We present a numerical study of exciton-polariton (polariton) condensation in a staggered polariton graphene showing a gapped s-band at the $K$ and $K'$ valleys. The condensation occurs at $K$ or $K'$, at the kinetically-favorable negative mass extrema of the valence band. Considering attractive polariton-polariton interaction allows to generate a spatially extended condensate. Spontaneous symmetry breaking occurring during the condensate build-up leads to the formation of valley-polarized domains following the Kibble-Zurek scenario. The selection of a single valley breaks time-reversal symmetry and the walls separating domains exhibit a topologically-protected chiral current. This current therefore emerges as a result of the interplay between the non-trivial valley topology and the condensation-induced symmetry breaking.
We study non-equilibrium polariton superfluids in the optical parametric oscillator (OPO) regime using a two-component Gross-Pitaevskii equation with pumping and decay. We identify a regime above OPO threshold, where the system undergoes spontaneous symmetry breaking and is unstable towards vortex formation without any driving rotation. Stable vortex solutions differ from metastable ones; the latter can persist in OPO superfluids but can only be triggered externally. Both spontaneous and triggered vortices are characterised by a generalised healing length, specified by the OPO parameters only.
We study the formation of topological defects (quantum vortices) during the formation of a 2D polariton condensate at the $Γ$ point of a honeycomb lattice via the Kibble-Zurek mechanism. The lattice modifies the single-particle dispersion. The typical interaction energies at the quench time correspond to the linear part of the dispersion. The resulting scaling exponent for the density of topological defects is numerically found as $0.95\pm0.05$. This value differs from the one expected for 2D massive particles (1/2), but is indeed compatible with the one expected for a linear dispersion. We mo…
It is shown that monolayer graphene deposited on a spatially-periodic gate behaves as a polaritonic crystal. Its band structure depending on the applied gate voltage is studied. The scattering of electromagnetic radiation from such a crystal is presented calculated and analyzed in terms of Fano-type resonances between the reflected continuum and plasmon-polariton modes forming narrow bands.
Electrodynamics of single-layer graphene is studied in the scaling regime. At any finite temperature, there is a weakly damped collective thermo-plasma polariton mode whose dispersion and wavelength dependent damping is determined analytically. The electric and magnetic fields associated with this mode decay exponentially in the direction perpendicular to the graphene layer, but unlike the surface plasma polariton modes of metals, the decay length and the mode frequency are strongly temperature dependent. This may lead to new ways of generation and manipulation of these modes.
We consider a polariton microcavity resonantly driven by two external lasers which simultaneously pump both lower and upper polariton branches at normal incidence. In this setup, we study the occurrence of instabilities of the pump-only solutions towards the spontaneous formation of patterns. Their appearance is a consequence of the spontaneous symmetry breaking of translational and rotational invariance due to interaction induced parametric scattering. We observe the evolution between diverse patterns which can be classified as single-pump, where parametric scattering occurs at the same energ…
We consider a hybrid structure formed by graphene and an insulating antiferromagnet, separated by a dielectric of thickness up to $d\simeq 500 \,nm$. When uncoupled, both graphene and the antiferromagnetic surface host their own polariton modes coupling the electromagnetic field with plasmons in the case of graphene, and with magnons in the case of the antiferromagnet. We show that the hybrid structure can host two new types of hybrid polariton modes. First, a surface magnon-plasmon polariton whose dispersion is radically changed by the carrier density of the graphene layer, including a change…
Exploring the properties of strongly correlated systems through quantum simulation with photons, cold atoms or polaritons represents an active area of research. In fact, the latter permits to shed the light on the behavior of complex systems which are hardly to be addressed in the laboratory or tackled numerically. In this study we discuss an analogue of graphene formed by exciton-polariton spin vortices arranged into a hexagonal lattice. We show how the graphene-type dispersion at different energy scales arises for several types of exciton-polariton spin vortices. In contrast to previous stud…
Transverse-electric (TE) surface plasmon polaritons are unique eigenmodes of a homogeneous graphene layer that are tunable with the chemical potential and temperature. However, as their dispersion curve spectrally lies just below the light line, they cannot be resonantly excited by an externally incident wave. Here, we propose a way of exciting the TE modes and tuning their peaks in the transmission by introducing a one-dimensional graphene grating. Using the scattering-matrix formalism, we show that periodic modulations of graphene make the transmission more pronounced, potentially allowing f…
With the unique possibilities for controlling light in nanoscale devices, graphene plasmonics has opened new perspectives to the nanophotonics community with potential applications in metamaterials, modulators, photodetectors, and sensors. This paper briefly reviews the recent exciting progress in graphene plasmonics. We begin with a general description for optical properties of graphene, particularly focusing on the dispersion of graphene-plasmon polaritons. The dispersion relation of graphene-plasmon polaritons of spatially extended graphene is expressed in terms of the local response limit …
We discuss the properties of surface plasmons-polaritons in graphene and describe three possible ways of coupling electromagnetic radiation in the terahertz (THz) spectral range to this type of surface waves. (i) the attenuated total reflection (ATR) method using a prism in the Otto configuration, (ii) graphene micro-ribbon arrays or monolayers with modulated conductivity, (iii) a metal stripe on top of the graphene layer, and (iv) graphene-based gratings. The text provides a number of original results along with their detailed derivation and discussion.
We study the propagation of a Bose-Einstein condensate (BEC) of long-lifetime exciton polaritons in a high-quality microcavity with an embedded semiconductor quantum well or a graphene layer using the Gross-Pitaevskii equation. It is shown that in these heterostructures the BEC of the long-lifetime polaritons can propagate over the distance up to 0.5 mm. The obtained results are consistent with the recent experimental observations for GaAs/AlGaAs microcavity. It is demonstrated that the BEC density in a polariton trace in a microcavity with embedded graphene at large distances from the excitat…
The dispersion relation of surface plasmon polaritons in graphene that includes optical losses is often obtained for complex wave vectors while the frequencies are assumed to be real. This approach, however, is not suitable for describing the temporal dynamics of optical excitations and the spectral properties of graphene. Here, we propose an alternative approach that calculates the dispersion relation in the complex frequency and real wave vector space. This approach provides a clearer insight into the optical properties of a graphene layer and allows us to find the surface plasmon modes of a…
Surface plasmon polaritons in planar graphene superlattices with one-dimensional periodic mo-dulation of the band gap were studied. The interminiband contribution to the optical conductivity of this system was found by the equation of motion method for two cases: the Fermi level falls within one of the minigaps and the Fermi level is located within one of the minibands. It was shown that the optical conductivity of the system varies significantly in these cases. The spectra of surface plasmon polaritons in the system differs for them.
Bose-Einstein condensate of exciton polaritons in a semiconductor microcavity is a macroscopically populated coherent quantum state subject to concurrent pumping and decay. Debates about the fundamental nature of the condensed phase in this open quantum system still persist. Here, we gain a new insight into the spontaneous condensation process by imaging long-lifetime exciton polaritons in a high-quality inorganic microcavity in the single-shot optical excitation regime, without averaging over multiple condensate realisations. In this highly non-stationary regime, a condensate is strongly infl…
Phonon polaritons in natural anisotropic crystals hold great promise for infrared nano-optics. However, the direct electrical control of these polaritons is difficult, preventing the development of active polaritonic devices. Here we propose the heterostructures of graphene on a biaxial crystal (α-phase molybdenum trioxide) slab and theoretically study the hybridized plasmon-phonon polaritons with dependence on the Fermi level of graphene from three aspects: dispersion relationships, iso-frequency contours, and the quantum spin Hall effects. We demonstrate the distinct wavelength tunability of…
We provide an analytical solution to the problem of scattering of electromagnetic radiation by a square-wave grating with a flat graphene sheet on top. We show that for deep groves there is a strong plasmonic response with light absorption in the graphene sheet reaching more than 45%, due to the excitation of surface plasmon-polaritons. The case of grating with a graphene sheet presenting an induced periodic modulation of the conductivity is also discussed.
It is shown that one can explore the optical conductivity of graphene, together with the ability of controlling its electronic density by an applied gate voltage, in order to achieve resonant coupling between an external electromagnetic radiation and surface plasmon-polaritons in the graphene layer. This opens the possibility of electrical control of the intensity of light reflected inside a prism placed on top of the graphene layer, by switching between the regimes of total reflection and total absorption. The predicted effect can be used to build graphene-based opto-electronic switches.
We predict the spontaneous modulated emission from a pair of exciton-polariton condensates due to coherent (Josephson) and dissipative coupling. We show that strong polariton-polariton inter- action generates complex dynamics in the weak-lasing domain way beyond Hopf bifurcations. As a result, the exciton-polariton condensates exhibit self-induced oscillations and emit an equidistant frequency comb light spectrum. A plethora of possible emission spectra with asymmetric peak dis- tributions appears due to spontaneously broken time-reversal symmetry. The lasing dynamics is affected by the shot n…
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…
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…
We develop a rigorous quantum-mechanical theory of the nonlinear optical process of difference frequency generation of surface plasmon-polaritons in Landau-quantized graphene. Although forbidden in the electric-dipole approximation, the second-order susceptibility is surprisingly high, equivalent to the bulk magnitude above $10^{-3}$ m/V. We consider the graphene monolayer as a nonlinear optical component of a monolithic photonic chip with integrated pump fields. The nonlinear power conversion efficiency of the order of tens $μ$W/W$^2$ is predicted from structures of $10-100$ $μ$m size. We inv…
We study Klein tunneling in polariton graphene. We show that the photonic spin-orbit coupling associated with the energy splitting between TE and TM photonic modes can be described as an emergent gauge field. It suppresses the Klein tunnelling in small energy range close to the Dirac points. Thanks to polariton spin-anisotropic interactions, polarized optical pumping allows to create potential barriers acting on a single polariton spin. We show that the resulting spin-dependent Klein tunneling can be used to create a perfectly transmitting polarization rotator operating at microscopic scale.
We predict spontaneous generation of superfluid polariton currents in planar microcavities with lateral periodic modulation of both potential and decay rate. A spontaneous breaking of spatial inversion symmetry of a polariton condensate emerges at a critical pumping, and the current direction is stochastically chosen. We analyse the stability of the current with respect to the fluctuations of the condensate. A peculiar spatial current domain structure emerges, where the current direction is switched at the domain walls, and the characteristic domain size and lifetime scale with the pumping pow…
We predict the formation and superfluidity of polaritons in an optical microcavity formed by excitons in gapped graphene embedded there and microcavity photons. The Rabi splitting related to the creation of an exciton in a graphene layer in the presence of the band gap is obtained. The analysis of collective excitations as well as the sound velocity is presented. We show that the superfluid density and temperature of the Kosterlitz-Thouless phase transition are decreasing functions of the energy gap.
We present a scheme of interaction-induced topological bandstructures based on the spin anisotropy of exciton-polaritons in semiconductor microcavities. We predict theoretically that this scheme allows the engineering of topological gaps, without requiring a magnetic field or strong spin-orbit interaction (transverse electric-transverse magnetic splitting). Under non-resonant pumping, we find that an initially topologically trivial system undergoes a topological transition upon the spontaneous breaking of phase symmetry associated with polariton condensation. Under resonant coherent pumping, w…
We study the spectra and damping of surface plasmon-polaritons in double graphene layer structures. It is shown that application of bias voltage between layers shifts the edge of plasmon absorption associated with the interband transitions. This effect could be used in efficient plasmonic modulators. We reveal the influence of spatial dispersion of conductivity on plasmonic spectra and show that it results in the shift of cutoff frequency to the higher values.
In the present work we theoretically investigated the excitation of surface plasmon-polaritons (SPPs) in deformed graphene by attenuated total reflection method. We considered the Otto geometry for SPPs excitation in graphene. Efficiency of SPPs excitation strongly depends on the SPPs propagation direction. The frequency and the incident angle of the most effective excitation of SPPs strongly depend on the polarization of the incident light. Our results may open up the new possibilities for strain-induced molding flow of light at nanoscales.
The combination of plasmonic nanoparticles and graphene enhances the responsivity and spectral selectivity of graphene-based photodetectors. However, the small area of the metal-graphene junction, where the induced electron-hole pairs separate, limits the photoactive region to sub-micron length scales. Here, we couple graphene with a plasmonic grating and exploit the resulting surface plasmon polaritons to deliver the collected photons to the junction region of a metal-graphene-metal photodetector. This results into a 400% enhancement of responsivity and a 1000% increase in photoactive length,…
There is growing experimental interest in coupling cavity photons to the cyclotron resonance excitations of electron liquids in high-mobility semiconductor quantum wells or graphene sheets. These media offer unique platforms to carry out fundamental studies of exciton-polariton condensation and cavity quantum electrodynamics in a regime in which electron-electron interactions are expected to play a pivotal role. Focusing on graphene, we present a theoretical study of the impact of electron-electron interactions on a quantum Hall polariton fluid, that is a fluid of magneto-excitons resonantly c…
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 …
This paper is withdrawn by the authors. We theoretically examine graphene plasmon polaritons (GPP) supported by a sheet of graphene sandwiched between two dielectric media. The influence of the dielectric environment on GPP's is studied within local and nonlocal descriptions of graphene's conductivity. We demonstrate that a local-response approximation invariably leads, counter-intuitively, to a substrate-independent surface plasmon frequency. On the other hand, the nonlocal description of the electron gas allows the presence of non-vertical inter-band transitions which changes the results qua…
Tamm polaritons (TPs) are formed at the interface between two semi-infinite periodic dielectric structures (Bragg mirrors) or other reflectors. Contrary to usual surface polaritons, TPs exist inside the "light cone", even though their amplitude also decreases exponentially with the distance from the interface as it is characteristic of evanescent waves. They couple to elementary excitations in the materials or structures that form the interface, such as metal plasmons or semiconductor excitons. Here we discuss the formation of TPs in the far-infrared (FIR) spectral range, in the optical-phonon…
The Bose-Einstein condensation (BEC) of magnetoexcitonic polaritons in a graphene layer embedded in a optical microcavity in a high magnetic field $B$ is predicted. The essential property of this system (in contrast, e.g., to a quantum well embedded in a cavity) is stronger influence of magnetic field and weaker influence of disorder. A two-dimensional (2D) magnetoexcitonic polaritons gas is considered in a planar harmonic electric field potential applied to excitons or a parabolic shape of the optical cavity causing the trapping of microcavity photons. It is shown that the effective polariton…
We theoretically explore nonresonantly pumped polaritonic graphene, a system consisting of a honeycomb lattice of micropillars in the regime of strong light-matter coupling. We demonstrate that, depending on the parameters of the structure, such as intensity of the pump and coupling strength between the pillars, the system shows rich variety of macroscopic ordering, including analogs of ferromagnetic, antiferromagnetic, and resonant valence bond phases. Transitions between these phases are associated with dramatic reshaping of the spectrum of the system connected with spontaneous appearance of…
We demonstrate a dynamic surface plasmonic modulation of graphene-nanowire hybrid structures in visible light range, which was thought to be a tough task for graphene based field effect transistor modulator previously. Static modulation depth of as high as 0.07 dB/μm has been achieved experimentally. Carefully simulation indicates the strongly focused electromagnetic field and dramatically enhanced electric field at the interface between a silver NW and a graphene sheet are key roles for bringing the optical response of the device to the visible range. Furthermore, the modulation behaviors nea…
The propagation of a surface plasmon-polariton along a stack of doped graphene sheets is considered. This auxiliary problem is used to discuss: (i) the scattering of such a mode at an interface between the stack and the vacuum; (ii) the scattering at an interface where there is a sudden change of the electronic doping. The formalism is then extended to the {\it barrier problem}. In this system rich physics is found for the plasmonic mode, showing: total reflection, total transmission, Fabry-Pérot oscillations, and coupling to photonic modes.
We present a theory of the cavity quantum electrodynamics of the graphene cyclotron resonance. By employing a canonical transformation, we derive an effective Hamiltonian for the system comprised of two neighboring Landau levels dressed by the cavity electromagnetic field (integer quantum Hall polaritons). This generalized Dicke Hamiltonian, which contains terms that are quadratic in the electromagnetic field and respects gauge invariance, is then used to calculate thermodynamic properties of the quantum Hall polariton system. Finally, we demonstrate that the generalized Dicke description fail…
A graphene sheet gated with a ridged ground plane, creating a soft-boundary (SB) graphene nanoribbon, is considered. By adjusting the ridge parameters and bias voltage a channel can be created on the graphene which can guide TM surface plasmon polaritons (SPP). Two types of modes are found; fundemental and higher-order modes with no apparent cutoff frequency and with energy distributed over the created channel, and edge modes with energy concen-trated at the soft-boundary edge. Dispersion curves, electric near-field patterns, and current distributions of these modes are determined. Since the l…
In the present paper, the collective near-field effects in a two-graphene sheets plasmonic waveguide loaded with an array of Ag$_2$Se quantum dots excited by external radiation are theoretically studied. This research aims to develop a theoretical approach to realizing controllable excitation and the propagation of surface plasmon polaritons (SPPs) in planar graphene waveguides. The proposed model is based on the semiclassical description that implies the dispersion equation's solution for SPPs excited in two coupled graphene sheets and the embedded quantum dots' energy spectra analysis. Using…
We investigate the process of condensation of exciton-polaritons in a one-dimensional nanowire, predicting spontaneous formation of domains of uncondensed excitons and condensed polaritons. We demonstrate a universal scaling law for the density of domains, which results from the competition between characteristic timescales present in the system. However, we find that the system does not follow the standard Kibble-Żurek scenario of a nonequilibrium phase transition.
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 the statistics of microcavity polariton Bose-Einstein condensation by measuring photoluminescence dynamics from a GaAs microcavity excited by single laser excitation pulses. We directly observe fluctuations (jitter) of the polariton condensation onset time and model them using a master equation for the occupancy probabilities. The jitter of the condensation onset time is an inherent property of the condensate formation and its magnitude is approximately equal to the rise time of the condensate density. We investigate temporal correlations between the emission of condensate in op…
Based on the studies of propagation of an exciton-polariton condensate in a patterned optical microcavity with an embedded graphene layer, we propose a design of a Y-shaped electrically-controlled optical switch. The polaritons are driven by a time-independent force due to the microcavity wedge shape and by a time-dependent drag force owing to the interaction of excitons in graphene and the electric current running in a neighboring quantum well. It is demonstrated that one can control the polariton flow direction by changing the direction of the electric current. The simulations also show that…
Exciton-polariton lattices allow to implement topologically protected photonic edge states at optical frequencies. Taking advantage of the interacting character of polaritons, we show that several topological phases, belonging to the Quantum Anomalous Hall family, can occur in polariton graphene with the TE-TM spin-orbit coupling and an effective Zeeman field. This Zeeman field can be entirely controlled by the non-linearity of the macro-occupied mode created by circularly polarized resonant pumping. The topological phases found are distinct from the ones of normal graphene in presence of a co…
We report on the simultaneous observation of spontaneous symmetry breaking and long-range spatial coherence both in the strong and the weak-coupling regime in a semiconductor microcavity. Under pulsed excitation, the formation of a stochastic order parameter is observed in polariton and photon lasing regimes. Single-shot measurements of the Stokes vector of the emission exhibit the buildup of stochastic polarization. Below threshold, the polarization noise does not exceed 10%, while above threshold we observe a total polarization of up to 50% after each excitation pulse, while the polarization…
Recent advances in nanophotonics have brought about coherent light sources with chaotic circular polarization; a low-dimensional chaotic evolution of optical spin was evidenced in laser diodes. Here we propose a mechanism that gives rise to light with a spatiotemporal spin chaos resembling turbulent states in hydrodynamics. The spin-chaotic radiation is emitted by exciton polaritons under resonant optical pumping in arbitrarily sized planar microcavities, including, as a limiting case, pointlike systems with only three degrees of freedom. The underlying mechanism originates in the interplay be…
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…
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）
Artifical superlattice (SL) potentials have been employed extensively for band structure engineering of two-dimensional (2D) Dirac electron gas in graphene. While such engineered electronic band structures can modify optical or plasmonic properties of graphene, an emergent polaritonic behavior beyond weak perturbative effects (e.g. anisotropic Drude weights) has not been reported. Here, we show that an extreme modulation of one-dimensional (1D) SL potentials in monolayer graphene deforms the underlying Dirac band dispersion and introduces ladder-like energy levels near the Fermi surface, which…
