Topological magnetoplasmon

Probing Topological Thermal Flux in Equilibrium Using Electron Beams

Near nonreciprocal media at finite temperature, fluctuating near fields exhibit imbalanced thermal populations in opposite directions, generating equilibrium topological thermal fluxes that circulate the media. While the existence of these fluxes remains unconfirmed, we propose exploiting their interaction with free electron beams for detection. We establish a general framework to quantify thermal flux at any location near an object of arbitrary shape. This reveals unexplored properties of thermal flux spectra depending on their orientation. Further, we connect the electron scattering rate to the equilibrium thermal flux. As a specific example, electrons encountering a planar surface's perpendicular thermal flux preferentially scatter transversely. This measurable scattering distribution, i.e., via angle-resolved electron microscopy, allows us to recover the thermal flux spectrum. Additionally, electron interactions with equilibrium thermal fluxes surrounding local structures offer a novel approach to generating electron vortex beams.

Wideband isolator based on one-way surface magnetoplasmons with ultra-high isolation

In this paper, we present a new type of isolator based on one-way surface magnetoplasmons (SMPs) at microwave frequencies, and it is the first time that an experimental prototype of isolator with wideband and ultra-high isolation is realized using SMP waveguide. The proposed model with gyromagnetic and dielectric layers is systematically analyzed to obtain the dispersion properties of all the possible modes, and a one-way SMP mode is found to have the unidirectional transmission property. In simulation and experiment with metallic waveguide loaded with yttrium-iron-garnet (YIG) ferrite, the scattering parameters and the field distributions agree well with the analysis and verify the one-way transmission property. The isolation is found to be as high as 80 dB and the typical value of insertion loss is 1 dB. Besides, the one-way transmission band can be controlled by changing the magnetic bias. From theoretical analysis and simulation, it is found that with a tiny value of 10 Oe of the magnetic bias, the relative bandwidth can be tuned to be greater than 50%. Compared with conventional isolators, this one-way SMP isolator has the advantages of ultra-high isolation, wide relative frequency band, and requires much smaller bias field, which has promising potential in non-reciprocal applications.

Topological electromagnetic waves in dispersive and lossy plasma crystals

Topological photonic crystals, which offer topologically protected and back-scattering-immune transport channels, have recently gained significant attention for both scientific and practical reasons. Although most current studies focus on dielectric materials with weak dispersions, this study focuses on topological phases in dispersive materials and presents a numerical study of Chern insulators in gaseous-phase plasma cylinder cells. We develop a numerical framework to address the complex material dispersion arising from the plasma medium and external magnetic fields and identify Chern insulator phases that are experimentally achievable. Using this numerical tool, we also explain the flat bands commonly observed in periodic plasmonic structures, via local resonances, and how edge states change as the edge termination is periodically modified. This work opens up opportunities for exploring band topology in new materials with non-trivial dispersions and has potential radio frequency (RF) applications, ranging from plasma-based lighting to plasma propulsion engines.

Broadband unidirectional surface plasmon polaritons with low loss

Unidirectional surface plasmon polaritons (SPPs) have been proven to truly exist at an interface between a magnetized semiconductor and an opaque isotropic material, however, they suffer rather serious leakage loss (with propagation length shorter than two wavelengths) caused by nonlocality. In this work, we investigate an alternative category of unidirectional SPPs existing on a nonreciprocal plasmonic platform with a cladding composed of a dielectric heterostructure transversely terminated by metal. This unidirectional SPP mode exists for small wavenumbers within the entire upper bulk-mode bandgap of the magnetized semiconductor, hence it is robust against nonlocal effects over a broad band. In contrast to previous unidirectional SPPs, the leakage loss of the present unidirectional SPPs is significantly reduced by more than five times, since the portion of modal energy distributed in the cladding is substantially increased. A similar reduction in absorption losses associated with semiconductor dissipation is observed. Though the nonlocality induces a backward-propagating SPP with extremely large wavenumbers, it can be suppressed even at very small level of dissipation. Therefore, our proposed plasmonic waveguide actually exhibits exceptional unidirectional characteristics.

Zero-Frequency Chiral Magnonic Edge States Protected by Nonequilibrium Topology

Topological bosonic excitations must, in contrast to their fermionic counterparts, appear at finite energies. This is a key challenge for magnons, as it prevents straightforward excitation and detection of topologically protected magnonic edge states and their use in magnonic devices. In this Letter, we show that in a nonequilibrium state, in which the magnetization is pointing against the external magnetic field, the topologically protected chiral edge states in a magnon Chern insulator can be lowered to zero frequency, making them directly accessible by existing experimental techniques. We discuss the spin-orbit torque required to stabilize this nonequilibrium state, and show explicitly using numerical Landau-Lifshitz-Gilbert simulations that the edge states can be excited with a microwave field. Finally, we consider a propagating spin wave spectroscopy experiment, and demonstrate that the edge states can be directly detected.

Photonic helicoid-like surface states in chiral metamaterials

We investigate the photonic topological phases in chiral metamaterials characterized by the magnetoelectric tensors with diagonal chirality components. The underlying medium is considered a photonic analogue of the topological semimetal featured with a Weyl cone and a cylindrical surface in the frequency-wave vector space. As the 'spin'-degenerate condition is satisfied, the photonic system can be rearranged as two hybrid modes that are completely decoupled. By introducing the pseudospin states as the basis for the hybrid modes, the photonic system is described by two subsystems in the form of spin-orbit Hamiltonians of spin 1, which result in nonzero spin Chern numbers that determine the topological properties. Surface modes at the interface between vacuum and the chiral metamaterial exist in their common gap in the wave vector space, which are analytically formulated by algebraic equations. In particular, the surface modes form a pair of spiral surface sheets wrapping around the Weyl cone, resembling the helicoid surface states that occur in topological semimetals. At the Weyl frequency, the surface modes contain two Fermi arc-like states that concatenate to yield a straight line segment.

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.

Quantum-Squeezing-Induced Point-Gap Topology and Skin Effect

We theoretically predict the squeezing-induced point-gap topology together with a symmetry-protected Z_{2} "skin effect" in a one-dimensional (1D) quadratic-bosonic system. Protected by a time-reversal symmetry, such a topology is associated with a novel Z_{2} invariant (similar to quantum spin-Hall insulators), which is fully capable of characterizing the occurrence of the Z_{2} skin effect. Focusing on zero energy, the parameter regime of this skin effect in the phase diagram just corresponds to a "real- and point-gap coexisting topological phase." Moreover, this phase associated with the symmetry-protected Z_{2} skin effect is experimentally observable by detecting the steady-state power spectral density. Our Letter is of fundamental interest in enriching non-Bloch topological physics by introducing quantum squeezing and has potential applications for the engineering of symmetry-protected sensors based on the Z_{2} skin effect.

Two-Dimensional Plasmons in Laterally Confined 2D Electron Systems

The collective oscillations of charge density (plasmons) in conductive solids are basic excitations that determine the dynamic response of the system. In infinite two-dimensional (2D) electron systems, plasmons have gapless dispersion covering a broad spectral range from subterahertz to infrared, which is promising in light-matter applications. We discuss the state-of-the-art physics of 2D plasmons, especially in confined 2D electron systems in stripe and disk geometry, using the simplest approach for conductivity. When the metal gate is placed in the vicinity of the 2D electron system, an analytical description of the plasmon frequency and damping can be easily obtained. We also analyze gated plasmons in the disk when it was situated at various distances from the gate, and discuss in detail the nontrivial behavior of the damping. We predict that it is not a simple sum of the radiative and collisional dampings, but has a nonmonotonic dependence on the system parameters. For high-mobility 2D systems, this opens the way to achieve the maximal quality factor of plasma resonances. Lastly, we discuss the recently discovered near-gate 2D plasmons propagating along the laterally confined gate, even without applied bias voltage and having gapless dispersion when the gate has the form of a stripe, and discrete spectrum when the gate is in the form of disk. It allows for one to drive the frequency and spatial propagation of such plasmons.

Synthesis and Characterization of Magnetoplasmonic Air-Stable Au@FeCo

The synthesis of FeCo alloys as highly magnetic nanoparticles has been valuable, as far as applications for magnetic nanoparticles are concerned. However, recently, a field of magnetoplasmonics in which magnetic nanoparticles such as the FeCo alloys doped with plasmonic materials such as Au and Ag to create a hybrid nanostructure with both properties has emerged. These magnetoplasmonic metamaterials have greatly enhanced the limit of detection of analytes in spectroscopic methods, as well as providing a more widely applicable nanoparticle to broaden the use of FeCo alloys even further. Herein, we discuss the synthesis of high-yield and fairly monodisperse spherical FeCo and Au-doped FeCo (Au@FeCo) with varying compositions of Au synthesized via the thermal decomposition of iron pentacarbonyl (Fe(CO)₅) and dicobalt octacarbonyl (Co₂(CO)₈), followed by the addition of Au atoms using triphenylphosphine gold(I) chloride ((Ph₃P)AuCl) via both coprecipitation and by delayed addition methods. The products were separated using a hand-held magnet, and then characterized via ultraviolet-visible light (UV-vis), scanning electron microscopy coupled with energy-dispersive X-ray analysis (SEM-EDX), high-resolution transmission electron microscopy (HRTEM), X-ray diffraction (XRD), flame atomic absorption spectrometry (F-AAS), and magnetization measurements. Optical studies revealed a plasmonic peak at 550 nm in the Au@FeCo nanoparticles that had a gold content (%Au) of >2% (by weight), determined using F-AAS. Colocation of the Fe, Co, and Au were demonstrated through EDX analysis. Location of the Au atoms in the core were seen through high-resolution bright-field imaging. To understand the use of these nanoparticles for potential application in therapeutics and/or electronics, resistance measurements were performed to assess power loss as a function of frequency. We also achieved magnetization values as high as 150 emu/g and as low as 50 emu/g for gold-loaded samples based on %Au by weight. This paves the way to continue to develop magneto-plasmonic structures chemically using these synthesis strategies.

Photonic topological phases in Tellegen metamaterials

We investigate the photonic topological phases in Tellegen metamaterials characterized by the antisymmetric magnetoelectric tensors with real-valued quantities. The underlying medium is considered a photonic analogue of the topological semimetal featured with a displaced Weyl cone in the frequency-wave vector space. As the 'spin'-degenerate condition is satisfied, the photonic system consists of two hybrid modes that are completely decoupled. By introducing the pseudospin states as the basis for the hybrid modes, the photonic system is described by two subsystems in terms of the spin-orbit Hamiltonians with spin 1, which result in nonzero spin Chern numbers that determine the topological properties. Surface modes at the interface between two Tellegen metamaterials with opposite sign of the magnetoelectric parameter exist at their common gap in the wave vector space, which are analytically formulated by algebraic equations. In particular, two types of surface modes are tangent to or wrapping around the Weyl cones, which form a pair of bended and a pair of twisted surface sheets. At the Weyl frequency, the surface modes contain a typical and two open Fermi arc-like states that concatenate to yield an infinite straight line. Topological features of the Tellegen metamaterials are further illustrated with the robust transport of surface modes at an irregular boundary.

Plasmonic gain in current biased tilted Dirac nodes

Surface plasmons, which allow tight confinement of light, suffer from high intrinsic electronic losses. It has been shown that stimulated emission from excited electrons can transfer energy to plasmons and compensate for the high intrinsic losses. To-date, these realizations have relied on introducing an external gain media coupled to the surface plasmon. Here, we propose that plasmons in two-dimensional materials with closely located electron and hole Fermi pockets can be amplified, when an electrical current bias is applied along the displaced electron-hole pockets, without the need for an external gain media. As a prototypical example, we consider WTe₂ from the family of 1T[Formula: see text]-MX₂ materials, whose electronic structure can be described within a type-II tilted massive Dirac model. We find that the nonlocal plasmonic response experiences prominent gain for experimentally accessible currents on the order of mAμm^-1. Furthermore, the group velocity of the plasmon found from the isofrequency curves imply that the amplified plasmons are highly collimated along a direction perpendicular to the Dirac node tilt when the electrical current is applied along it.

Photonic Weyl semimetals in pseudochiral metamaterials

We investigate the photonic topological phases in pseudochiral metamaterials characterized by the magnetoelectric tensors with symmetric off-diagonal chirality components. The underlying medium is considered a photonic analogue of the type-II Weyl semimetal featured with two pairs of tilted Weyl cones in the frequency-wave vector space. As the ’spin’-degenerate condition is satisfied, the photonic system consists of two hybrid modes that are completely decoupled. By introducing the pseudospin states as the basis for the hybrid modes, the photonic system is described by two subsystems in terms of the spin-orbit Hamiltonians with spin 1, which result in nonzero spin Chern numbers that determine the topological properties. Surface modes at the interface between vacuum and the pseudochiral metamaterial exist in their common gap in the wave vector space, which are analytically formulated by algebraic equations. In particular, the surface modes are tangent to both the vacuum light cone and the Weyl cones, which form two pairs of crossing surface sheets that are symmetric about the transverse axes. At the Weyl frequency, the surface modes that connect the Weyl points form four Fermi arc-like states as line segments. Topological features of the pseudochiral metamaterials are further illustrated with the robust transport of surface modes at an irregular boundary.

Large-area unidirectional surface magnetoplasmons using uniaxial μ-near-zero material

We have theoretically investigated surface magnetoplasmons (SMPs) in a waveguide consisting of a uniaxial μ-near-zero (UMNZ) material slab sandwiched between two ferrite materials with opposite remanences. It is shown that this waveguide can support robust unidirectional SMP (USMP), whose electric field extends almost uniformly in the UMNZ layer, hence USMP can acquire modal sizes far larger than the wavelength. We have demonstrated that such large-area USMP (LUSMP) provides many degrees of freedom to manipulate waves. Using LUSMP, waves can be completely trapped with hot spots of wavelength size.

Quantum Internal Structure of Plasmons

Plasmons are usually described in terms of macroscopic quantities such as electric fields and currents. However, as fundamental excitations of metals, they are also quantum objects with internal structure. We demonstrate that this can induce an intrinsic dipole moment which is tied to the quantum geometry of the Hilbert space of plasmon states. This quantum geometric dipole offers a unique handle for manipulation of plasmon dynamics via density modulations and electric fields. As a concrete example, we demonstrate that scattering of plasmons with a nonvanishing quantum geometric dipole from impurities is nonreciprocal, skewing in different directions in a valley-dependent fashion. This internal structure can be used to control plasmon trajectories in two dimensional materials.

Chiral and multiple one-way surface states on photonic gyroelectric metamaterials with small Chern number

Topological one-way surface states allow light to pass through sharp corners without reflection. In order to enhance the capability of surface routing devices, multiple one-way surface modes are usually required. Different from previously reported multiple surface modes achieved with large Chern number photonic media, we realize multiple surface waves on a continuous medium with small Chern number, i.e., |C| = 1. The new topological phase is found when the hyperbolic and double semi-ellipsoid-like cone bands are simultaneously gapped by vacuum state. We also find the degeneracy of multiple one-way surface waves in the double semi-ellipsoid-like metamaterials. The propagation direction of the waves is determined by their own ellipticities. Our results may help to construct surface state devices with multiplexing capability and higher coupling efficiency.

Topological phases and bulk-edge correspondence of magnetized cold plasmas

Plasmas have been recently studied as topological materials. However, a comprehensive picture of topological phases and topological phase transitions in cold magnetized plasmas is still missing. Here we systematically map out all the topological phases and establish the bulk-edge correspondence in cold magnetized plasmas. We find that for the linear eigenmodes, there are 10 topological phases in the parameter space of density n, magnetic field B, and parallel wavenumber k_z, separated by the surfaces of Langmuir wave-L wave resonance, Langmuir wave-cyclotron wave resonance, and zero magnetic field. For fixed B and k_z, only the phase transition at the Langmuir wave-cyclotron wave resonance corresponds to edge modes. A sufficient and necessary condition for the existence of this type of edge modes is given and verified by numerical solutions. We demonstrate that edge modes exist not only on a plasma-vacuum interface but also on more general plasma-plasma interfaces. This finding broadens the possible applications of these exotic excitations in space and laboratory plasmas.

Magnetized plasma can be regarded as topological matter. Here the authors identify a necessary and sufficient condition for the existence of topological edge mode and find that cold magnetized plasma has ten topological phases in the plasma frequency, cyclotron frequency and wave-vector space.

Terahertz magnetoplasmon resonances in coupled cavities formed in a gated two-dimensional electron gas

We report on both experiments and theory of low-terahertz frequency range (up to 400 GHz) magnetoplasmons in a gated two-dimensional electron gas at low (<4K) temperatures. The evolution of magnetoplasmon resonances was observed as a function of magnetic field at frequencies up to ∼400 GHz. Full-wave 3D simulations of the system predicted the spatial distribution of plasmon modes in the 2D channel, along with their frequency response, allowing us to distinguish those resonances caused by bulk and edge magnetoplasmons in the experiments. Our methodology is anticipated to be applicable to the low temperature (<4K) on-chip terahertz measurements of a wide range of other low-dimensional mesoscopic systems.

Nonreciprocal and Topological Plasmonics

Metals, semiconductors, metamaterials, and various two-dimensional materials with plasmonic dispersion exhibit numerous exotic physical effects in the presence of an external bias, for example an external static magnetic field or electric current. These physical phenomena range from Faraday rotation of light propagating in the bulk to strong confinement and directionality of guided modes on the surface and are a consequence of the breaking of Lorentz reciprocity in these systems. The recent introduction of relevant concepts of topological physics, translated from condensed-matter systems to photonics, has not only given a new perspective on some of these topics by relating certain bulk properties of plasmonic media to the surface phenomena, but has also led to the discovery of new regimes of truly unidirectional, backscattering-immune, surface-wave propagation. In this article, we briefly review the concepts of nonreciprocity and topology and describe their manifestation in plasmonic materials. Furthermore, we use these concepts to classify and discuss the different classes of guided surface modes existing on the interfaces of various plasmonic systems.

Chiral surface plasmon-enhanced chiral spectroscopy: principles and applications

In this review, the development context and scientific research results of chiral surface plasmons (SPs) in recent years are classified and described in detail. First, the principle of chiral SPs is introduced through classical and quantum theory. Following this, the classification and properties of different chiral structures, as well as the superchiral near-field, are introduced in detail. Second, we describe the excitation and propagation properties of chiral SPs, which lays a good foundation for the application of chiral SPs and their chiral spectra in various fields. After that, we have summarized the recent research results of chiral SPs and their applications in the areas of biology, two-dimensional materials, topological materials, analytical chemistry, chiral sensing, chiral optical force, and chiral light detection. Chiral SPs are a new type of optical phenomenon that have useful application potential in many fields and are worth exploring.

Plasmonic Dirac Cone in Twisted Bilayer Graphene

We discuss plasmons of biased twisted bilayer graphene when the Fermi level lies inside the gap. The collective excitations are a network of chiral edge plasmons (CEP) entirely composed of excitations in the topological electronic edge states that appear at the AB-BA interfaces. The CEP form a hexagonal network with a unique energy scale ε_{p}=(e^{2})/(ε_{0}εt_{0}) with t_{0} the moiré lattice constant and ε the dielectric constant. From the dielectric matrix we obtain the plasmon spectra that has two main characteristics: (i) a diverging density of states at zero energy, and (ii) the presence of a plasmonic Dirac cone at ℏω∼ε_{p}/2 with sound velocity v_{D}=0.0075c, which is formed by zigzag and armchair current oscillations. A network model reveals that the antisymmetry of the plasmon bands implies that CEP scatter at the hexagon vertices maximally in the deflected chiral outgoing directions, with a current ratio of 4/9 into each of the deflected directions and 1/9 into the forward one. We show that scanning near-field microscopy should be able to observe the predicted plasmonic Dirac cone and its broken symmetry phases.

Plasmonic Nonreciprocity Driven by Band Hybridization in Moiré Materials

We propose a new current-driven mechanism for achieving significant plasmon dispersion nonreciprocity in systems with narrow, strongly hybridized electron bands. The magnitude of the effect is controlled by the strength of electron-electron interactions α, which leads to its particular prominence in moiré materials, characterized by α≫1. Moreover, this phenomenon is most evident in the regime where Landau damping is quenched and plasmon lifetime is increased. The synergy of these two effects holds great promise for novel optoelectronic applications of moiré materials.

Recent advances in 2D, 3D and higher-order topological photonics

Over the past decade, topology has emerged as a major branch in broad areas of physics, from atomic lattices to condensed matter. In particular, topology has received significant attention in photonics because light waves can serve as a platform to investigate nontrivial bulk and edge physics with the aid of carefully engineered photonic crystals and metamaterials. Simultaneously, photonics provides enriched physics that arises from spin-1 vectorial electromagnetic fields. Here, we review recent progress in the growing field of topological photonics in three parts. The first part is dedicated to the basics of topological band theory and introduces various two-dimensional topological phases. The second part reviews three-dimensional topological phases and numerous approaches to achieve them in photonics. Last, we present recently emerging fields in topological photonics that have not yet been reviewed. This part includes topological degeneracies in nonzero dimensions, unidirectional Maxwellian spin waves, higher-order photonic topological phases, and stacking of photonic crystals to attain layer pseudospin. In addition to the various approaches for realizing photonic topological phases, we also discuss the interaction between light and topological matter and the efforts towards practical applications of topological photonics.

Physical Violations of the Bulk-Edge Correspondence in Topological Electromagnetics

In this Letter, we discuss two general classes of apparent violations of the bulk-edge correspondence principle for continuous topological photonic materials, associated with the asymptotic behavior of the surface modes for diverging wave numbers. Considering a nonreciprocal plasma as a model system, we show that the inclusion of spatial dispersion (e.g., hydrodynamic nonlocality) formally restores the bulk-edge correspondence by avoiding an unphysical response at large wave numbers. Most importantly, however, our findings show that, for the considered cases, the correspondence principle is physically violated for all practical purposes, as a result of the unavoidable attenuation of highly confined modes even if all materials are assumed perfect, with zero intrinsic bulk losses, due to confinement-induced Landau damping or nonlocality-induced radiation leakage. Our work helps clarifying the subtle and rich topological wave physics of continuous media.

Topological kink plasmons on magnetic-domain boundaries

Two-dimensional topological materials bearing time reversal-breaking magnetic fields support protected one-way edge modes. Normally, these edge modes adhere to physical edges where material properties change abruptly. However, even in homogeneous materials, topology still permits a unique form of edge modes – kink modes – residing at the domain boundaries of magnetic fields within the materials. This scenario, despite being predicted in theory, has rarely been demonstrated experimentally. Here, we report our observation of topologically-protected high-frequency kink modes – kink magnetoplasmons (KMPs) – in a GaAs/AlGaAs two-dimensional electron gas (2DEG) system. These KMPs arise at a domain boundary projected from an externally-patterned magnetic field onto a uniform 2DEG. They propagate unidirectionally along the boundary, protected by a difference of gap Chern numbers (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pm1$$\end{document}±1) in the two domains. They exhibit large tunability under an applied magnetic field or gate voltage, and clear signatures of nonreciprocity even under weak-coupling to evanescent photons.

Topological kink modes are peculiar edge excitations that take place at domain boundaries of magnetic fields inside homogeneous materials. Here, the authors experimentally observe kink magnetoplasmons in a 2D electron gas using custom-shaped strong permanent magnets on top of a GaAs/AlGaAs heterojunction.

Magnetoplasmon excitation and hybridization in gyroelectric cylinders

We investigate magnetoplasmon resonances and their coupling effects in gyroelectric cylinders. In individual cylinders, the dipole plasmon can be excited by plane wave illumination, and the dipole plasmon splits into lower energy and higher energy rotational magnetoplasmons in the presence of an external magnetic field. With respect to the external magnetic field, the two magnetoplasmons carry either right-handed chirality or left-handed chirality. In addition, originally dark plasmons can also be excited as the magnetic field increases. They are lower-order bulk plasmons (such as the radial breathing mode). In cylindrical dimers, the optically bright modes are combinations of magnetoplasmons with the same chirality. If the magnetic fields are antiparallel, the absorption spectra will be different for light incident from two opposite directions. This asymmetry can be well understood by carrying out eigenstate analysis, where the eigenstate does not possess mirror symmetry respecting the dimer axis. The dark modes engineering and asymmetrical optical behavior could have potential for terahertz device applications.

Multiple harmonics control of edge pseudomagnetoplasmons in strained grapheme

Valley-resolved edge plasmons are relevant to nano-optics at subwavelength scales. However, less attention has been paid to their tunable properties in time domain. In this work we investigate edge pseudomagnetoplasmons in a strained graphene modulated by multiple harmonics with frequency in the THz regime. The edge plasmon is described by a set of nonlinear hydrodynamic equations, which are self-consistently solved by the flux-corrected transport method. Without the applied voltage, there exist two unidirectional-propagating edge-plasmon modes with weak valley polarization P. It is demonstrated that by varying the amplitude of multiple harmonics one can alter both the amplitude and the polarity of the valley polarization in the edge plasmon. One can achieve a full valley polarization P=1 at the instant of half cycle of the multiple harmonics and P=-1 at the instant of one cycle. The edge-plasmon density and the transverse velocity vanish for the frozen valley.

Topologically protected Dirac plasmons in a graphene superlattice

Topological optical states exhibit unique immunity to defects, rendering them ideal for photonic applications. A powerful class of such states is based on time-reversal symmetry breaking of the optical response. However, existing proposals either involve sophisticated and bulky structural designs or can only operate in the microwave regime. Here we show a theoretical demonstration for highly confined topologically protected optical states to be realized at infrared frequencies in a simple two-dimensional (2D) material structure—a periodically patterned graphene monolayer—subject to a magnetic field of only 2 tesla. In our graphene honeycomb superlattice structures, plasmons exhibit substantial nonreciprocal behavior at the superlattice junctions under moderate static magnetic fields, leading to the emergence of topologically protected edge states and localized bulk modes. This approach is simple and robust for realizing topologically nontrivial optical states in 2D atomic layers, and could pave the way for building fast, nanoscale, defect-immune photonic devices.

Current proposals suitable for experimental realization of topologically protected optical states rely on complicated structures or only operate in the microwave regime. Here, Pan et al. propose topological Dirac plasmons to be realized at infrared frequencies in a periodically patterned graphene monolayer, subject to a magnetic field of only 2 Tesla.

Infrared Topological Plasmons in Graphene

We propose a two-dimensional plasmonic platform-periodically patterned monolayer graphene-which hosts topological one-way edge states operable up to infrared frequencies. We classify the band topology of this plasmonic system under time-reversal-symmetry breaking induced by a static magnetic field. At finite doping, the system supports topologically nontrivial band gaps with mid-gap frequencies up to tens of terahertz. By the bulk-edge correspondence, these band gaps host topologically protected one-way edge plasmons, which are immune to backscattering from structural defects and subject only to intrinsic material and radiation loss. Our findings reveal a promising approach to engineer topologically robust chiral plasmonic devices and demonstrate a realistic example of high-frequency topological edge states.

Topological Exciton Bands in Moiré Heterojunctions

Moiré patterns are common in van der Waals heterostructures and can be used to apply periodic potentials to elementary excitations. We show that the optical absorption spectrum of transition metal dichalcogenide bilayers is profoundly altered by long period moiré patterns that introduce twist-angle dependent satellite excitonic peaks. Topological exciton bands with nonzero Chern numbers that support chiral excitonic edge states can be engineered by combining three ingredients: (i) the valley Berry phase induced by electron-hole exchange interactions, (ii) the moiré potential, and (iii) the valley Zeeman field.