We explore topological transitions in the type of propagation of surface electromagnetic modes in massive anisotropic tilted Dirac systems. The presence of tilting and mass gives rise to an indirect band gap that strongly modifies the joint density of states compared to the gapless system. New van Hove singularities appear, and the interplay between intra and interband transitions leads to an anisotropic optical conductivity with imaginary parts acquiring opposite signs in orthogonal directions, opening the possibility of having hyperbolic propagation of plasmons. Isofrequency contours and low plasmon losses, as obtained from the dispersion relation, show that transitions between purely anisotropic quasi-elliptical and well-defined, highly directional, hyperbolic modes are attainable only when tilt and mass coexist. Fine-tuning in the THz regime suggests that this might be useful as a dynamical probe of concurring tilt and mass in Dirac materials.
Surface plasmons, which allow extreme confinement of light, suffer from high intrinsic electronic losses. It has been shown that stimulated emission of 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 experience gain, when an electrical current bias is applied along the displaced electron-hole pockets, without the need for an extern…
Anomalous acoustic plasmons in two-dimensional over-tilted Dirac bands
Sichuan Normal University（四川师范大学）；Beijing Forestry University（北京林业大学）；High Magnetic Field Laboratory, HFIPS, Chinese Academy of Sciences（中国科学院合肥物质科学研究院高磁场科学中心）；School of Physics, Beijing Institute of Technology（北京理工大学物理学院）
We predict the existence of a novel long-lived gapless plasmon mode in a type-II Dirac semimetal (DSM). This gapless mode arises from the out-of-phase oscillations of the density fluctuations in the electron and the hole pockets of a type-II DSM. It originates beyond a critical wave-vector along the direction of the tilt axis, owing to the momentum separation of the electron and hole pockets. A similar out-of-phase plasmon mode arises in other multi-component charged fluids as well, but generally it is Landau damped and lies within the particle-hole continuum. In the case of a type-II DSM, the…
In the presence of an external vertical electric field and strain, it is evident that 1T${^\prime}$-MoS$_2$ exhibits tilted Dirac bands which are valley-spin-polarized. Additionally, this material experiences a topological phase change between a topological insulator and band insulator for a critical value of the electric field. Using linear response theory, we calculated the polarization function which is in turn employed to obtain the dielectric function. This latter quantity is subsequently utilized in calculations to determine the plasmons dispersion relation, their decay rate and impurity…
Surface effects on the plasmons in two-dimemsional heterostructures: Application to tilted semi-Dirac materials
Hunter College, City University of New York（纽约市立大学亨特学院）；The Graduate School and University Center, The City University of New York（纽约市立大学研究生院与大学中心）；The University of Tampa（坦帕大学）；Medgar Evers College of City University of New York（纽约市立大学梅加尔·伊弗斯学院）；US Air Force Research Laboratory（美国空军研究实验室）
Motivated by the recent emergence of a new class of anisotropic 2D materials, we examine their electromagnetic modes and demonstrate that a broad class of the materials can host highly directional hyperbolic plasmons. Their propagation direction can be manipulated on-the-spot by gate doping, enabling hyperbolic beams reflection, refraction and bending. The realization of these natural 2D hyperbolic media opens up a new avenue in dynamic control of hyperbolic plasmons not possible in the 3D version.
We study theoretically and numerically spasing conditions and optical dynamics of a composite hyperbolic metamaterial interacting with gain molecules. By combining Maxwell-Bloch equations with Green's function approach, we calculate lasing frequency and threshold population inversion for various gain density in the gain layer. We demonstrate high level of enhancement for photonic density of states in spacious spectral range provided by hyperbolic metastructures. We find that direct dipole-dipole interactions between molecules in the gain layer has a negligible effect on spasing conditions. We …
In the fast growing two-dimensional (2D) materials family, anisotropic 2D materials, with their intrinsic in-plane anisotropy, exhibit a great potential in optoelectronics. One such typical material is black phosphorus (BP), with a layer-dependent and highly tunable band gap. Such intrinsic anisotropy adds a new degree of freedom to the excitation, detection and control of light. Particularly, hyperbolic plasmons with hyperbolic q-space dispersion are predicted to exist in BP films, where highly directional propagating polaritons with divergent densities of states are hosted. Combined with a t…
Hyperbolic exciton-plasmon polaritons in MoS$_2$/MoOCl$_2$ van der Waals heterostructures
Universidad Politécnica de Madrid（马德里理工大学）；Instituto de Sistemas Optoelectrónicos y Microtecnología, Universidad Politécnica de Madrid（马德里理工大学光电子与微技术研究所）；Departamento de Ingeniería Electrónica, E.T.S.I de Telecomunicación, Universidad Politécnica de Madrid（马德里理工大学电信工程学院电子工程系）
A hyperbolic plasmonic surface supports highly directional propagating polaritons with extremely large density of states. Such plasmon polaritons have been realized in artificially structured metasurfaces. However, the upper bound of the achievable plasmon wave vector is limited by the structure size, which calls for a natural hyperbolic surface without any structuring. Here, we experimentally demonstrate a natural hyperbolic plasmonic surface based on thin films of WTe2 in the light wavelength range of 16 to 23 microns by far infrared absorption spectroscopy. The topological transition from t…
In hyperbolic 2D materials, energy is channeled to their deep subwavelength polaritonic modes via four narrow beams. Here we consider the launching of surface polaritons in the hyperbolic 2D materials and demonstrate that efficient uni-directional excitation is possible with an elliptically polarized electric dipole, with the optimal choice of dipole ellipticity depending on the materials optical constants. The selection rules afforded by the choice of dipole polarization allow turning off up to two beams, and even three if the dipole is placed close to an edge. This makes the dipole a directi…
$8-Pmmn$ borophene is a polymorph of borophene which hosts an anisotropic tilted Dirac cone. Using a low energy effective Hamiltonian for borophene, we analytically calculate the density-density response function of borophene and study its anisotropic plasmon dispersion and screening properties. We find that the anisotropic plasmon mode in $8-Pmmn$ borophene, remains undamped for higher energies along the mirror symmetry direction. The friedel oscillation in borophene is found to decay as $r^{-3}$ in the large $r$ limit, with both the amplitude as well as the periodicity of the Friedel oscilla…
Hexagonal boron nitride (h-BN) is a natural hyperbolic material, for which the dielectric constants are the same in the basal plane (epsilon^t = epsilon^x = epsilon^y) but have opposite signs (epsilon^t*epsilon^z < 0) from that in the normal plane (epsilon^z). Due to this property, finite-thickness slabs of h-BN act as multimode waveguides for propagation of hyperbolic phonon polaritons - collective modes that originate from the coupling between photons and electric dipoles in phonons. However, control of these hyperbolic phonon polaritons modes has remained challenging, mostly because their e…
A comprehensive analysis of hybrid TM-TE polarized surface electromagnetic waves supported by different few-layer anisotropic metasurfaces is presented. A generalized 4$\times$4 T-matrix formalism for arbitrary anisotropic 2D layers is developed, from which the general relations for the surface waves dispersions and scattering coefficients are deduced. Using this formalism and the effective conductivity approach, the dispersions and iso-frequency contours (IFCs) topology of the surface waves in various hybrid uniaxial metasurfaces are studied. The existence of hyperbolic plasmon-exciton polari…
Black phosphorus presents a very anisotropic crystal structure, making it a potential candidate for hyperbolic plasmonics, characterized by a permittivity tensor where one of the principal components is metallic and the other dielectric. Here we demonstrate that atomically thin black phosphorus can be engineered to be a hyperbolic material operating in a broad range of the electromagnetic spectrum from the entire visible spectrum to ultraviolet. With the introduction of an optical gain, a new hyperbolic region emerges in the infrared. The character of this hyperbolic plasmon depends on the int…
We develop a general theoretical framework of integrated paired photon-plasmon generation through spontaneous wave mixing in nonlinear plasmonic and metamaterial nanostructures, rigorously accounting for material dispersion and losses in quantum regime through the electromagnetic Green function. We identify photon-plasmon correlations in layered metal-dielectric structures with 70% internal heralding quantum efficiency, and reveal novel mechanism of broadband generation enhancement due to topological transition in hyperbolic metamaterials.
We theoretically investigate general existence conditions for broadband bulk large-wavevector (high-k) propagating waves (such as volume plasmon polaritons in hyperbolic metamaterials) in subwavelength periodic multilayer structures. Describing the elementary excitation in the unit cell of the structure by a generalized resonance pole of a reflection coefficient, and using Bloch's theorem, we derive analytical expressions for the band of large-wavevector propagating solutions. We apply our formalism to determine the high-k band existence in two important cases: the well-known metal-dielectric,…
Negative refraction of highly squeezed polaritons is a fundamental building block for nanophotonics, since it can enable many unique applications, such as deep-subwavelength imaging. However, the phenomenon of all-angle negative refraction of highly squeezed polaritons, such as graphene plasmons with their wavelength squeezed by a factor over 100 compared to free-space photons, was reported to work only within a narrow bandwidth (<1 THz). Demonstrating this phenomenon within a broad frequency range remains a challenge that is highly sought after due to its importance for the manipulation of li…
We study the electromagnetic response of two- and quasi-two-dimensional hyperbolic materials, on which a simple dipole source can excite a well-confined and tunable surface plasmon polariton (SPP). The analysis is based on the Green's function for an anisotropic two-dimensional surface, which nominally requires the evaluation of a two-dimensional Sommerfeld integral. We show that for the SPP contribution this integral can be evaluated efficiently in a mixed continuous-discrete form as a continuous spectrum contribution (branch cut integral) of a residue term, in distinction to the isotropic ca…
The past decade has witnessed numerous discoveries of two-dimensional (2D) semimetals and insulators, whereas 2D metals are rarely identified. Borophene, a monolayer boron sheet, has recently emerged as a perfect 2D metal with unique structure and electronic properties. Here we study collective excitations in borophene, which exhibit two major plasmon modes with low damping rates extending from infrared to ultraviolet regime. The anisotropic 1D plasmon originates from electronic excitations of tilted Dirac cones in borophene, analogous to that in heavily doped Dirac semimetals. These features …
Light-matter interaction in two-dimension photonic materials allows for confinement and control of free-space radiation on sub-wavelength scales. Most notably, the van der Waals heterostructure obtained by stacking graphene (G) and hexagonal Boron Nitride (hBN) can provide for hybrid hyperbolic plasmon phonon-polaritons (HP3). Here, we present a polariton diode effect and low-bias control of HP3 modes confined in G-hBN. Using broadband infrared synchrotron radiation coupled to a scattering-type near-field optical microscope, we launch HP3 waves over both hBN Reststrahlen bands and observe the …
Metals are canonical plasmonic media at infrared and optical wavelengths, allowing one to guide and manipulate light at the nano-scale. A special form of optical waveguiding is afforded by highly anisotropic crystals revealing the opposite signs of the dielectric functions along orthogonal directions. These media are classified as hyperbolic and include crystalline insulators, semiconductors and artificial metamaterials. Layered anisotropic metals are also anticipated to support hyperbolic waveguiding. Yet this behavior remains elusive, primarily because interband losses arrest the propagation…
Recently studied hyperbolic materials host unique phonon-polariton (PP) modes. The ultra-short wavelengths of these modes, which can be much smaller than those of conventional exciton-polaritons, are of high interest for extreme sub-diffraction nanophotonics schemes. Polar hyperbolic materials such as hexagonal boron nitride can be used to realize strong long-range coupling between PP modes and extraneous charge degrees of freedom. The latter, in turn, can be used to control and probe PP modes. Of special interest is coupling between PP modes and plasmons in an adjacent graphene sheet, which o…
Surface plasmon polaritons in graphene couple strongly to surface phonons in polar substrates leading to hybridized surface plasmon-phonon polaritons (SPPPs). We demonstrate that a surface acoustic wave (SAW) can be used to launch propagating SPPPs in graphene/h-BN heterostructures on a piezoelectric substrate like AlN, where the SAW-induced surface modulation acts as a dynamic diffraction grating. The efficiency of the light coupling is greatly enhanced by the introduction of the h-BN film as compared to the bare graphene/AlN system. The h-BN interlayer not only significantly changes the disp…
We investigate unusual surface plasmons polariton (SPP) propagation and light-matter interactions in ultrathin black phosphorus (BP) films, a 2D material that exhibits exotic electrical and physical properties due to its extremely anisotropic crystal structure. Recently, it has been speculated that the ultra-confined surface plasmons supported by BP may present various topologies of wave propagation bands, ranging from anisotropic elliptic to hyperbolic, across the mid- and near-infrared regions of the electromagnetic spectrum. By carefully analyzing the natural nonlocal anisotropic optical co…
In this paper we reveal the physics behind the formation of tri- and tetra-hyperbolic phases in anisotropic metamaterials without magnetoelectric coupling and describe the anti-crossing splitting phenomenon in the hyperbolic dispersion which arises due to the hybridization of the plasmonic and magnetic Bloch high-k polaritons. This considerably deepens the understanding of the high-k polaritons and the topology of the optical iso-frequency surfaces in k-space and will find applications in optical nano-resolution imaging and emission rate and directivity control. To accomplish this, we develop …
Hexagonal boron nitride (hBN) is a natural hyperbolic material which can also accommodate highly dispersive surface phonon-polariton modes. In this paper, we examine theoretically the mid-infrared optical properties of graphene-hBN heterostructures derived from their coupled plasmon-phonon modes. We found that the graphene plasmon couples differently with the phonons of the two Reststrahlen bands, owing to their different hyperbolicity. This also leads to distinctively different interaction between an external quantum emitter and the plasmon-phonon modes in the two bands, leading to substantia…
Nonlocal electrodynamics of two-dimensional anisotropic magneto-plasmons
Aeronautics Institute of Technology（航空技术学院）；University of Southern Denmark（南丹麦大学）；Universidade Federal do Ceará（塞阿拉联邦大学）；University of Antwerp（安特卫普大学）；Danish Institute for Advanced Study, University of Southern Denmark（南丹麦大学丹麦高等研究院）；Universidade do Minho（米尼奥大学）
Spatiotemporal Visualization of Long-Range Anisotropic Plasmon Polaritons in Hyperbolic MoOCl2
The University of Chicago（芝加哥大学）；James Franck Institute, The University of Chicago（詹姆斯·弗兰克研究所，芝加哥大学）；Department of Chemistry, The University of Chicago（化学系，芝加哥大学）；Department of Physics, The University of Chicago（物理系，芝加哥大学）
The observation of the electrically tunable and highly confined plasmons in graphene has stimulated the exploration of interesting properties of plasmons in other two dimensional materials. Recently, hyperbolic plasmon resonance modes are observed in exfoliated WTe2 films, a type-II Weyl semimetal with layered structure, providing a platform for the assembly of plasmons with hyperbolicity and exotic topological properties. However, the plasmon modes were observed in relatively thick and small-area films, which restrict the tunability and application for plasmons. Here, large-area (~ cm) WTe2 f…
Drift-Induced Nonreciprocal Hyperbolic Polaritons in Graphene/$α$-MoO$_3$ Heterostructures
Universidad Politécnica de Madrid（马德里理工大学）；Instituto de Sistemas Optoelectrónicos y Microtecnología, Universidad Politécnica de Madrid（马德里理工大学光电子与微技术研究所）；Departamento de Ingeniería Electrónica, E.T.S.I de Telecomunicación, Universidad Politécnica de Madrid（马德里理工大学电信工程学院电子工程系）
We investigate the field and spin-momentum coupling of edge plasmons hosted by general two-dimensional materials and identify sweet spots depending on the polarisation plane, ellipticity and the position of an electric dipole relative to the plane and edge. Exciting the dipole at these sweet spots by propagating light leads to uni-directional propagating edge plasmons or edge modes are totally suppressed. We also extent previous approximate treatments [A. Fetter Phys. Rev. B 32, 7676 (1985)] to include anisotropy and hyperbolic systems, elucidating its predictions for the existence of edge mod…
Layered topological insulators, for example, Bi$_2$Se$_3$ are optically hyperbolic materials in a range of THz frequencies. Such materials possess deeply subdiffractional, highly directional collective modes: hyperbolic phonon-polaritons. In thin crystals the dispersion of such modes is split into discrete subbands and is strongly influenced by electron surface states. If the surface states are doped, then hybrid collective modes result from coupling of the phonon-polaritons with surface plasmons. The strength of the hybridization can be controlled by an external gate that varies the chemical …
Hyperbolic polaritons exhibit large photonic density of states and can be collimated in certain propagation directions. The majority of hyperbolic polaritons are sustained in man-made metamaterials. However, natural-occurring hyperbolic materials also exist. Particularly, natural in-plane hyperbolic polaritons in layered materials have been demonstrated in MoO3 and WTe2, which are based on phonon and plasmon resonances respectively. Here, by determining the anisotropic optical conductivity (dielectric function) through optical spectroscopy, we predict that monolayer black phosphorus naturally …
We study radiative energy transfer between a donor-acceptor pair across a hyperbolic metamaterial slab. We show that similar to a perfect lens a hyperbolic lens allows for giant energy transfer rates. For a realistic realization of a hyperbolic multilayer metamaterial we find an enhancement of up to three orders of magnitude with respect to the transfer rates across a plasmonic silver film of the same size especially for frequencies which coincide with the epsilon-near zero and the epsilonnear pole frequencies. Furthermore, we compare exact results based on the S-matrix method with results obt…
Confined modes at the edge arbitrarily inclined with respect to optical axes of nonmagnetic anisotropic 2D materials are considered. By developing the exact Wiener-Hopf and approximated Fetter methods we studied edge modes dispersions, field and charge density distributions. The 2D layer is described by the Lorentz-type conductivities in one or both directions, which is realistic for natural anisotropic 2D materials and resonant hyperbolic metasurfaces. We demonstrate that, due to anisotropy, the edge mode exists only at wave vectors exceeding the nonzero threshold value if the edge is tilted …
The hyperbolic phonon-polaritons within the Reststrahlen band of hBN are of great interest for applications in nanophotonics as they are capable of propagating light signals with low losses over large distances. However, due to the phononic nature of the polaritons in hBN, amplitude modulation of its signal proves to be difficult and has been underexplored. In this paper, we propose theoretically a broadband efficient amplitude modulator for hyperbolic rays in hBN operating in the frequency range between 1450 cm$^{-1}$ and 1550 cm$^{-1}$. The modulating region comprises a few tens of nanometer…
Naturally occurring hyperbolic plasmonic media is rare, and was only recently observed in the 1T$'$ phase of WTe$_2$. We elucidate on the physical origin of this strong infrared hyperbolic response, and attribute it to band-nested anisotropic interband transitions. Such phenomenon does not occur in general anisotropic materials, at least not in their pristine state. However, band-nested anisotropic interband transitions can in principle be induced via proper electronic band nesting. We illustrate this principle and demonstrate a topological elliptic-to-hyperbolic transition in MoTe$_2$ via str…
In mirror-symmetric systems, there is a possibility of the realization of extended gapless electronic states characterized as nodal lines or rings. Strain induced modifications to these states lead to emergence of different classes of nodal rings with qualitatively different physical properties. Here we study optical response and the electromagnetic wave propagation in type I nodal ring semimetals, in which the low-energy quasiparticle dispersion is parabolic in momentum $k_x$ and $k_y$ and is linear in $k_z$. This leads to a highly anisotropic dielectric permittivity tensor in which the optic…
The radiation dynamics of optical emitters can be manipulated by properly designed material structures providing high local density of photonic states, a phenomenon often referred to as the Purcell effect. Plasmonic nanorod metamaterials with hyperbolic dispersion of electromagnetic modes are believed to deliver a significant Purcell enhancement with both broadband and non-resonant nature. Here, we have investigated finite-size cavities formed by nanorod metamaterials and shown that the main mechanism of the Purcell effect in these hyperbolic resonators originates from the cavity hyperbolic mo…
In this work, we study the near-field radiative heat transfer between two suspended sheets of anisotropic 2D materials. It is found that the radiative heat transfer can be enhanced with orders-of-magnitude over the blackbody limit for nanoscale separation. The enhancement is attributed to the excitation of anisotropic and hyperbolic plasmonic modes. Meanwhile, a large thermal modulation effect, depending on the twisted angle of principal axes between the upper and bottom sheets of anisotropic 2D materials, is revealed. The near-field radiative heat transfer for different concentrations of elec…
We study the optical properties of quantum dipole emitters coupled to hyperbolic metamaterial nano-resonators using a semi-analytical quasinormal mode approach. We show that coupling to metamaterial nano-resonators can lead to significant Purcell enhancements that are nearly an order of magnitude larger than those of plasmonic resonators with comparable geometry. However, the associated single photon output $β$-factors are extremely low (around 10$\%$), far smaller than those of comparable sized metallic resonators (70$\%$). Using a quasinormal mode expansion of the photon Green function, we d…
In this work, we study the near-field heat transfer between composite nanostructures. It is demonstrated that thermally excited surface plasmon polaritons, surface phonon polaritons, and hyperbolic phonon polaritons in such composite nanostructures significantly enhance the near-field heat transfer. To further analyze the underlying mechanisms, we calculate energy transmission coefficients and obtain the near-field dispersion relations. The dispersion relations of composite nanostructures are substantially different from those of isolated graphene, silicon carbide (SiC) films, and SiC nanowire…
Natural hyperbolic materials (HMs) in two dimensions (2D) have an extraordinarily high anisotropy and a hyperbolic dispersion relation. Some of them can even sustain hyperbolic polaritons with great directional propagation and light compression to deeply sub-wavelength scales due to their inherent anisotropy. Herein, the anisotropic optical features of 2D natural HMs are reviewed. Four hyperbolic polaritons (i.e., phonon polaritons, plasmon polaritons, exciton-polaritons, and shear polaritons) as well as their generation mechanism are discussed in detail. The natural merits of 2D HMs hold prom…
Strongly anisotropic media where the principal components of the dielectric tensor have opposite signs are called hyperbolic. Such materials length exhibit unique nanophotonic properties enabled by the highly directional propagation of slow-light modes localized at deeply sub-diffractional scales. While artificial hyperbolic metamaterials have been demonstrated, they suffer from high plasmonic losses and require complex nanofabrication, which in turn induces the size-dependent limitations on optical confinement. The low-loss, mid-infrared, natural hyperbolic material, hexagonal boron nitride i…
