Collective excitations spectrum of Dirac electrons in mono and bilayer graphene in the presence of a uniform magnetic field is investigated. Analytical results for inter-Landau band plasmon spectrum within the self-consistent-field approach are obtained. SdH type oscillations that are a monotonic function of the magnetic field are observed in the plasmon spectrum of both mono- and bi-layer graphene systems. The results presented are also compared with those obtained in conventional 2DEG. The chiral nature of the quasiparticles in mono and bilayer graphene system results in the observation of $π$ and $2π$ Berry's phase in the SdH- type oscillations in the plasmon spectrum.
In this work, we determine the effects of temperature on the magnetoplasmon spectrum of an electrically modulated graphene monolayer as well as the two-dimensional electron gas (2DEG). The intra-Landau-band magnetoplasmon spectrum within the Self Consistent Field (SCF) approach is investigated for both the aforementioned systems. Results obtained not only exhibit Shubnikov-de Hass (SdH) oscillations but also commensurability oscillations (Weiss oscillations). These oscillations are periodic as a function of inverse magnetic field. We find that both the magnetic oscillations, SdH and Weiss, hav…
We theoretically study electrically tunable magnetoplasmons in a monolayer of silicene or germanene. We derive the dynamical response function and take into account the effects of strong spin-orbit coupling (SOC) and of an external electric filed $E_z$ perpendicular to the plane of the buckled silicene/germanene. Employing the random-phase approximation we analyze the magnetoplasmon spectrum. The dispersion relation has the same form as in a two-dimensional electron gas with the cyclotron and plasma frequencies modified due to the SOC and the field $E_z$. In the absence of SOC and $E_z$, our r…
We show that in graphene epitaxially grown on SiC the Drude absorption is transformed into a strong terahertz plasmonic peak due to natural nanoscale inhomogeneities, such as substrate terraces and wrinkles. The excitation of the plasmon modifies dramatically the magneto-optical response and in particular the Faraday rotation. This makes graphene a unique playground for plasmon-controlled magneto-optical phenomena thanks to a cyclotron mass 2 orders of magnitude smaller than in conventional plasmonic materials such as noble metals.
Two-dimensional materials supporting deep-subwavelength plasmonic modes can also exhibit strong magneto-optical responses. Here, we theoretically investigate magnetoplasmons (MPs) in monolayer black phosphorus (BP) structures under moderate static magnetic fields. We consider three different structures, namely, a continuous BP monolayer, an edge formed by a semi-infinite sheet, and finally, a triangular wedge configuration. Each of these structures shows strongly anisotropic magneto-optical responses induced both by the external magnetic field and by the intrinsic anisotropy of the BP lattice.…
We study the propagation of edge magnetoplasmons by time-resolved current measurements in a sample which allows for selective detection of edge states in the quantum Hall regime. We observe two decoupled modes of edge and inter-edge magnetoplasmons at filling factors close to 3. From the analysis of the propagation velocities of each mode the internal spatial parameters of the edge structure are derived.
We present a theoretical study of magnetoplasmon spectrum of a two-dimensional electron gas in the presence of Rashba spin-orbit interaction (RSOI), one-dimensional weak electric modulation and a perpendicular magnetic field. The intra-Landau-band magnetoplasmon spectrum is determined in the presence of spin-orbit interaction within the self consistent field approach at finite temperature. Due to Rashba effect, the spin of finite-momentum electrons feels a magnetic field perpendicular to the electron momentum in the inversion plane. The magnetoplasmon spectrum of the modulated two-dimensional …
The magnetoplasmon spectrum of a magnetically modulated two-dimensional electron gas (MM2DEG) is investigated. We derive the inter and intra Landau band magnetoplasmon spectrum within the self consistent field approach. The derivation is performed at zero temperature as well as at finite temperature. Results are presented for the inter and intra Landau band magnetoplasmon spectrum as a function of the inverse magnetic field. As a result of magnetic modulation, magnetic Weiss oscillations are found to occur in the magnetoplasmon spectrum. Furthermore, our finite temperature theory facilitates a…
We investigate magnetoplasmon dynamics localized on the edges of graphene vortex Hall fluid. The vortex matter captures an anomalous term that causes vortex localization near fluid boundary and creates a double boundary layer, $Δ_0\propto (β-1)\ell_B$ with $β$ being filling factor. The term also has qualitative effect on resonant excitations of edge magnetoplasmons. We found that for sharp edges under experimental conditions, graphene Edge Magnetoplasmon (EMP) resonances have similar behavior as in recent experiments. Gradual distinctions arise for smooth edges in the presence of the anomalous…
We report the magnetic field-dependent far-infrared reflectivity of polycrystalline bismuth. We observe four distinct absorptions that we attribute to magnetoplasmon resonances, which are collective modes of an electron-hole liquid in magnetic field and become optical and acoustic resonances of the electron-hole system in the small-field limit. The acoustic mode is expected only when the masses of distinct components are very different, which is the case in bismuth. In a polycrystal, where the translational symmetry is broken, a big shift of spectral weight to acoustic plasmon is possible. Thi…
The present paper is devoted to the theoretical study of the spectrum of low-frequency electronic density oscillations running along the boundary of two contacting two-dimensional electronic systems in the perpendicular magnetic field. For the first time, such waves were predicted in the Institute of Radio-engineering and Electronics of RAS (V.A. Volkov, S.A. Mikhailov, 1992), studied experimentally in the papers of foreign investigations and called inter-edge magnetoplasmons (IEMP). When the two-dimensional system is finite and has the half-plane shape, the internal boundary becomes external …
We investigate electron dynamics at the graphene edge by studying the propagation of collective edge magnetoplasmon (EMP) excitations. By timing the travel of narrow wave-packets on picosecond time scales around exfoliated samples, we find chiral propagation with low attenuation at a velocity which is quantized on Hall plateaus. We extract the carrier drift contribution from the EMP propagation and find it to be slightly less than the Fermi velocity, as expected for an abrupt edge. We also extract the characteristic length for Coulomb interaction at the edge and find it to be smaller than for …
Ultrastrong coupling of topologically protected edge and bulk magnetoplasmons without a dedicated cavity
TU Dortmund University（多特蒙德工业大学）；Warsaw University of Technology（华沙理工大学）；Institute of High Pressure Physics PAS（波兰科学院高压物理研究所）；University Duisburg-Essen（杜伊斯堡-埃森大学）；LNCMI, CNRS-UGA-UPS-INSA-EMFL（法国国家强磁场实验室）
The plasmon frequency in standard electron gases with a parabolic single-particle dispersion is a purely classical quantity that is not sensitive to electron interactions or the equation of state. We demonstrate that this canonical result no longer holds for plasmons in three-dimensional semimetals, which can thus be used to probe many-body effects in these systems. In particular, we show that the plasmon frequency in an external magnetic field displays quantum oscillations, which is not the case for the electron gas. Using the random phase approximation, results are presented for the magnetop…
In the frame of the Hartree-Fock approximation, the dispersion of magnetoplasmons in Graphene is derived for all types of transitions for filling factors $ν\leq 6$. The optical conductivity components of the magnetoplasmon curves are calculated. It is shown that the electron-electron interactions lead to a strong re-normalization of the apparent Fermi velocity of Graphene which is different for different types of transitions.
Within dissipationless limit the magnetic field dependence of magnetoplasmon spectrum for unbounded 2DEG system found to intersect the cyclotron resonance line, and, then approaches the frequency given by light dispersion relation. Recent experiments done for macroscopic disc-shape 2DEG systems confirm theory expectations.
We present infrared transmission spectroscopy study of the inter-Landau-level excitations in quasi-neutral epitaxial graphene nanoribbon arrays. We observed a substantial deviation in energy of the $L_{0(-1)}$$\to$$L_{1(0)}$ transition from the characteristic square root magnetic-field dependence of two-dimensional graphene. This deviation arises from the formation of upper-hybrid mode between the Landau level transition and the plasmon resonance. In the quantum regime the hybrid mode exhibits a distinct dispersion relation, markedly different from that expected for conventional two-dimensiona…
A deeper sense of advantages over the planar quantum dots and the foreseen applications in the single-electron devices and quantum computation have given vertically stacked quantum dots (VSQD) a width of interest. Here, we embark on the collective excitations in a quantum wire made-up of vertically stacked, self-assembled InAs/GaAs quantum dots in the presence of an applied magnetic field in the symmetric gauge. We compute and illustrate the influence of an applied magnetic field on the behavior characteristics of the density of states, Fermi energy, and collective (magnetoplasmon) excitations…
We report on a tunable - by magnetic field and gate voltage - conversion of terahertz radiation into a dc current in spatially modulated bilayer graphene. We experimentally demonstrate that the underlying physics is related to the so-called ratchet effect. Our key findings are the direct observation of a sharp cyclotron resonance in the photocurrent and the demonstration of two effects caused by electron-electron interaction: the plasmonic splitting of the resonance due to long-range Coulomb coupling and the partial suppression of its second harmonic due to fast interparticle collisions. We de…
It is known that peculiar plasmons whose frequencies are purely imaginary exist in the interior of a two-dimensional electronic system described by the Drude model. We show that when an external magnetic field is applied to the system, these bulk plasmons are still non-oscillating and are isolated from the magnetoplasmons by the energy gap of the cyclotron frequency. These are mainly in a transverse magnetic mode and can combine with a transverse electronic mode locally at an edge of the system to form edge magnetoplasmons. With this observation, we reveal the intrinsic long lifetime of edge m…
Incorporating ferromagnetic dopants, such as chromium or vanadium, into thin films of the three-dimensional (3D) topological insulator (TI) (Bi,Sb)2Te3 has recently led to the realisation of the quantum anomalous Hall effect (QAHE), a unique phase of quantum matter. These materials are of great interest, since they may support electrical currents that flow without resistance via edge channels, even at zero magnetic field. To date, the QAHE has been investigated using low-frequency transport measurements. However, transport requires contacting the sample and results can be difficult to interpre…
We study the magnetoplasmon collective mode excitations of integer quantum Hall systems in a parabolically confined quantum well nanostructure in the presence of a tilted magnetic field by using the time-dependent Hartree-Fock approximation. For even integer filling, we find that the dispersion of a spin density mode has a magneto-roton minimum at finite wavevectors, at a few times 10^6 cm^{-1} for parallel fields of order 1-10 Tesla, only in the direction perpendicular to the in-plane magnetic field, while the mode energy increases monotonously with wavevector parallel to the in-plane magneti…
We investigate intrinsic and extrinsic decay of edge magnetoplasmons (EMPs) in graphene quantum Hall (QH) systems by high-frequency electronic measurements. From EMP resonances in disk shaped graphene, we show that the dispersion relation of EMPs is nonlinear due to interactions, giving rise to intrinsic decay of EMP wavepacket. We also identify extrinsic dissipation mechanisms due to interaction with localized states in bulk graphene from the decay time of EMP wavepackets. We indicate that, owing to the unique linear and gapless band structure, EMP dissipation in graphene can be lower than th…
Chiral Light-Matter Interactions with Thermal Magnetoplasmons in Graphene Nanodisks
University of Southern Denmark（南丹麦大学）；POLIMA—Center for Polariton-driven Light–Matter Interactions, University of Southern Denmark（极化子驱动光-物质相互作用中心，南丹麦大学）；Danish Institute for Advanced Study, University of Southern Denmark（丹麦高等研究院，南丹麦大学）；Instituto de Química Física Blas Cabrera (IQF), CSIC（布拉斯·卡布雷拉物理化学研究所，西班牙国家研究委员会）
We determine the collective excitations spectrum and discuss the numerical results for a parabolically confined density modulated quasi-one dimensional electron gas (1DEG) in the presence of an external magnetic field. We derive the inter-and intra-band magnetoplasmon spectrum within the Self Consistent Field (SCF) approach. In this work we focus on magnetoplasmon oscillations in this system and as such results are presented for the intra-Landau-band magnetoplasmon spectrum that exhibits oscillatory behavior, these oscillations are not with constant period in 1/B and are significantly effected…
Auger relaxation in 2D strongly correlated electron gas can be represented as an Auger-like process for neutral magnetoplasmon excitations. The case of "dielectric" state with lack of free electrons (i.e. at integer filling $ν$) is considered. Really the Auger-like process is a coalescence of two magnetoplasmons which are converted into a single one of a different plasmon mode with zero 2D wave-vector. This event turns out to be energetically allowed for magnetoplasmons near their roton minima where the spectrum has the infinite density of states. As a result the additional possibility appears…
Recent experiments have elucidated that novel nonequilibrium states inherent in the so-called hydrodynamic regime are realized in ultrapure metals with sufficiently strong momentum-conserving scattering. In this letter, we formulate a theory of electron hydrodynamics with broken inversion symmetry under magnetic fields and find that novel terms emerge in hydrodynamic equations which play a crucial role for the realization of the nonreciprocal responses. Specifically, we clarify that there exist a novel type of nonreciprocal collective modes dubbed nonreciprocal surface magnetoplasmons arising …
In this work we study magnetotransport properties in electronic double layers of strongly correlated electron liquids. For sufficiently clean high-mobility samples, the high-temperature regime of transport in these systems can be described in pure hydrodynamic terms. We concentrate on the magnetic field dependence of longitudinal drag effect mediated by the interlayer Coulomb scattering and identify several mechanisms of transresistance which is caused by viscous flows, magnetoplasmon resonance, and dissipative thermal fluxes. In particular, we elucidate how Hall viscosity enters magnetodrag a…
A two-dimensional electron gas in a static external magnetic field exhibits two distinct collective excitation modes. The lower frequency mode propagates along the periphery of the domain almost freely with an extended lifetime, which is referred to as edge magnetoplasmons. Peculiar phenomena caused by a capacitive interaction between nearest neighbor domains are known, such as the emergence of Tomonaga-Luttinger liquid and charge density fractionalization. Meanwhile, the number of coupled domains investigated in the past has been limited to a small number. Here, we performed calculations usin…
The discovery of the hydrodynamic electron liquid (HEL) in graphene [D. Bandurin \emph{et al.}, Science {\bf 351}, 1055 (2016) and J. Crossno \emph{et al.}, Science {\bf 351}, 1058 (2016)] has marked the birth of the solid-state HEL which can be probed near room temperature in a table-top setup. Here we examine the terahertz (THz) magneto-optical (MO) properties of a graphene HEL. Considering the case where the magnetic length $l_B=\sqrt{\hbar/eB}$ is comparable to the mean-free path $l_{ee}$ for electron-electron interaction in graphene, the MO conductivities are obtained by taking a momentum…
We calculate the low-frequency magnetoplasmon excitation spectrum for a square array of quantum dots on a two-dimensional (2D) graphene layer. The confining potential is linear in the distance from the center of the quantum dot. The electron eigenstates in a magnetic field and confining potential are mapped onto a 2D plane of electron-hole pairs in an effective magnetic field without any confinement. The tight-binding model for the array of quantum dots leads to a wavefunction with inter-dot mixing of the quantum numbers associated with an isolated quantum dot. For chosen confinement, magnetic…
Discussed in the present study are details of the behavior of low-frequency "acoustic" ($ac$) modes in the spectrum of edge magnetoplasma oscillations in axially symmetric degenerate 2D electron systems where electron density distribution $n(\vec r)$ behaves as $n(\vec r \to R)\to 0$ when $r$ approaches the external radius $R$ of the domain occupied by electrons. It is shown that finding the dependence of the spectrum of $ac$-modes on radial ($l$) and azimuthal ($m$) indices when both $l$ and $m$ are small requires axially symmetric solution of the relevant problem. The desires is achieved in …
Cavity modification of magnetoplasmon mode through coupling with intersubband polaritons
ETH Zürich（苏黎世联邦理工学院）；National Institute of Optics (CNR-INO)（意大利国家光学研究所）；School of Electronic and Electrical Engineering, University of Leeds（利兹大学电子与电气工程学院）；Department of Electrical and Computer Engineering, University of Waterloo（滑铁卢大学电气与计算机工程系）；Pitaevskii BEC Center, CNR-INO and Dipartimento di Fisica, Università di Trento（特伦托大学物理系及CNR-INO皮塔耶夫斯基玻色-爱因斯坦凝聚中心）；Centre de Nanosciences et de Nanotechnologies (C2N), CNRS UMR 9001, University of Paris-Saclay（巴黎萨克雷大学纳米科学与工程研究中心）
We show that near an armchair edge of a wide graphene channel, and in the presence of a smooth step-like electrostatic lateral confining potential, the chirality, spectrum, spatial structure, and number of the fundamental edge magnetoplasmons (EMPs), in the $ν=2$ regime of the quantum Hall effect, depend strongly on the position of the Fermi level $E_{F}$. (i) When $E_{F}$ is small enough and intersects four degenerate states of the zero Landau level (LL) at one location and two degenerate states of this level at a different one, two fundamental, counter propagating EMPs exist with opposite ch…
Massless Dirac electrons in graphene fill Landau levels with energies scaled as square roots of their numbers. Coulomb interaction between electrons leads to mixing of different Landau levels. The relative strength of this interaction depends only on dielectric susceptibility of surrounding medium and can be large in suspended graphene. We consider influence of Landau level mixing on the properties of magnetoexcitons and magnetoplasmons - elementary electron-hole excitations in graphene in quantizing magnetic field. We show that, at small enough background dielectric screening, the mixing lead…
We investigated theoretically the Coulomb drag effect in coupled 2D electron gases in a wide interval of magnetic field and temperature $ 1/τ\ll ω_c \ll E_F/\hbar$, $T \ll E_F$, $τ$ being intralayer scattering time, $ω_c$ being the cyclotron frequency. We show that the quantization of the electron spectrum leads to rich parametric dependences of drag transresistance on temperature and magnetic field. This is in contrast to usual resistance. New small energy scales are found to cut typical excitation energies to values lower than temperature. This may lead to a linear temperature dependence of …
Electronic Coulomb excitations in monolayer silicene are investigated by using the Lindhard dielectric function and a newly developed generalized tight-binding model (G-TBM). G-TBM simultaneously contains the atomic interactions, the spin-orbit coupling, the Coulomb interactions, and the various external fields at an arbitrary chemical potential. We exhibit the calculation results of the electrically tunable magnetoplasmons and the strong magnetic field modulation of plasmon behaviors. The two intriguing phenomena are well explained by determining the dominant transition channels in the dielec…
Inter-Landau-level transitions in the bilayer graphene at high perpendicular magnetic field at the filling-factor v<<1 have been studied. The next-nearest-neighbor transitions, energy difference between dimer and non-dimer sites and layer asymmetry are included. The influence of Coulomb interaction is taken into account. The magnetoplasmon excitations in bilayer graphene at small momenta are considered in the frame of the Hartree-Fock approximation. It is shown that asymmetry in cyclotron resonance of clean bilayer graphene depends on magnetic field. At lower magnetic fields the energy splitti…
The electromagnetic mode spectrum of single-layer graphene subjected to a quantizing magnetic field is computed taking into account intraband and interband contributions to the magneto-optical conductivity. We find that a sequence of weakly decaying quasi-transverse-electric modes, separated by magnetoplasmon polariton modes, emerge due to the quantizing magnetic field. The characteristics of these modes are tuneable, by changing the magnetic field or the Fermi energy.
Plasmons in two-dimensional electron systems with nonparabolic bands, such as graphene, feature strong dependence on electron-electron interactions. We use a many-body approach to relate plasmon dispersion at long wavelengths to Landau Fermi-liquid interactions and quasiparticle velocity. An identical renormalization is shown to arise for the magnetoplasmon resonance. For a model with N>>1 fermion species, this approach predicts a power-law dependence for plasmon frequency vs. carrier concentration, valid in a wide range of doping densities, both high and low. Gate tunability of plasmons in gr…
We present theoretical calculations for the cyclotron resonance and various magnetoplasmon modes of a Coulomb interacting two-dimensional GaAs electron gas (2DEG) modulated as a lateral superlattice of quantum dots subjected to an external perpendicular constant magnetic field. We use a real-time excitation approach based on the Liouville-von Neumann equation for the density operator, that can go beyond linear response delivering information of all longitudinal and transverse collective modes of interest to the same order. We perform an extensive analysis of the coexisting collective modes due…
We consider a graphene sheet encapsulated in a two-dimensional metallic grating and a substrate ($\mathrm{Al_{2}O_{3}}$) and subjected to an external magnetic field (in Faraday configuration). The grating consists of a thin perfectly conducting metal film perforated with a 2D periodic array of square holes. According to our calculations, significant changes in the spectra of the Faraday rotation angle of the transmitted wave and of the magnetic circular dichroism should be expected in this situation compared to bare graphene. We explain this enhancement by the excitation of graphene magnetopla…
We investigate the resonance energy transfer (RET) rate between two quantum emitters near a suspended graphene sheet in vacuum under the influence of an external magnetic field. We perform the analysis for low and room temperatures and show that, due to the extraordinary magneto-optical response of graphene, it allows for an active control and tunability of the RET even in the case of room temperature. We also demonstrate that the RET rate is extremely sensitive to small variations of the applied magnetic field, and can be tuned up to a striking six orders of magnitude for quite realistic valu…
Two-dimensional electron systems subjected to a perpendicular magnetic field absorb electromagnetic radiation via the cyclotron resonance (CR). Here we report a qualitative breach of this well-known behaviour in graphene. Our study of the terahertz photoresponse reveals a resonant burst at the main overtone of the CR, drastically exceeding the signal detected at the position of the ordinary CR. In accordance with the developed theory, the photoresponse dependencies on the magnetic field, doping level, and sample geometry suggest that the origin of this anomaly lies in the near-field magnetoabs…
Quantum wires occupy a unique status among the semiconducting nanostructures with reduced dimensionality -- no other system seems to have engaged researchers with as many appealing features to pursue. This paper aims at a core issue related with the magnetoplasmon excitations in the quantum wires characterized by the confining harmonic potential and subjected to a longitudinal electric field and a perpendicular magnetic field in the symmetric gauge. Despite the substantive complexity, we obtain the exact analytical expressions for the eigenfunction and eigenenergy, using the scheme of ladder o…
We study the frictional drag due to Coulomb and phonon mediated electron-electron interaction in a double layer electron system exposed to a perpendicular magnetic field. Within the random phase approximation we calculate the dispersion relation of the intra Landau level magnetoplasmons at finite temperatures and distinguish their contribution to the magnetodrag. We calculate the transresistivity $ρ_{Drag}$ as a function of magnetic field $B$, temperature $T$, and interlayer spacing $Λ$ for a matched electron density. For $Λ=200$ nm we find that $ρ_{Drag}$ is solely due to phonon exchange and …
Plasmons, which are collective charge oscillations, offer the potential to use optical signals in nano-scale electric circuits. Recently, plasmonics using graphene have attracted interest, particularly because of the tunable plasmon frequency through the carrier density $n$. However, the $n$ dependence of the plasmon velocity is weak ($\propto n^{1/4}$) and it is difficult to tune the frequency over orders of magnitude. Here, we demonstrate that the velocity of plasmons in graphene can be changed over two orders of magnitude by applying a magnetic field $B$ and by the presence/absence of a gat…
This article reviews the fundamental issues associated with the magnetoplasmon excitations investigated in a semiconducting quantum wire characterized by a harmonic confining potential and subjected to an applied (perpendicular) magnetic field. We embark on the charge-density excitations in a two-subband model within the framework of Bohm-Pines's random-phase approximation. The problem involves two length scales: ${\it l}_0=\sqrt{\hbar/m^*ω_0}$ and ${\it l}_c=\sqrt{\hbar/m^*ω_c}$, which characterize the strengths of the confinement and the magnetic field ($B$). Essentially, we focus on the dev…
The electronic properties of twisted bilayer graphene (TBG) can be dramatically different from those of a single graphene layer, in particular when the two layers are rotated relative to each other by a small angle. TBG has recently attracted a great deal of interest, sparked by the discovery of correlated insulating and superconducting states, for twist angle $θ$ close to a so-called 'magic angle' $\approx 1.1°$. In this work, we unveil, via near-field optical microscopy, a collective plasmon mode in charge-neutral TBG near the magic angle, which is dramatically different from the ordinary si…
