Hermitian Skin Effect.

Quantum Hall systems host chiral edge states extending along the one-dimensional boundary of any two-dimensional sample. In solid state materials, the edge states serve as perfectly robust transport channels that produce a quantized Hall conductance; due to their chirality, and the topological protection by the Chern number of the bulk band structure, they cannot be spatially localized by defects or disorder. Here, we show experimentally that the chiral edge states of a lossy quantum Hall system can be localized. In a gyromagnetic photonic crystal exhibiting the quantum Hall topological phase, an appropriately structured loss configuration imparts the edge states' complex energy spectrum with a feature known as point-gap winding. This intrinsically non-Hermitian topological invariant is distinct from the Chern number invariant of the bulk (which remains intact) and induces mode localization via the "non-Hermitian skin effect." The interplay of the two topological phenomena-the Chern number and point-gap winding-gives rise to a non-Hermitian generalization of the paradigmatic Chern-type bulk-boundary correspondence principle. Compared to previous realizations of the non-Hermitian skin effect, the skin modes in this system have superior robustness against local defects and disorders.

Three-dimensional flat Landau levels in an inhomogeneous acoustic crystal.

When electrons moving in two dimensions (2D) are subjected to a strong uniform magnetic field, they form flat bands called Landau levels (LLs). LLs can also arise from pseudomagnetic fields (PMFs) induced by lattice distortions. In three-dimensional (3D) systems, there has been no experimental demonstration of LLs  as a type of flat band thus far. Here, we report the experimental realization of a flat 3D LL in an acoustic crystal. Starting from a lattice whose bandstructure exhibits a nodal ring, we design an inhomogeneous distortion corresponding to a specific pseudomagnetic vector potential (PVP). This distortion causes the nodal ring states to break up into LLs, including a zeroth LL that is flat along all three directions. These findings suggest the possibility of using nodal ring materials to generate 3D flat bands, allowing access to strong interactions and other attractive physical regimes in 3D.

Near-field directionality governed by asymmetric dipole-matter interactions.

Directionally molding the near-field and far-field radiation lies at the heart of nanophotonics and is crucial for applications such as on-chip information processing and chiral quantum networks. The most fundamental model for radiating structures is a dipolar source located inside homogeneous matter. However, the influence of matter on the directionality of dipolar radiation is oftentimes overlooked, especially for the near-field radiation. As background, the dipole-matter interaction is intrinsically asymmetric and does not fulfill the duality principle, originating from the inherent asymmetry of Maxwell's equations, i.e., electric charge and current density are ubiquitous but their magnetic counterparts are non-existent to elusive. We find that the asymmetric dipole-matter interaction could offer an enticing route to reshape the directionality of not only the near-field radiation but also the far-field radiation. As an example, both the near-field and far-field radiation directionality of the Huygens dipole (located close to a dielectric-metal interface) would be reversed if the dipolar position is changed from the dielectric region to the metal region.

Low-Velocity-Favored Transition Radiation.

When a charged particle penetrates through an optical interface, photon emissions emerge-a phenomenon known as transition radiation. Being paramount to fundamental physics, transition radiation has enabled many applications from high-energy particle identification to novel light sources. A rule of thumb in transition radiation is that the radiation intensity generally decreases with the decrease of particle velocity v; as a result, low-energy particles are not favored in practice. Here, we find that there exist situations where transition radiation from particles with extremely low velocities (e.g., v/c<10^{-3}) exhibits comparable intensity as that from high-energy particles (e.g., v/c=0.999), where c is the light speed in free space. The comparable radiation intensity implies an extremely high photon extraction efficiency from low-energy particles, up to 8 orders of magnitude larger than that from high-energy particles. This exotic phenomenon of low-velocity-favored transition radiation originates from the interference of the excited Ferrell-Berreman modes in an ultrathin epsilon-near-zero slab. Our findings may provide a promising route toward the design of integrated light sources based on low-energy electrons and specialized detectors for beyond-standard-model particles.

Interfacial Cherenkov radiation from ultralow-energy electrons.

Cherenkov radiation occurs only when a charged particle moves with a velocity exceeding the phase velocity of light in that matter. This radiation mechanism creates directional light emission at a wide range of frequencies and could facilitate the development of on-chip light sources except for the hard-to-satisfy requirement for high-energy particles. Creating Cherenkov radiation from low-energy electrons that has no momentum mismatch with light in free space is still a long-standing challenge. Here, we report a mechanism to overcome this challenge by exploiting a combined effect of interfacial Cherenkov radiation and umklapp scattering, namely the constructive interference of light emission from sequential particle-interface interactions with specially designed (umklapp) momentum-shifts. We find that this combined effect is able to create the interfacial Cherenkov radiation from ultralow-energy electrons, with kinetic energies down to the electron-volt scale. Due to the umklapp scattering for the excited high-momentum Bloch modes, the resulting interfacial Cherenkov radiation is uniquely featured with spatially separated apexes for its wave cone and group cone.

Free-electron Brewster-transition radiation.

We reveal a mechanism to enhance particle-matter interactions by exploiting the pseudo-Brewster effect of gain materials, presenting an enhancement of at least four orders of magnitude for light emission. This mechanism is enabled by the emergence of an unprecedented phase diagram that maps all phenomena of free-electron transition radiation into three distinct phases in a gain-thickness parameter space, namely, the conventional, intermediate, and Brewster phases, when an electron penetrates a dielectric slab with a modest gain and a finite thickness. Essentially, our revealed mechanism corresponds to the free-electron transition radiation in the Brewster phase, which also features ultrahigh directionality, always at the Brewster angle, regardless of the electron velocity. Counterintuitively, we find that the intensity of this free-electron Brewster-transition radiation is insensitive to the Fabry-Pérot resonance condition and, thus, the variation of slab thickness, and moreover, a weaker gain could lead to a stronger enhancement for light emission.

Stiefel-Whitney topological charges in a three-dimensional acoustic nodal-line crystal.

Band topology of materials describes the extent Bloch wavefunctions are twisted in momentum space. Such descriptions rely on a set of topological invariants, generally referred to as topological charges, which form a characteristic class in the mathematical structure of fiber bundles associated with the Bloch wavefunctions. For example, the celebrated Chern number and its variants belong to the Chern class, characterizing topological charges for complex Bloch wavefunctions. Nevertheless, under the space-time inversion symmetry, Bloch wavefunctions can be purely real in the entire momentum space; consequently, their topological classification does not fall into the Chern class, but requires another characteristic class known as the Stiefel-Whitney class. Here, in a three-dimensional acoustic crystal, we demonstrate a topological nodal-line semimetal that is characterized by a doublet of topological charges, the first and second Stiefel-Whitney numbers, simultaneously. Such a doubly charged nodal line gives rise to a doubled bulk-boundary correspondence-while the first Stiefel-Whitney number induces ordinary drumhead states of the nodal line, the second Stiefel-Whitney number supports hinge Fermi arc states at odd inversion-related pairs of hinges. These results experimentally validate the two Stiefel-Whitney topological charges and demonstrate their unique bulk-boundary correspondence in a physical system.

Bulk-Plasmon-Mediated Free-Electron Radiation Beyond the Conventional Formation Time.

Free-electron radiation is a fundamental photon emission process that is induced by fast-moving electrons interacting with optical media. Historically, it has been understood that, just like any other photon emission process, free-electron radiation must be constrained within a finite time interval known as the "formation time," whose concept is applicable to both Cherenkov radiation and transition radiation, the two basic mechanisms describing radiation from a bulk medium and from an interface, respectively. Here, this work reveals an alternative mechanism of free-electron radiation far beyond the previously defined formation time. It occurs when a fast electron crosses the interface between vacuum and a plasmonic medium supporting bulk plasmons. While emitted continuously from the crossing point on the interface-thus consistent with the features of transition radiation-the extra radiation beyond the conventional formation time is supported by a long tail of bulk plasmons following the electron's trajectory deep into the plasmonic medium. Such a plasmonic tail mixes surface and bulk effects, and provides a sustained channel for electron-interface interaction. These results also settle the historical debate in Ferrell radiation, regarding whether it is a surface or bulk effect, from transition radiation or plasmonic oscillation.

Higher-order topological polariton corner state lasing.

Unlike conventional laser, the topological laser is able to emit coherent light robustly against disorders and defects because of its nontrivial band topology. As a promising platform for low-power consumption, exciton polariton topological lasers require no population inversion, a unique property that can be attributed to the part-light-part-matter bosonic nature and strong nonlinearity of exciton polaritons. Recently, the discovery of higher-order topology has shifted the paradigm of topological physics to topological states at boundaries of boundaries, such as corners. However, such topological corner states have never been realized in the exciton polariton system yet. Here, on the basis of an extended two-dimensional Su-Schrieffer-Heeger lattice model, we experimentally demonstrate the topological corner states of perovskite polaritons and achieved polariton corner state lasing with a low threshold (approximately microjoule per square centimeter) at room temperature. The realization of such polariton corner states also provides a mechanism of polariton localization under topological protection, paving the way toward on-chip active polaritonics using higher-order topology.

Topological antichiral surface states in a magnetic Weyl photonic crystal.

Chiral edge states that propagate oppositely at two parallel strip edges are a hallmark feature of Chern insulators which were first proposed in the celebrated two-dimensional (2D) Haldane model. Subsequently, counterintuitive antichiral edge states that propagate in the same direction at two parallel strip edges were discovered in a 2D modified Haldane model. Recently, chiral surface states, the 2D extension of one-dimensional (1D) chiral edge states, have also been observed in a photonic analogue of a 3D Haldane model. However, despite many recent advances in antichiral edge states and chiral surface states, antichiral surface states, the 2D extension of 1D antichiral edge states, have never been realized in any physical system. Here, we report the experimental observation of antichiral surface states by constructing a 3D modified Haldane model in a magnetic Weyl photonic crystal with two pairs of frequency-shifted Weyl points (WPs). The 3D magnetic Weyl photonic crystal consists of gyromagnetic cylinders with opposite magnetization in different triangular sublattices of a 3D honeycomb lattice. Using microwave field-mapping measurements, unique properties of antichiral surface states have been observed directly, including the antichiral robust propagation, tilted surface dispersion, a single open Fermi arc connecting two projected WPs and a single Fermi loop winding around the surface Brillouin zone (BZ). These results extend the scope of antichiral topological states and enrich the family of magnetic Weyl semimetals.

Continuum of Bound States in a Non-Hermitian Model.

In a Hermitian system, bound states must have quantized energies, whereas free states can form a continuum. We demonstrate how this principle fails for non-Hermitian systems, by analyzing non-Hermitian continuous Hamiltonians with an imaginary momentum and Landau-type vector potential. The eigenstates, which we call "continuum Landau modes" (CLMs), have Gaussian spatial envelopes and form a continuum filling the complex energy plane. We present experimentally realizable 1D and 2D lattice models that host CLMs; the lattice eigenstates are localized and have other features matching the continuous model. One of these lattices can serve as a rainbow trap, whereby the response to an excitation is concentrated at a position proportional to the frequency. Another lattice can act a wave funnel, concentrating an input excitation onto a boundary over a wide frequency bandwidth. Unlike recent funneling schemes based on the non-Hermitian skin effect, this requires a simple lattice design with reciprocal couplings.

Photonic Majorana quantum cascade laser with polarization-winding emission.

Topological cavities, whose modes are protected against perturbations, are promising candidates for novel semiconductor laser devices. To date, there have been several demonstrations of topological lasers (TLs) exhibiting robust lasing modes. The possibility of achieving nontrivial beam profiles in TLs has recently been explored in the form of vortex wavefront emissions enabled by a structured optical pump or strong magnetic field, which are inconvenient for device applications. Electrically pumped TLs, by contrast, have attracted attention for their compact footprint and easy on-chip integration with photonic circuits. Here, we experimentally demonstrate an electrically pumped TL based on photonic analogue of a Majorana zero mode (MZM), implemented monolithically on a quantum cascade chip. We show that the MZM emits a cylindrical vector (CV) beam, with a topologically nontrivial polarization profile from a terahertz (THz) semiconductor laser.

Unsupervised Data-Driven Classification of Topological Gapped Systems with Symmetries.

A remarkable breakthrough in topological phase classification is the establishment of the topological periodic table, which is mainly based on the classifying space analysis or K theory, but not based on concrete Hamiltonians that possess finite bands or arise in a lattice. As a result, it is still difficult to identify the topological phase of an arbitrary Hamiltonian; the common practice is, instead, to check the incomplete and still growing list of topological invariants one by one, very often by trial and error. Here, we develop unsupervised classifications of topological gapped systems with symmetries, and demonstrate the data-driven construction of the topological periodic table without a priori knowledge of topological invariants. This unsupervised data-driven strategy can take into account spatial symmetries, and further classify phases that were previously classified as trivial in the past. Our Letter introduces machine learning into topological phase classification and paves the way for intelligent explorations of new phases of topological matter.

Higher-Order Topological States in Thermal Diffusion.

Unlike conventional topological materials that carry topological states at their boundaries, higher-order topological materials are able to support topological states at boundaries of boundaries, such as corners and hinges. While band topology has been recently extended into thermal diffusion for thermal metamaterials, its realization is limited to a 1D thermal lattice, lacking access to the higher-order topology. In this work, the experimental realization is reported of a higher-order thermal topological insulator in a generalized 2D diffusion lattice. The topological corner states for thermal diffusion are observed in the bandgap of diffusion rate of the bulk, as a consequence of the anti-Hermitian nature of the diffusion Hamiltonian. The topological protection of these thermal corner states is demonstrated with the stability of their diffusion profile in the presence of amorphous deformation. This work constitutes the first realization of higher-order topology in purely diffusive systems and opens the door for future thermal management with topological protection beyond 1D geometries.

Erratum: Observation of π/2 Modes in an Acoustic Floquet System [Phys. Rev. Lett. 129, 254301 (2022)].

This corrects the article DOI: 10.1103/PhysRevLett.129.254301.

Discovery of a maximally charged Weyl point.

The hypothetical Weyl particles in high-energy physics have been discovered in three-dimensional crystals as collective quasiparticle excitations near two-fold degenerate Weyl points. Such momentum-space Weyl particles carry quantised chiral charges, which can be measured by counting the number of Fermi arcs emanating from the corresponding Weyl points. It is known that merging unit-charged Weyl particles can create new ones with more charges. However, only very recently has it been realised that there is an upper limit - the maximal charge number that a two-fold Weyl point can host is four - achievable only in crystals without spin-orbit coupling. Here, we report the experimental realisation of such a maximally charged Weyl point in a three-dimensional photonic crystal. The four charges support quadruple-helicoid Fermi arcs, forming an unprecedented topology of two non-contractible loops in the surface Brillouin zone. The helicoid Fermi arcs also exhibit the long-pursued type-II van Hove singularities that can reside at arbitrary momenta. This discovery reveals a type of maximally charged Weyl particles beyond conventional topological particles in crystals.

A metamaterial-free fluid-flow cloak.

The model of ideal fluid flow around a cylindrical obstacle exhibits a long-established physical picture, where originally straight streamlines are deflected over the whole space by the obstacle. Inspired by transformation optics and metamaterials, recent theories have proposed the concept of fluid cloaking, which is able to recover the straight streamlines, as if the obstacle did not exist. However, such a cloak, similar to all previous transformation-optics-based devices, relies on complex metamaterials with inhomogeneous parameters and is difficult to implement. Here we deploy the theory of scattering cancellation and report on the experimental realization of a fluid-flow cloak without metamaterials. This cloak is realized by engineering the geometry of the fluid channel, which effectively cancels the dipole-like scattering of the obstacle. The cloaking effect is demonstrated through the direct observation of recovered straight streamlines in the fluid flow. Our work sheds new light on conventional fluid control and may find application in microfluidic devices.

Topological Chern vectors in three-dimensional photonic crystals.

The paradigmatic example of a topological phase of matter, the two-dimensional Chern insulator1-5, is characterized by a topological invariant consisting of a single integer, the scalar Chern number. Extending the Chern insulator phase from two to three dimensions requires generalization of the Chern number to a three-vector6,7, similar to the three-dimensional (3D) quantum Hall effect8-13. Such Chern vectors for 3D Chern insulators have never been explored experimentally. Here we use magnetically tunable 3D photonic crystals to achieve the experimental demonstration of Chern vectors and their topological surface states. We demonstrate Chern vector magnitudes of up to six, higher than all scalar Chern numbers previously realized in topological materials. The isofrequency contours formed by the topological surface states in the surface Brillouin zone form torus knots or links, whose characteristic integers are determined by the Chern vectors. We demonstrate a sample with surface states forming a (2, 2) torus link or Hopf link in the surface Brillouin zone, which is topologically distinct from the surface states of other 3D topological phases. These results establish the Chern vector as an intrinsic bulk topological invariant in 3D topological materials, with surface states possessing unique topological characteristics.