Persistent Chirality-Induced Spin-Selectivity Effect in Circular Helix Molecules.

The spin-orbit coupling (SOC), the dynamics of the nonequilibrium transport process, and the breaking of time-reversal and space-inversion symmetries have been regarded as key factors for the emergence of chirality-induced spin selectivity (CISS) and chirality-dependent spin currents in helix molecules. In this work, we demonstrated the generation of persistent CISS currents in various circular single-stranded DNAs and 310-helix proteins for the first time, regardless of whether an external magnetic flux is applied or not. This new CISS effect presents only in equilibrium transport processes, distinct from the traditional CISS observed in nonequilibrium transport processes and linear helix molecules; we term it as the PCISS effect. Notably, PCISS manifests irrespective of whether the SOC is chirality-driven or stems from heavy-metal substrates, making it an efficient way to generate chirality-locked pure spin currents. Our research establishes a novel paradigm for examining the underlying physics of the CISS effect.

Evolution and global charge conservation for polarization singularities emerging from non-Hermitian degeneracies.

Core concepts in singular optics, especially the polarization singularities, have rapidly penetrated the surging fields of topological and non-Hermitian photonics. For open photonic structures with non-Hermitian degeneracies in particular, polarization singularities would inevitably encounter another sweeping concept of Berry phase. Several investigations have discussed, in an inexplicit way, connections between both concepts, hinting at that nonzero topological charges for far-field polarizations on a loop are inextricably linked to its nontrivial Berry phase when degeneracies are enclosed. In this work, we reexamine the seminal photonic crystal slab that supports the fundamental two-level non-Hermitian degeneracies. Regardless of the invariance of nontrivial Berry phase (concerning near-field Bloch modes defined on the momentum torus) for different loops enclosing both degeneracies, we demonstrate that the associated far polarization fields (defined on the momentum sphere) exhibit topologically inequivalent patterns that are characterized by variant topological charges, including even the trivial scenario of zero charge. Moreover, the charge carried by the Fermi arc actually is not well defined, which could be different on opposite bands. It is further revealed that for both bands, the seemingly complex evolutions of polarizations are bounded by the global charge conservation, with extra points of circular polarizations playing indispensable roles. This indicates that although not directly associated with any local charges, the invariant Berry phase is directly linked to the globally conserved charge, physical principles underlying which have all been further clarified by a two-level Hamiltonian with an extra chirality term. Our work can potentially trigger extra explorations beyond photonics connecting Berry phase and singularities.

Switchable Terahertz Metasurfaces for Spin-Selective Absorption and Anomalous Reflection Based on Vanadium Dioxide.

Conventional chiral metasurfaces are constrained by predetermined functionalities and have limited versatility. To address these constraints, we propose a novel chirality-switchable terahertz (THz) metasurface with integrated heating control circuits tailored for spin-selective anomalous reflection, leveraging the phase-change material vanadium dioxide (VO2). The reversible and abrupt insulator-to-metal phase transition feature of VO2 is exploited to facilitate a chiral meta-atom with spin-selectivity capabilities. By employing the Pancharatnam-Berry phase principle, complete 2π reflection phase coverage is achieved by adjusting the orientation of the chiral structure. At the resonant frequency of 0.137 THz, the designed metasurface achieves selective absorption of a circularly polarized wave corresponding to the state of the VO2 patches. Concurrently, it reflects the circularly polarized wave of the opposite chirality anomalously at an angle of 28.4° while maintaining its handedness. This chirality-switchable THz metasurface exhibits promising potential across various applications, including wireless communication data capacity enlargement, polarization modulation, and chirality detection.

Topological transition in measurement-induced geometric phases.

The state of a quantum system, adiabatically driven in a cycle, may acquire a measurable phase depending only on the closed trajectory in parameter space. Such geometric phases are ubiquitous and also underline the physics of robust topological phenomena such as the quantum Hall effect. Equivalently, a geometric phase may be induced through a cyclic sequence of quantum measurements. We show that the application of a sequence of weak measurements renders the closed trajectories, hence the geometric phase, stochastic. We study the concomitant probability distribution and show that, when varying the measurement strength, the mapping between the measurement sequence and the geometric phase undergoes a topological transition. Our finding may impact measurement-induced control and manipulation of quantum states-a promising approach to quantum information processing. It also has repercussions on understanding the foundations of quantum measurement.

Polarization-Insensitive Transmissive Metasurfaces Using Pancharatnam-Berry and Resonant Phases in Microwave Band.

Most of the existing metasurfaces are effective for the incident wave with the specific circularly polarized (CP) or linearly polarized (LP) state, that is the polarization-sensitive metasurface. This drawback dramatically hinders the practical use of the metasurface. Herein, this paper presents a strategy of polarization-insensitive transmissive microwave metasurfaces to manipulate the incident wave with arbitrary CP and LP states. The metasurface consists of polarization-insensitive unit cells. For the left circularly polarized (LCP) and right circularly polarized (RCP) incident waves, the same abrupt phase covering 0° to 360° can be realized by combining the Pancharatnam-Berry (PB) and resonant phases. As the arbitrary LP wave can decompose into the LCP and RCP waves, metasurfaces consisting of designed unit cells are valid for any polarization states. The polarization-insensitive transmissive microwave metalens and orbital angular momentum multiplexing metasurface working at 23 GHz are devised for verification. Simulation and measurement results verify the availability of the approach. The proposed method is suitable for designing microwave-transmissive metasurfaces capable of polarization insensitivity.

Ubiquitous Topological States of Phonons in Solids: Silicon as a Model Material.

Research on topological physics of phonons has attracted enormous interest but demands appropriate model materials. Our ab initio calculations identify silicon as an ideal candidate material containing extraordinarily rich topological phonon states. In silicon, we identify various topological nodal lines characterized by quantized Berry phase π, which gives drumhead surface states observable from any surface orientations. Remarkably, a novel type of topological nexus phonon is discovered which is featured by double Fermi-arc-like surface states but requires neither inversion nor time-reversal symmetry breaking. Versatile topological states can be created from the nexus phonons, such as Hopf nodal links by strain. Furthermore, we generalize the symmetry analysis to other centrosymmetric systems and find numerous candidate materials, demonstrating the ubiquitous existence of topological phonons in solids. These findings open up new opportunities for studying topological phonons in realistic materials and their influence on surface physics.

Terahertz Metagrating Emitters with Beam Steering and Full Linear Polarization Control.

We report the realization of broadband THz plasmonic metagrating emitters for simultaneous beam steering and all-optical linear polarization control. Two types of metagratings are designed and experimentally demonstrated. First, the plasmonic meta-atoms are arranged in a metagrating with a binary phase modulation which results in the nonlinear generation of THz waves to the ±1 diffraction orders, with complete suppression of the zeroth order. Complete tunability of the diffracted THz linear polarization direction is demonstrated through simple rotation of the pump polarization. Then, the concept of lateral phase shift is introduced into the design of the metagratings using interlaced phase gradients. By controlling the spatial shift of the submetagrating, we are able to continuously control the linear polarization states of the generated THz waves. This method results in a higher nonlinear diffraction efficiency relative to binary phase modulation. These functional THz metagratings show exciting promise to meet the challenges associated with the current diverse array of applications utilizing THz technology.

Optical edge detection based on high-efficiency dielectric metasurface.

Optical edge detection is a useful method for characterizing boundaries, which is also in the forefront of image processing for object detection. As the field of metamaterials and metasurface is growing fast in an effort to miniaturize optical devices at unprecedented scales, experimental realization of optical edge detection with metamaterials remains a challenge and lags behind theoretical proposals. Here, we propose a mechanism of edge detection based on a Pancharatnam-Berry-phase metasurface. We experimentally demonstrated broadband edge detection using designed dielectric metasurfaces with high optical efficiency. The metasurfaces were fabricated by scanning a focused laser beam inside glass substrate and can be easily integrated with traditional optical components. The proposed edge-detection mechanism may find important applications in image processing, high-contrast microscopy, and real-time object detection on compact optical platforms such as mobile phones and smart cameras.

Integrated Terahertz Generator-Manipulators Using Epsilon-near-Zero-Hybrid Nonlinear Metasurfaces.

In terahertz (THz) technologies, generation and manipulation of THz waves are two key processes usually implemented by different device modules. Integrating THz generation and manipulation into a single compact device will advance the applications of THz technologies in various fields. Here, we demonstrate a hybrid nonlinear plasmonic metasurface incorporating an epsilon-near-zero (ENZ) indium tin oxide (ITO) layer to seamlessly combine efficient generation and manipulation of THz waves across a wide frequency band. The coupling between the plasmonic resonance of the metasurface and the ENZ mode of the ITO thin film enhances the THz conversion efficiency by more than 4 orders of magnitude. Meanwhile, such a hybrid device is capable of shaping the polarization and wavefront of the emitted THz beam via the engineered nonlinear Pancharatnam-Berry (PB) phases of the plasmonic meta-atoms. The presented hybrid nonlinear metasurface opens a new avenue toward miniaturized integrated THz devices and systems with advanced functionalities.

On the Quantization of AB Phase in Nonlinear Systems.

Self-intersecting energy band structures in momentum space can be induced by nonlinearity at the mean-field level, with the so-called nonlinear Dirac cones as one intriguing consequence. Using the Qi-Wu-Zhang model plus power law nonlinearity, we systematically study in this paper the Aharonov-Bohm (AB) phase associated with an adiabatic process in the momentum space, with two adiabatic paths circling around one nonlinear Dirac cone. Interestingly, for and only for Kerr nonlinearity, the AB phase experiences a jump of π at the critical nonlinearity at which the Dirac cone appears and disappears (thus yielding π-quantization of the AB phase so long as the nonlinear Dirac cone exists), whereas for all other powers of nonlinearity, the AB phase always changes continuously with the nonlinear strength. Our results may be useful for experimental measurement of power-law nonlinearity and shall motivate further fundamental interest in aspects of geometric phase and adiabatic following in nonlinear systems.

Vanishing quantum oscillations in Dirac semimetal ZrTe5.

One of the characteristics of topological materials is their nontrivial Berry phase. Experimental determination of this phase largely relies on a phase analysis of quantum oscillations. We study the angular dependence of the oscillations in a Dirac material [Formula: see text] and observe a striking spin-zero effect (i.e., vanishing oscillations accompanied with a phase inversion). This indicates that the Berry phase in [Formula: see text] remains nontrivial for arbitrary field direction, in contrast with previous reports. The Zeeman splitting is found to be proportional to the magnetic field based on the condition for the spin-zero effect in a Dirac band. Moreover, it is suggested that the Dirac band in [Formula: see text] is likely transformed into a line node other than Weyl points for the field directions at which the spin zero occurs. The results underline a largely overlooked spin factor when determining the Berry phase from quantum oscillations.

Nonlinear Topological Effects in Optical Coupled Hexagonal Lattice.

Topological physics in optical lattices have attracted much attention in recent years. The nonlinear effects on such optical systems remain well-explored and a large amount of progress has been achieved. In this paper, under the mean-field approximation for a nonlinearly optical coupled boson-hexagonal lattice system, we calculate the nonlinear Dirac cone and discuss its dependence on the parameters of the system. Due to the special structure of the cone, the Berry phase (two-dimensional Zak phase) acquired around these Dirac cones is quantized, and the critical value can be modulated by interactions between different lattices sites. We numerically calculate the overall Aharonov-Bohm (AB) phase and find that it is also quantized, which provides a possible topological number by which we can characterize the quantum phases. Furthermore, we find that topological phase transition occurs when the band gap closes at the nonlinear Dirac points. This is different from linear systems, in which the transition happens when the band gap closes and reopens at the Dirac points.

Zero-field magnetic response functions in Landau levels.

We present a fresh perspective on the Landau level quantization rule; that is, by successively including zero-field magnetic response functions at zero temperature, such as zero-field magnetization and susceptibility, the Onsager's rule can be corrected order by order. Such a perspective is further reinterpreted as a quantization of the semiclassical electron density in solids. Our theory not only reproduces Onsager's rule at zeroth order and the Berry phase and magnetic moment correction at first order but also explains the nature of higher-order corrections in a universal way. In applications, those higher-order corrections are expected to curve the linear relation between the level index and the inverse of the magnetic field, as already observed in experiments. Our theory then provides a way to extract the correct value of Berry phase as well as the magnetic susceptibility at zero temperature from Landau level fan diagrams in experiments. Moreover, it can be used theoretically to calculate Landau levels up to second-order accuracy for realistic models.

Nontrivial Berry phase in magnetic BaMnSb2 semimetal.

The subject of topological materials has attracted immense attention in condensed-matter physics because they host new quantum states of matter containing Dirac, Majorana, or Weyl fermions. Although Majorana fermions can only exist on the surface of topological superconductors, Dirac and Weyl fermions can be realized in both 2D and 3D materials. The latter are semimetals with Dirac/Weyl cones either not tilted (type I) or tilted (type II). Although both Dirac and Weyl fermions have massless nature with the nontrivial Berry phase, the formation of Weyl fermions in 3D semimetals require either time-reversal or inversion symmetry breaking to lift degeneracy at Dirac points. Here we demonstrate experimentally that canted antiferromagnetic BaMnSb2 is a 3D Weyl semimetal with a 2D electronic structure. The Shubnikov-de Hass oscillations of the magnetoresistance give nearly zero effective mass with high mobility and the nontrivial Berry phase. The ordered magnetic arrangement (ferromagnetic ordering in the ab plane and antiferromagnetic ordering along the c axis below 286 K) breaks the time-reversal symmetry, thus offering us an ideal platform to study magnetic Weyl fermions in a centrosymmetric material.

High-Resolution Quantitative Phase Imaging of Plasmonic Metasurfaces with Sensitivity down to a Single Nanoantenna.

Optical metasurfaces have emerged as a new generation of building blocks for multifunctional optics. Design and realization of metasurface elements place ever-increasing demands on accurate assessment of phase alterations introduced by complex nanoantenna arrays, a process referred to as quantitative phase imaging. Despite considerable effort, the widefield (nonscanning) phase imaging that would approach resolution limits of optical microscopy and indicate the response of a single nanoantenna still remains a challenge. Here, we report on a new strategy in incoherent holographic imaging of metasurfaces, in which unprecedented spatial resolution and light sensitivity are achieved by taking full advantage of the polarization selective control of light through the geometric (Pancharatnam-Berry) phase. The measurement is carried out in an inherently stable common-path setup composed of a standard optical microscope and an add-on imaging module. Phase information is acquired from the mutual coherence function attainable in records created in broadband spatially incoherent light by the self-interference of scattered and leakage light coming from the metasurface. In calibration measurements, the phase was mapped with the precision and spatial background noise better than 0.01 and 0.05 rad, respectively. The imaging excels at the high spatial resolution that was demonstrated experimentally by the precise amplitude and phase restoration of vortex metalenses and a metasurface grating with 833 lines/mm. Thanks to superior light sensitivity of the method, we demonstrated for the first time to our knowledge the widefield measurement of the phase altered by a single nanoantenna while maintaining the precision well below 0.15 rad.

Emergent electromagnetism in condensed matter.

Electrons in solids constitute quantum many-body systems showing a variety of phenomena. It often happens that the eigen states of the Hamiltonian are classified into subgroups separated by energy gaps. Band structures in solids and spin polarization in Mott insulators are two representative examples. The subspace spanned by these wavefunctions belonging to each of this subgroup can be regarded as a manifold in Hilbert space, and concepts concerning differential geometry become relevant. Connection and curvature are two key quantities, which correspond to the vector potential and field strength of electromagnetism, respectively. Therefore, one can construct an effective electromagnetic field from the structure of the Hilbert space, which is called an "emergent electromagnetic field". In this article, we review the physics related to this emergent electromagnetic field in solids, including the gauge theory of strongly correlated electrons, various Hall effects, multiferroics, topological matter, magnetic texture such as skyrmions, and the shift current in noncentrosymmetric materials.

Recipe for Dirac Phonon States with a Quantized Valley Berry Phase in Two-Dimensional Hexagonal Lattices.

The topological quantum states in two-dimensional (2D) materials are fascinating subjects of research, which usually highlight electron-related systems. In this work, we present a recipe that leads to Dirac phonon states with a quantized valley Berry phase in 2D hexagonal lattices by first-principles calculations. We show that candidates possessing the 3-fold rotational symmetry at the corners of the hexagonal Brillouin zone host valley Dirac phonons, which are guaranteed to remain intact with respect to perturbations. We identify that such special topological features populated by Dirac phonons can be realized in various 2D materials. In particular, the monolayer CrI3, an attractive 2D magnetic semiconductor with exotic applications in spintronics, is an ideal platform to investigate nontrivial phonons in experiments. We further confirm that the phonon Berry phase is quantized to ± π at two inequivalent valleys. The phonon edge states terminated at the projection of phonon Dirac cones are clearly visible. This work demonstrates that 2D hexagonal lattices with attractive valley Dirac phonons will extend the knowledge of valley physics, providing wide applications of topological phonons.

Ultrathin Nonlinear Metasurface for Optical Image Encoding.

Security of optical information is of great importance in modern society. Many cryptography techniques based on classical and quantum optics have been widely explored in the linear optical regime. Nonlinear optical encryption in which encoding and decoding involve nonlinear frequency conversions represents a new strategy for securing optical information. Here, we demonstrate that an ultrathin nonlinear photonic metasurface, consisting of meta-atoms with 3-fold rotational symmetry, can be used to hide optical images under illumination with a fundamental wave. However, the hidden image can be read out from second harmonic generation (SHG) waves. This is achieved by controlling the destructive and constructive interferences of SHG waves from two neighboring meta-atoms. In addition, we apply this concept to obtain gray scale SHG imaging. Nonlinear metasurfaces based on space variant optical interference open new avenues for multilevel image encryption, anticounterfeiting, and background free image reconstruction.

Versatile Polarization Generation with an Aluminum Plasmonic Metasurface.

All forms of light manipulation rely on light-matter interaction, the primary mechanism of which is the modulation of its electromagnetic fields by the localized electromagnetic fields of atoms. One of the important factors that influence the strength of interaction is the polarization of the electromagnetic field. The generation and manipulation of light polarization have been traditionally accomplished with bulky optical components such as waveplates, polarizers, and polarization beam splitters that are optically thick. The miniaturization of these devices is highly desirable for the development of a new class of compact, flat, and broadband optical components that can be integrated together on a single photonics chip. Here we demonstrate, for the first time, a reflective metasurface polarization generator (MPG) capable of producing light beams of any polarizations all from a linearly polarized light source with a single optically thin chip. Six polarization light beams are achieved simultaneously including four linear polarizations along different directions and two circular polarizations, all conveniently separated into different reflection angles. With the Pancharatnam-Berry phase-modulation method, the MPG sample was fabricated with aluminum as the plasmonic metal instead of the conventional gold or silver, which allowed for its broadband operation covering the entire visible spectrum. The versatility and compactness of the MPG capable of transforming any incident wave into light beams of arbitrary polarizations over a broad spectral range are an important step forward in achieving a complete set of flat optics for integrated photonics with far-reaching applications.

GaN Metalens for Pixel-Level Full-Color Routing at Visible Light.

Metasurface-based components are known to be one of the promising candidates for developing flat optical systems. However, their low working efficiency highly limits the use of such flat components for feasible applications. Although the introduction of the metallic mirror has been demonstrated to successfully enhance the efficiency, it is still somehow limited for imaging and sensing applications because they are only available for devices operating in a reflection fashion. Here, we demonstrate three individual GaN-based metalenses working in a transmission window with extremely high operation efficiency at visible light (87%, 91.6%, and 50.6% for blue, green, and red light, respectively). For the proof of concept, a multiplex color router with dielectric metalens, which is capable of guiding individual primary colors into different spatial positions, is experimentally verified based on the design of out-of-plane focusing metalens. Our approach with low-cost, semiconductor fabrication compatibility and high working efficiency characteristics offers a way for establishing a complete set of flat optical components for a wide range of applications such as compact imaging sensors, optical spectroscopy, and high-resolution lithography, just named a few.