Topology and geometry under the nonlinear electromagnetic spotlight

Nonlinear optical signatures of topological Dirac fermion

Dirac fermion in topological materials exhibits intriguing nonlinear optical responses. However, their direct correlation with the linearly dispersed band remains elusive experimentally. Here, we take topological semimetal ZrSiS as a paradigm, unveiling three unique nonlinear optical signatures of Dirac fermion. These signatures include strong quadrupolar response, quantum interference effect, and exponential divergent four-wave mixing (FWM), all of which are described by the prominent third-order nonlinear optical susceptibility. Resonantly enhanced by linear bands, quadrupolar second harmonic generation in centrosymmetric bulk overwhelms the electric-dipole contribution at the surface with inherent inversion symmetry breaking. Furthermore, owing to the interference between multiple resonant transition pathways within linear bands, difference-frequency FWM is several orders of magnitude stronger than sum-frequency FWM and third harmonic generation. The difference-frequency FWM further displays an inverse-square divergence toward degenerate excitation, whose scaling law perfectly matches with the long-sought behavior of Dirac fermion. These signatures lay the solid foundation toward the practical applications of topological materials in nonlinear optoelectronics and photonics.

Magnetic parity violation and parity-time-reversal-symmetric magnets

Parity-time-reversal symmetry (PTsymmetry), a symmetry for the combined operations of space inversion (P) and time reversal (T), is a fundamental concept of physics and characterizes the functionality of materials as well asPandTsymmetries. In particular, thePT-symmetric systems can be found in the centrosymmetric crystals undergoing the parity-violating magnetic order which we call the odd-parity magnetic multipole order. While this spontaneous order leavesPTsymmetry intact, the simultaneous violation ofPandTsymmetries gives rise to various emergent responses that are qualitatively different from those allowed by the nonmagneticP-symmetry breaking or by the ferromagnetic order. In this review, we introduce candidates hosting the intriguing spontaneous order and overview the characteristic physical responses. Various off-diagonal and/or nonreciprocal responses are identified, which are closely related to the unusual electronic structures such as hidden spin-momentum locking and asymmetric band dispersion.

Engineering Anomalously Large Electron Transport in Topological Semimetals

Anomalous transport of topological semimetals has generated significant interest for applications in optoelectronics, nanoscale devices, and interconnects. Understanding the origin of novel transport is crucial to engineering the desired material properties, yet their orders of magnitude higher transport than single-particle mobilities remain unexplained. This work demonstrates the dramatic mobility enhancements result from phonons primarily returning momentum to electrons due to phonon-electron dominating over phonon-phonon scattering. Proving this idea, proposed by Peierls in 1932, requires tuning electron and phonon dispersions without changing symmetry, topology, or disorder. This is achieved by combining de Haas - van Alphen (dHvA), electron transport, Raman scattering, and first-principles calculations in the topological semimetals MX2 (M = Nb, Ta and X = Ge, Si). Replacing Ge with Si brings the transport mobilities from an order magnitude larger than single particle ones to nearly balanced. This occurs without changing the crystal structure or topology and with small differences in disorder or Fermi surface. Simultaneously, Raman scattering and first-principles calculations establish phonon-electron dominated scattering only in the MGe2 compounds. Thus, this study proves that phonon-drag is crucial to the transport properties of topological semimetals and provides insight to engineer these materials further.

Ultrafast Carrier Relaxation Dynamics in a Nodal-Line Semimetal PtSn4

Topological Dirac nodal-line semimetals host topologically nontrivial electronic structure with nodal-line crossings around the Fermi level, which could affect the photocarrier dynamics and lead to novel relaxation mechanisms. Herein, by using time- and angle-resolved photoemission spectroscopy, we reveal the previously inaccessible linear dispersions of the bulk conduction bands above the Fermi level in a Dirac nodal-line semimetal PtSn4, as well as the momentum and temporal evolution of the gapless nodal lines. A surprisingly ultrafast relaxation dynamics within a few hundred femtoseconds is revealed for photoexcited carriers in the nodal line. Theoretical calculations suggest that such ultrafast carrier relaxation is attributed to the multichannel scatterings among the complex metallic bands of PtSn4 via electron-phonon coupling. In addition, a unique dynamic relaxation mechanism contributed by the highly anisotropic Dirac nodal-line electronic structure is also identified. Our work provides a comprehensive understanding of the ultrafast carrier dynamics in a Dirac nodal-line semimetal.

The regulation and its application of the charge decay rate in triboelectric nanogenerator

The decay rate of charge in the friction layer is one of the key factors affecting the output performance of triboelectric nanogenerators (TENG). Reducing the decay rate of the triboelectric charge can increase the charge-carrying capacity of the friction layer and improve the output current and voltage of the TENG. This makes a friction generator more suitable for discontinuous driving environments. In contrast, increasing the decay rate of the charge in the friction layer can greatly improve the recovery time of the device, although it reduces the output performance of the generator. This is conducive to the application of friction generator in the field of sensors. In this study, polystyrene (PS) and carbon nanotubes (CNTs) were added to polyvinylidene fluoride (PVDF) nanofibers to adjust the charge decay time in the friction layer, thereby regulating the output performance of the friction generator and sensor. When the amount of added PS in the PVDF nanofiber reached 20%, the charge density on the friction surface increased by 1.9 times, and the charge decay time decreased by 64 times; when 0.1 wt% CNTs were added in the PVDF nanofiber, the charge decay time increased by more than 10 times. The former is more conducive to improving the power generation performance of the TENG, and the latter significantly improves the stability and repeatability of TENG-based sensors.

Nonlinear optical diode effect in a magnetic Weyl semimetal

Diode effects are of great interest for both fundamental physics and modern technologies. Electrical diode effects (nonreciprocal transport) have been observed in Weyl systems. Optical diode effects arising from the Weyl fermions have been theoretically considered but not probed experimentally. Here, we report the observation of a nonlinear optical diode effect (NODE) in the magnetic Weyl semimetal CeAlSi, where the magnetization introduces a pronounced directionality in the nonlinear optical second-harmonic generation (SHG). We demonstrate a six-fold change of the measured SHG intensity between opposite propagation directions over a bandwidth exceeding 250 meV. Supported by density-functional theory, we establish the linearly dispersive bands emerging from Weyl nodes as the origin of this broadband effect. We further demonstrate current-induced magnetization switching and thus electrical control of the NODE. Our results advance ongoing research to identify novel nonlinear optical/transport phenomena in magnetic topological materials and further opens new pathways for the unidirectional manipulation of light.

Defect-induced helicity dependent terahertz emission in Dirac semimetal PtTe2 thin films

Nonlinear transport enabled by symmetry breaking in quantum materials has aroused considerable interest in condensed matter physics and interdisciplinary electronics. However, achieving a nonlinear optical response in centrosymmetric Dirac semimetals via defect engineering has remained a challenge. Here, we observe the helicity dependent terahertz emission in Dirac semimetal PtTe2 thin films via the circular photogalvanic effect under normal incidence. This is activated by a controllable out-of-plane Te-vacancy defect gradient, which we unambiguously evidence with electron ptychography. The defect gradient lowers the symmetry, which not only induces the band spin splitting but also generates the giant Berry curvature dipole responsible for the circular photogalvanic effect. We demonstrate that the THz emission can be manipulated by the Te-vacancy defect concentration. Furthermore, the temperature evolution of the THz emission features a minimum in the THz amplitude due to carrier compensation. Our work provides a universal strategy for symmetry breaking in centrosymmetric Dirac materials for efficient nonlinear transport.

Large nonlinear optical magnetoelectric response in a noncentrosymmetric magnetic Weyl semimetal

Weyl semimetals resulting from either inversion (P) or time-reversal (T) symmetry breaking have been revealed to show the record-breaking large optical response due to intense Berry curvature of Weyl-node pairs. Different classes of Weyl semimetals with both P and T symmetry breaking potentially exhibit optical magnetoelectric (ME) responses, which are essentially distinct from the previously observed optical responses in conventional Weyl semimetals, leading to the versatile functions such as directional dependence for light propagation and gyrotropic effects. However, such optical ME phenomena of (semi)metallic systems have remained elusive so far. Here, we show the large nonlinear optical ME response in noncentrosymmetric magnetic Weyl semimetal PrAlGe, in which the polar structural asymmetry and ferromagnetic ordering break P and T symmetry. We observe the giant second harmonic generation (SHG) arising from the P symmetry breaking in the paramagnetic phase, being comparable to the largest SHG response reported in Weyl semimetal TaAs. In the ferromagnetically ordered phase, it is found that interference between this nonmagnetic SHG and the magnetically induced SHG emerging due to both P and T symmetry breaking results in the magnetic field switching of SHG intensity. Furthermore, such an interference effect critically depends on the light-propagating direction. The corresponding magnetically induced nonlinear susceptibility is significantly larger than the prototypical ME material, manifesting the existence of the strong nonlinear dynamical ME coupling. The present findings establish the unique optical functionality of P- and T-symmetry broken ME topological semimetals.

Orbital Magneto-Nonlinear Anomalous Hall Effect in Kagome Magnet Fe_{3}Sn_{2}

It has been theoretically predicted that perturbation of the Berry curvature by electromagnetic fields gives rise to intrinsic nonlinear anomalous Hall effects that are independent of scattering. Two types of nonlinear anomalous Hall effects are expected. The electric nonlinear Hall effect has recently begun to receive attention, while very few studies are concerned with the magneto-nonlinear Hall effect. Here, we combine experiment and first-principles calculations to show that the kagome ferromagnet Fe_{3}Sn_{2} displays such a magneto-nonlinear Hall effect. By systematic field angular and temperature-dependent transport measurements, we unambiguously identify a large anomalous Hall current that is linear in both applied in-plane electric and magnetic fields, utilizing a unique in-plane configuration. We clarify its dominant orbital origin and connect it to the magneto-nonlinear Hall effect. The effect is governed by the intrinsic quantum geometric properties of Bloch electrons. Our results demonstrate the significance of the quantum geometry of electron wave functions from the orbital degree of freedom and open up a new direction in Hall transport effects.

Quantifying the photocurrent fluctuation in quantum materials by shot noise

The DC photocurrent can detect the topology and geometry of quantum materials without inversion symmetry. Herein, we propose that the DC shot noise (DSN), as the fluctuation of photocurrent operator, can also be a diagnostic of quantum materials. Particularly, we develop the quantum theory for DSNs in gapped systems and identify the shift and injection DSNs by dividing the second-order photocurrent operator into off-diagonal and diagonal contributions, respectively. Remarkably, we find that the DSNs can not be forbidden by inversion symmetry, while the constraint from time-reversal symmetry depends on the polarization of light. Furthermore, we show that the DSNs also encode the geometrical information of Bloch electrons, such as the Berry curvature and the quantum metric. Finally, guided by symmetry, we apply our theory to evaluate the DSNs in monolayer GeS and bilayer MoS2 with and without inversion symmetry and find that the DSNs can be larger in centrosymmetric phase.

Giant intrinsic photovoltaic effect in one-dimensional van der Waals grain boundaries

The photovoltaic effect lies at the heart of eco-friendly energy harvesting. However, the conversion efficiency of traditional photovoltaic effect utilizing the built-in electric effect in p-n junctions is restricted by the Shockley-Queisser limit. Alternatively, intrinsic/bulk photovoltaic effect (IPVE/BPVE), a second-order nonlinear optoelectronic effect arising from the broken inversion symmetry of crystalline structure, can overcome this theoretical limit. Here, we uncover giant and robust IPVE in one-dimensional (1D) van der Waals (vdW) grain boundaries (GBs) in a layered semiconductor, ReS2. The IPVE-induced photocurrent densities in vdW GBs are among the highest reported values compared with all kinds of material platforms. Furthermore, the IPVE-induced photocurrent is gate-tunable with a polarization-independent component along the GBs, which is preferred for energy harvesting. The observed IPVE in vdW GBs demonstrates a promising mechanism for emerging optoelectronics applications.

Design of High-Performance Organic Nonlinear Optical and Terahertz Crystals by Controlling the van der Waals Volume

In the development of new organic crystals for nonlinear optical and terahertz (THz) applications, it is very challenging to achieve the essentially required non-centrosymmetric molecular arrangement. Moreover, the resulting crystal structure is mostly unpredictable due to highly dipolar molecular components with complex functional substituents. In this work, new organic salt crystals with top-level macroscopic optical nonlinearity by controlling the van der Waals volume (VvdW ), rather than by trial and error, are logically designed. When the VvdW of molecular ionic components varies, the corresponding crystal symmetry shows an observable trend: change from centrosymmetric to non-centrosymmetric and back to centrosymmetric. All non-centrosymmetric crystals exhibit an isomorphic P1 crystal structure with an excellent macroscopic second-order nonlinear optical response. Apart from the top-level macroscopic optical nonlinearity, new organic crystals introducing highly electronegative fluorinated substituents with strong secondary bonding ability show excellent performance in efficient and broadband THz wave generation, high crystal density, high thermal stability, and good bulk crystal growth ability.

Superconducting nonlinear transport in optically driven high-temperature K3C60

Optically driven quantum materials exhibit a variety of non-equilibrium functional phenomena, which to date have been primarily studied with ultrafast optical, X-Ray and photo-emission spectroscopy. However, little has been done to characterize their transient electrical responses, which are directly associated with the functionality of these materials. Especially interesting are linear and nonlinear current-voltage characteristics at frequencies below 1 THz, which are not easily measured at picosecond temporal resolution. Here, we report on ultrafast transport measurements in photo-excited K3C60. Thin films of this compound were connected to photo-conductive switches with co-planar waveguides. We observe characteristic nonlinear current-voltage responses, which in these films point to photo-induced granular superconductivity. Although these dynamics are not necessarily identical to those reported for the powder samples studied so far, they provide valuable new information on the nature of the light-induced superconducting-like state above equilibrium Tc. Furthermore, integration of non-equilibrium superconductivity into optoelectronic platforms may lead to integration in high-speed devices based on this effect.

Quantum Optics Measurement Scheme for Quantum Geometry and Topological Invariants

We show how a quantum optical measurement scheme based on heterodyne detection can be used to explore geometrical and topological properties of condensed matter systems. Considering a 2D material placed in a cavity with a coupling to the environment, we compute correlation functions of the photons exiting the cavity and relate them to the hybrid light-matter state within the cavity. Different polarizations of the intracavity field give access to all components of the quantum geometric tensor on contours in the Brillouin zone defined by the transition energy. Combining recent results based on the metric-curvature correspondence with the measured quantum metric allows us to characterize the topological phase of the material. Moreover, in systems where S_{z} is a good quantum number, the procedure also allows us to extract the spin Chern number. As an interesting application, we consider a minimal model for twisted bilayer graphene at the magic angle, and discuss the feasibility of extracting the Euler number.

Topological Circular Dichroism in Chiral Multifold Semimetals

Uncovering the physical contents of the nontrivial topology of quantum states is a critical problem in condensed matter physics. Here, we study the topological circular dichroism in chiral semimetals using linear response theory and first-principles calculations. We show that, when the low-energy spectrum respects emergent SO(3) rotational symmetry, topological circular dichroism is forbidden for Weyl fermions, and thus is unique to chiral multifold fermions. This is a result of the selection rule that is imposed by the emergent symmetry under the combination of particle-hole conjugation and spatial inversion. Using first-principles calculations, we predict that topological circular dichroism occurs in CoSi for photon energy below about 0.2 eV. Our Letter demonstrates the existence of a response property of unconventional fermions that is fundamentally different from the response of Dirac and Weyl fermions, motivating further study to uncover other unique responses.

Berry curvature dipole generation and helicity-to-spin conversion at symmetry-mismatched heterointerfaces

The Berry curvature dipole (BCD) is a key parameter that describes the geometric nature of energy bands in solids. It defines the dipole-like distribution of Berry curvature in the band structure and plays a key role in emergent nonlinear phenomena. The theoretical rationale is that the BCD can be generated at certain symmetry-mismatched van der Waals heterointerfaces even though each material has no BCD in its band structure. However, experimental confirmation of such a BCD induced via breaking of the interfacial symmetry remains elusive. Here we demonstrate a universal strategy for BCD generation and observe BCD-induced gate-tunable spin-polarized photocurrent at WSe2/SiP interfaces. Although the rotational symmetry of each material prohibits the generation of spin photocurrent under normal incidence of light, we surprisingly observe a direction-selective spin photocurrent at the WSe2/SiP heterointerface with a twist angle of 0°, whose amplitude is electrically tunable with the BCD magnitude. Our results highlight a BCD-spin-valley correlation and provide a universal approach for engineering the geometric features of twisted heterointerfaces.

Standing and traveling waves in a model of periodically modulated one-dimensional waveguide arrays

In the present work we study coherent structures in a one-dimensional discrete nonlinear Schrödinger lattice in which the coupling between waveguides is periodically modulated. Numerical experiments with single-site initial conditions show that, depending on the power, the system exhibits two fundamentally different behaviors. At low power, initial conditions with intensity concentrated in a single site give rise to transport, with the energy moving unidirectionally along the lattice, whereas high-power initial conditions yield stationary solutions. We explain these two behaviors, as well as the nature of the transition between the two regimes, by analyzing a simpler model where the couplings between waveguides are given by step functions. For the original model, we numerically construct both stationary and moving coherent structures, which are solutions reproducing themselves exactly after an integer multiple of the coupling period. For the stationary solutions, which are true periodic orbits, we use Floquet analysis to determine the parameter regime for which they are spectrally stable. Typically, the traveling solutions are characterized by having small-amplitude oscillatory tails, although we identify a set of parameters for which these tails disappear. These parameters turn out to be independent of the lattice size, and our simulations suggest that for these parameters, numerically exact traveling solutions are stable.

Strong bulk photovoltaic effect in engineered edge-embedded van der Waals structures

Bulk photovoltaic effect (BPVE), a second-order nonlinear optical effect governed by the quantum geometric properties of materials, offers a promising approach to overcome the Shockley-Quiesser limit of traditional photovoltaic effect and further improve the efficiency of energy harvesting. Here, we propose an effective platform, the nano edges embedded in assembled van der Waals (vdW) homo- or hetero-structures with strong symmetry breaking, low dimensionality and abundant species, for BPVE investigations. The BPVE-induced photocurrents strongly depend on the orientation of edge-embedded structures and polarization of incident light. Reversed photocurrent polarity can be observed at left and right edge-embedded structures. Our work not only visualizes the unique optoelectronic effect in vdW nano edges, but also provides an effective strategy for achieving BPVE in engineered vdW structures.

The Microscopic Mechanisms of Nonlinear Rectification on Si-MOSFETs Terahertz Detector

Studying the nonlinear photoresponse of different materials, including III-V semiconductors, two-dimensional materials and many others, is attracting burgeoning interest in the terahertz (THz) field. Especially, developing field-effect transistor (FET)-based THz detectors with preferred nonlinear plasma-wave mechanisms in terms of high sensitivity, compactness and low cost is a high priority for advancing performance imaging or communication systems in daily life. However, as THz detectors continue to shrink in size, the impact of the hot-electron effect on device performance is impossible to ignore, and the physical process of THz conversion remains elusive. To reveal the underlying microscopic mechanisms, we have implemented drift-diffusion/hydrodynamic models via a self-consistent finite-element solution to understand the dynamics of carriers at the channel and the device structure dependence. By considering the hot-electron effect and doping dependence in our model, the competitive behavior between the nonlinear rectification and hot electron-induced photothermoelectric effect is clearly presented, and it is found that the optimized source doping concentrations can be utilized to reduce the hot-electron effect on the devices. Our results not only provide guidance for further device optimization but can also be extended to other novel electronic systems for studying THz nonlinear rectification.

Topological Metamaterials

The topological properties of an object, associated with an integer called the topological invariant, are global features that cannot change continuously but only through abrupt variations, hence granting them intrinsic robustness. Engineered metamaterials (MMs) can be tailored to support highly nontrivial topological properties of their band structure, relative to their electronic, electromagnetic, acoustic and mechanical response, representing one of the major breakthroughs in physics over the past decade. Here, we review the foundations and the latest advances of topological photonic and phononic MMs, whose nontrivial wave interactions have become of great interest to a broad range of science disciplines, such as classical and quantum chemistry. We first introduce the basic concepts, including the notion of topological charge and geometric phase. We then discuss the topology of natural electronic materials, before reviewing their photonic/phononic topological MM analogues, including 2D topological MMs with and without time-reversal symmetry, Floquet topological insulators, 3D, higher-order, non-Hermitian and nonlinear topological MMs. We also discuss the topological aspects of scattering anomalies, chemical reactions and polaritons. This work aims at connecting the recent advances of topological concepts throughout a broad range of scientific areas and it highlights opportunities offered by topological MMs for the chemistry community and beyond.

Time-Reversal-Even Nonlinear Current Induced Spin Polarization

We propose a time-reversal-even spin generation in second order of electric fields, which dominates the current induced spin polarization in a wide class of centrosymmetric nonmagnetic materials, and leads to a novel nonlinear spin-orbit torque in magnets. We reveal a quantum origin of this effect from the momentum space dipole of the anomalous spin polarizability. First-principles calculations predict sizable spin generations in several nonmagnetic hcp metals, in monolayer TiTe_{2}, and in ferromagnetic monolayer MnSe_{2}, which can be detected in experiment. Our work opens up the broad vista of nonlinear spintronics in both nonmagnetic and magnetic systems.

Geometric deep optical sensing

Geometry, an ancient yet vibrant branch of mathematics, has important and far-reaching impacts on various disciplines such as art, science, and engineering. Here, we introduce an emerging concept dubbed "geometric deep optical sensing" that is based on a number of recent demonstrations in advanced optical sensing and imaging, in which a reconfigurable sensor (or an array thereof) can directly decipher the rich information of an unknown incident light beam, including its intensity, spectrum, polarization, spatial features, and possibly angular momentum. We present the physical, mathematical, and engineering foundations of this concept, with particular emphases on the roles of classical and quantum geometry and deep neural networks. Furthermore, we discuss the new opportunities that this emerging scheme can enable and the challenges associated with future developments.

Impinge Weyl advantages on light

Weyl semimetals are emerging topological materials with intriguing physical properties. Now this exotic matter may lead to novel photonic and optoelectronic applications.

Terahertz Nonlinear Hall Rectifiers Based on Spin-Polarized Topological Electronic States in 1T-CoTe2

The zero-magnetic-field nonlinear Hall effect (NLHE) refers to the second-order transverse current induced by an applied alternating electric field; it indicates the topological properties of inversion-symmetry-breaking crystals. Despite several studies on the NLHE induced by the Berry-curvature dipole in Weyl semimetals, the direct current conversion by rectification is limited to very low driving frequencies and cryogenic temperatures. The nonlinear photoresponse generated by the NLHE at room temperature can be useful for numerous applications in communication, sensing, and photodetection across a high bandwidth. In this study, observations of the second-order NLHE in type-II Dirac semimetal CoTe₂ under time-reversal symmetry are reported. This is determined by the disorder-induced extrinsic contribution on the broken-inversion-symmetry surface and room-temperature terahertz rectification without the need for semiconductor junctions or bias voltage. It is shown that remarkable photoresponsivity over 0.1 A W^-1 , a response time of approximately 710 ns, and a mean noise equivalent power of 1 pW Hz^-1/2 can be achieved at room temperature. The results open a new pathway for low-energy photon harvesting via nonlinear rectification induced by the NLHE in strongly spin-orbit-coupled and inversion-symmetry-breaking systems, promising a considerable impact in the field of infrared/terahertz photonics.

Giant photon momentum locked THz emission in a centrosymmetric Dirac semimetal

Strong second-order optical nonlinearities often require broken material centrosymmetry, thereby limiting the type and quality of materials used for nonlinear optical devices. Here, we report a giant and highly tunable terahertz (THz) emission from thin polycrystalline films of the centrosymmetric Dirac semimetal PtSe₂. Our PtSe₂ THz emission is turned on at oblique incidence and locked to the photon momentum of the incident pump beam. Notably, we find an emitted THz efficiency that is giant: It is two orders of magnitude larger than the standard THz-generating nonlinear crystal ZnTe and has values approaching that of the noncentrosymmetric topological material TaAs. Further, PtSe₂ THz emission displays THz sign and amplitude that is controlled by the incident pump polarization and helicity state even as optical absorption is only weakly polarization dependent and helicity independent. Our work demonstrates how photon drag can activate pronounced optical nonlinearities that are available even in centrosymmetric Dirac materials.

Topology and Symmetry in Quantum Materials

Interest in topological materials continues to grow unabated in view of their conceptual novelties as well as their potential as platforms for transformational new technologies. Electronic states in a topological material are robust against perturbations and support unconventional electromagnetic responses. The first-principles band-theory paradigm has been a key player in the field by providing successful prediction of many new classes of topological materials. This perspective presents a cross section through the recent work on understanding the role of geometry and topology in generating topological states and their responses to external stimuli, and as a basis for connecting theory and experiment within the band theory framework. In this work, effective strategies for topological materials discovery and impactful directions for future topological materials research are also commented.

Unveiling Weyl-related optical responses in semiconducting tellurium by mid-infrared circular photogalvanic effect

Elemental tellurium, conventionally recognized as a narrow bandgap semiconductor, has recently aroused research interests for exploiting Weyl physics. Chirality is a unique feature of Weyl cones and can support helicity-dependent photocurrent generation, known as circular photogalvanic effect. Here, we report circular photogalvanic effect with opposite signs at two different mid-infrared wavelengths which provides evidence of Weyl-related optical responses. These two different wavelengths correspond to two critical transitions relating to the bands of different Weyl cones and the sign of circular photogalvanic effect is determined by the chirality selection rules within certain Weyl cone and between two different Weyl cones. Further experimental evidences confirm the observed response is an intrinsic second-order process. With flexibly tunable bandgap and Fermi level, tellurium is established as an ideal semiconducting material to manipulate and explore chirality-related Weyl physics in both conduction and valence bands. These results are also directly applicable to helicity-sensitive optoelectronics devices.

Terahertz wave emission from the trigonal layered PtBi2

In this work, broadband terahertz (THz) wave emissions have been detected from the trigonal layered PtBi₂ on the excitation of the femtosecond laser pulses. Such THz generation is found to arise from the dominated linear photogalvanic effect, which is further discovered to strongly depend on the unique electronic structures of PtBi₂. Furthermore, an effective nonlinear susceptibility of PtBi₂ is also obtained and is nearly two orders of magnitude larger than that of the traditional nonlinear crystal for THz generation.

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Terahertz (THz) wave emission, topological semimetal, ultrafast photocurrent

Quantum Matter Overview

Quantum matter (novel phases of matter at zero temperature with exotic properties) is a growing field with applications in its own domain, and in providing foundational support to quantum sciences fields more generally. The ability to characterize and manipulate matter at the smallest scales continues to advance in fundamental ways. This review provides a plain-language, non-technical description of contemporary activity in quantum matter for a general science audience, and an example of these methods applied to quantum neuroscience. Quantum matter is the study of topologically governed phases of matter at absolute zero temperature that exhibit new kinds of emergent order and exotic properties related to topology and symmetry, entanglement, and electronic charge and magnetism, which may be orchestrated to create new classes of materials and computational devices (including in the areas of spintronics, valleytronics, and quantum computing). The paper is organized to discuss recent developments in quantum matter on the topics of short-range topologically protected materials (namely, topological semimetals), long-range entangled materials (quantum spin liquids and fractional quantum Hall states), and codes for characterizing and controlling quantum systems. A key finding is that a shift in the conceptualization of the field of quantum matter may be underway to expand the core focus on short-range topologically protected materials to also include geometry-based approaches and long-range entanglement as additionally important tools for the understanding, characterization, and manipulation of topological materials.

Intelligent infrared sensing enabled by tunable moiré quantum geometry

Quantum geometric properties of Bloch wave functions in solids, that is, Berry curvature and the quantum metric, are known to significantly influence the ground- and excited-state behaviour of electrons^1-5. The bulk photovoltaic effect (BPVE), a nonlinear phenomenon depending on the polarization of excitation light, is largely governed by the quantum geometric properties in optical transitions^6-10. Infrared BPVE has yet to be observed in graphene or moiré systems, although exciting strongly correlated phenomena related to quantum geometry have been reported in this emergent platform^11-14. Here we report the observation of tunable mid-infrared BPVE at 5 µm and 7.7 µm in twisted double bilayer graphene (TDBG), arising from the moiré-induced strong symmetry breaking and quantum geometric contribution. The photoresponse depends substantially on the polarization state of the excitation light and is highly tunable by external electric fields. This wide tunability in quantum geometric properties enables us to use a convolutional neural network^15,16 to achieve full-Stokes polarimetry together with wavelength detection simultaneously, using only one single TDBG device with a subwavelength footprint of merely 3 × 3 µm². Our work not only reveals the unique role of moiré engineered quantum geometry in tunable nonlinear light-matter interactions but also identifies a pathway for future intelligent sensing technologies in an extremely compact, on-chip manner.

Photovoltaic effect by soft phonon excitation

SignificanceThe quantum-mechanical geometric phase of electrons provides various phenomena such as the dissipationless photocurrent generation through the shift current mechanism. So far, the photocurrent generations are limited to above or near the band-gap photon energy, which contradicts the increasing demand of the low-energy photonic functionality. We demonstrate the photocurrent through the optical phonon excitations in ferroelectric BaTiO3 by using the terahertz light with photon energy far below the band gap. This photocurrent without electron-hole pair generation is never explained by the semiclassical treatment of electrons and only arises from the quantum-mechanical geometric phase. The observed photon-to-current conversion efficiency is as large as that for electronic excitation, which can be well accounted for by newly developed theoretical formulation of shift current.

Floquet solitons in square lattices: Existence, stability, and dynamics

In the present work, we revisit a recently proposed and experimentally realized topological two-dimensional lattice with periodically time-dependent interactions. We identify the fundamental solitons, previously observed in experiments and direct numerical simulations, as exact, exponentially localized, periodic in time solutions. This is done for a variety of phase-shift angles of the central nodes upon an oscillation period of the coupling strength. Subsequently, we perform a systematic Floquet stability analysis of the relevant structures. We analyze both their point and their continuous spectrum and find that the solutions are generically stable, aside from the possible emergence of complex quartets due to the collision of bands of continuous spectrum. The relevant instabilities become weaker as the lattice size gets larger. Finally, we also consider multisoliton analogs of these Floquet states, inspired by the corresponding discrete nonlinear Schrödinger (DNLS) lattice. When exciting initially multiple sites in phase, we find that the solutions reflect the instability of their DNLS multi-soliton counterparts, while for configurations with multiple excited sites in alternating phases, the Floquet states are spectrally stable, again analogously to their DNLS counterparts.

Nonlinear nanoelectrodynamics of a Weyl metal

Chiral Weyl fermions with linear energy-momentum dispersion in the bulk accompanied by Fermi-arc states on the surfaces prompt a host of enticing optical effects. While new Weyl semimetal materials keep emerging, the available optical probes are limited. In particular, isolating bulk and surface electrodynamics in Weyl conductors remains a challenge. We devised an approach to the problem based on near-field photocurrent imaging at the nanoscale and applied this technique to a prototypical Weyl semimetal TaIrTe₄ As a first step, we visualized nano-photocurrent patterns in real space and demonstrated their connection to bulk nonlinear conductivity tensors through extensive modeling augmented with density functional theory calculations. Notably, our nanoscale probe gives access to not only the in-plane but also the out-of-plane electric fields so that it is feasible to interrogate all allowed nonlinear tensors including those that remained dormant in conventional far-field optics. Surface- and bulk-related nonlinear contributions are distinguished through their "symmetry fingerprints" in the photocurrent maps. Robust photocurrents also appear at mirror-symmetry breaking edges of TaIrTe₄ single crystals that we assign to nonlinear conductivity tensors forbidden in the bulk. Nano-photocurrent spectroscopy at the boundary reveals a strong resonance structure absent in the interior of the sample, providing evidence for elusive surface states.

Direct Measurement of Helicoid Surface States in RhSi Using Nonlinear Optics

Despite the fundamental nature of the edge state in topological physics, direct measurement of electronic and optical properties of the Fermi arcs of topological semimetals has posed a significant experimental challenge, as their response is often overwhelmed by the metallic bulk. However, laser-driven currents carried by surface and bulk states can propagate in different directions in nonsymmorphic crystals, allowing for the two components to be easily separated. Motivated by a recent theoretical prediction G. Chang et al., Phys. Rev. Lett. 124, 166404 (2020)PRLTAO0031-900710.1103/PhysRevLett.124.166404, we have measured the linear and circular photogalvanic effect currents deriving from the Fermi arcs of the nonsymmorphic, chiral Weyl semimetal RhSi over the 0.45-1.1 eV incident photon energy range. Our data are in good agreement with the predicted spectral shape of the circular photogalvanic effect as a function of photon energy, although the direction of the surface photocurrent departed from the theoretical expectation over the energy range studied. Surface currents arising from the linear photogalvanic effect were observed as well, with the unexpected result that only two of the six allowed tensor element were required to describe the measurements, suggesting an approximate emergent mirror symmetry inconsistent with the space group of the crystal.