The linear energy dispersion of graphene electrons leads to a strongly nonlinear electromagnetic response of this material. We develop a general quantum theory of the third-order nonlinear local dynamic conductivity of graphene $σ_{αβγδ}(ω_1,ω_2,ω_3)$, which describes its nonlinear response to a uniform electromagnetic radiation. The derived analytical formulas describe a large number of different nonlinear phenomena such as the third harmonic generation, the four wave mixing, the saturable absorption, the second harmonic generation stimulated by a dc electric current, etc., which may be used in different terahertz and optoelectronic devices.
Graphene is a two-dimensional material with strongly nonlinear electrodynamics and optical properties. We present some of our recent theoretical results on the quantum and non-perturbative quasi-classical theories of nonlinear effects in graphene, influence of substrates on graphene nonlinearities, plasma oscillations in graphene in the nonlinear regime and other effects.
Graphene, the first truly two-dimensional (one atom thin) material, possesses strongly nonlinear electrodynamic and optical properties. At low (microwave, terahertz) frequencies this results from the unique electronic property of graphene - the "relativistic", linear energy dispersion of its electrons and holes. At high (infrared, visible) frequencies its nonlinear response functions have resonances due to the inter-band transitions between the electron and hole bands. The position of these resonances on the frequency axis depends on the Fermi energy, or the charge carrier density, which can b…
We show that an energy gap is induced in graphene by light-matter coupling to a circularly polarized photon mode in a cavity. Using many-body perturbation theory we compute the electronic spectra which exhibit photon-dressed sidebands akin to Floquet sidebands for laser-driven materials. In contrast with Floquet topological insulators, in which a strictly quantized Hall response is induced by light only for off-resonant driving in the high-frequency limit, the photon-dressed Dirac fermions in the cavity show a quantized Hall response characterized by an integer Chern number. Specifically for g…
Graphene bilayers with layer antisymmetric strains are studied using the Dirac-Harper model for a pair of single layer Dirac Hamiltonians coupled by a one-dimensional moiré-periodic interlayer tunneling amplitude. This model hosts low energy, nearly dispersionless bands near charge neutrality that support anomalous polarizations of its charge multipole distributions. These are analyzed introducing a generalized Berry curvature that encodes the field-induced dynamics of multipole fields allowed in a chiral medium with time reversal symmetry. The formulation identifies a reciprocity relation bet…
An electromagnetic response of a single graphene layer to a uniform, arbitrarily strong electric field $E(t)$ is calculated by solving the kinetic Boltzmann equation within the relaxation-time approximation. The theory is valid at low (microwave, terahertz, infrared) frequencies satisfying the condition $\hbarω\lesssim 2E_F$, where $E_F$ is the Fermi energy. We investigate the saturable absorption and higher harmonics generation effects, as well as the transmission, reflection and absorption of radiation incident on the graphene layer, as a function of the frequency and power of the incident r…
A Lorentz invariant version of a mass-gap graphene-like planar quantum electrodynamics, the parity-preserving $U(1)\times U(1)$ massive QED$_3$, exhibits attractive interaction in low-energy electron-polaron--electron-polaron $s$-wave scattering, favoring quasiparticles bound states, the $s$-wave bipolarons.
Quantum Electrodynamics of graphene Landau levels in a deep-subwavelength hyperbolic phonon polariton cavity
JEIP, UAR 3573 CNRS, Collège de France, PSL Research University（法国高等科学研究所、巴黎文理研究大学）；ICFO - Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology（巴塞罗那光子科学研究院、巴塞罗那科学技术研究院）；Dipartimento di Fisica dell’Università di Pisa（比萨大学物理系）；ICREA-Institució Catalana de Recerca i Estudis Avançats（加泰罗尼亚高级研究学院）
We extend the electrodynamics of two dimensional electron gases to account for the extrinsic spin Hall effect (SHE). The theory is applied to doped graphene decorated with a random distribution of absorbates that induce spin-orbit coupling (SOC) by proximity. The formalism extends previous semiclassical treatments of the SHE to the non-local dynamical regime. Within a particle-number conserving approximation, we compute the conductivity, dielectric function, and spin Hall angle in the small frequency and wave vector limit. The spin Hall angle is found to decrease with frequency and wave number…
An electrodynamic response of graphene to a strong electromagnetic radiation is considered. A hot electron model (HEM) is introduced and a corresponding system of nonlinear equations is formulated. Solutions of this system are found and discussed in detail for intrinsic and doped graphene: the hot electron temperature, non-equilibrium electron and holes densities, absorption coefficient and other physical quantities are calculated as functions of the incident wave frequency $ω$ and intensity $I$, of the equilibrium chemical potential $μ_0$ and temperature $T_0$, scattering parameters, as well …
We show that the Higgs mode of a superconductor, which is usually challenging to observe by far-field optics, can be made clearly visible using near-field optics by harnessing ultraconfined graphene plasmons. As near-field sources we investigate two examples: graphene plasmons and quantum emitters. In both cases the coupling to the Higgs mode is clearly visible. In the case of the graphene plasmons, the coupling is signaled by a clear anticrossing stemming from the interaction of graphene plasmons with the Higgs mode of the superconductor. In the case of the quantum emitters, the Higgs mode is…
We compute the terahertz third-order nonlinear conductance of metallic armchair graphene nanoribbons using time-dependent perturbation theory. Significant enhancement of the intrinsic third-order conductance over the result for instrinsic 2D single-layer graphene is observed over a wide range of temperatures. We also investigate the nonlinear response of extrinsic metallic acGNR with |E_F|<<200 meV. We find that the third-order conductance exhibits a strong Fermi level dependence at low temperatures. A third-order critical field strength of between 1 and 5 kV/m is computed for the Kerr conduct…
We present a finite-temperature diagrammatic perturbation theory of third harmonic generation (THG) in doped graphene. We carry out calculations of the third-order conductivity in the scalar potential gauge, highlighting a subtle cancellation between a Fermi surface contribution, which contains only power laws, and power-law contributions of inter-band nature. Only logarithms survive in the final result. We conclude by presenting quantitative results for the up-conversion efficiency at zero and finite temperature. Our results shed light on the on-going dispute over the dependence of THG on car…
A non-perturbative model for graphene optical nonlinearity is developed for the study of ultrafast pulse propagation along a monolayer, as in the case of graphene-comprising nanophotonic integrated waveguides. This graphene `hot electron' model (GHEM) builds upon earlier work, based on the Fermi-Dirac framework for 2D semiconductors, which was aimed mainly at steady-state absorptive response of a monolayer under free-space laser-beam illumination. Our extension adapts the GHEM to in-plane light-matter interaction along graphene monolayers under intense ps-pulse excitation that leads to the car…
Materials with massless Dirac fermions can possess exceptionally strong and widely tunable optical nonlinearities. Experiments on graphene monolayer have indeed found very large third-order nonlinear responses, but the reported variation of the nonlinear optical coefficient by orders of magnitude is not yet understood. A large part of the difficulty is the lack of information on how doping or chemical potential affects the different nonlinear optical processes. Here we report the first experimental study, in corroboration with theory, on third harmonic generation (THG) and four-wave mixing (FW…
Electromagnetic waves reflection, transmission and absorption by graphene - magnetic semiconductor - graphene sandwich-structure in magnetic field: Faraday geometry
The electrical conductivity of graphene with a nonzero mass-gap parameter is investigated starting from the first principles of quantum electrodynamics in (2+1)-dimensional space-time at any temperature. The formalism of the polarization tensor defined over the entire plane of complex frequency is used. At zero temperature we reproduce the results for both real and imaginary parts of the conductivity, obtained previously in the local approximation, and generalize them taking into account the effects of nonlocality. At nonzero temperature the exact analytic expressions for real and imaginary pa…
Using the microscopic nonlinear quantum theory of interaction of strong coherent electromagnetic radiation with a gapped bilayer graphene is developed for high harmonic generation at low-energy photon excitation-induced Lifshitz transitions. The Liouville-von Neumann equation for the density matrix is solved numerically at the nonadiabatic multiphoton excitation regime. By numerical solutions, we examine the rates of the second and third harmonics generation at the particle-hole annihilation in induced Lifshitz transitions by the two linearly polarized coherent electromagnetic waves propagatin…
The low-energy (intraband) range of the third harmonic generation of graphene in the terahertz regime is governed by the damping terms induced by the interactions. A controlled many-body description of the scattering processes is thus a compelling and desirable requirement. In this paper, using a Kadanoff-Baym approach, we systematically investigate the impact of many-body interaction on the third-harmonic generation (THG) of graphene, taking elastic impurity scattering as a benchmark example. We predict the onset in the mixed inter-intraband regime of novel incoherent features driven by the i…
Strongly nonlinear Bernstein modes in graphene reveal plasmon-enhanced near-field magnetoabsorption
University of Regensburg（雷根斯堡大学）；Institute of High Pressure Physics of the Polish Academy of Sciences（波兰科学院高压物理研究所）；National University of Singapore（新加坡国立大学）；Faculty of Physics, Ivan Franko National University of Lviv（利沃夫伊万·弗兰科国立大学物理学院）
The ab initio band structure of 2D graphene sheet is well reproduced by the third nearest neighbor tight binding model proposed by Reich et al [Phys. Rev. B 66, 035412]. For ribbon structures, the existing sets of tight binding parameters can successfully explain semi-conducting behavior of all armchair ribbon structures. However, they are still failing in describing accurately the slope of the bands while this feature is directly associated to the group velocity and the effective mass of electrons. In this work, both density functional theory and tight binding calculations were performed and …
Graphene is a nonlinear material which can be used as a saturable absorber, frequency mixer and frequency multiplier. We investigate the third harmonic generation from graphene lying on different substrates, consisting of a dielectric (dispersionless or polar), metalized or non-metalized on the back side. We show that the third harmonic intensity emitted from graphene lying on a substrate, can be increased by orders of magnitude as compared to the isolated graphene, due the LO-phonon resonances in a polar dielectric or due to the interference effects in the substrates metalized on the back sid…
We study narrow zigzag graphene nanoribbons (ZGNRs), employing density functional theory (DFT) simulations and the tight-binding (TB) method. The main result of these calculations is the braiding of the conduction and valence bands, generating Dirac cones for non-commensurate wave vectors $\vec{k}$. Employing a TB Hamiltonian, we show that the braiding is generated by the third-neighbor hopping (N3). We calculate the band structure, the density of states and the conductance, new conductance channels are opened, and the conductance at the Fermi energy assumes integer multiples of the quantum co…
Static Non-linearity in Graphene Field Effect Transistors
研究了GFET跨导器的静态线性性能指标，并建立了模型。给出了二阶和三阶谐波失真（HD 2、HD 3）、二阶和三阶互调失真（Δ IM 2、Δ IM 3）以及二阶和三阶交截点（AIIP 2、AIIP 3）的闭合表达式。通过使用GFET VerilogA分析模型和商业电路模拟器的大信号仿真验证的表达式。所提出的表达式可以在电路设计过程中使用，以预测GFET的偏置条件下，满足线性度要求。
Nonlinear nanophotonics leverages engineered nanostructures to funnel light into small volumes and intensify nonlinear optical processes with spectral and spatial control. Due to its intrinsically large and electrically tunable nonlinear optical response, graphene is an especially promising nanomaterial for nonlinear optoelectronic applications. Here we report on exceptionally strong optical nonlinearities in graphene-insulator-metal heterostructures, demonstrating an enhancement by three orders of magnitude in the third-harmonic signal compared to bare graphene. Furthermore, by increasing the…
In this work, we present numerical results for the second and third order conductivities of the plain graphene and gapped graphene monolayers associated with the second and third harmonic generation, the optical rectification and the optical Kerr effect. The frequencies considered here range from the microwave to the ultraviolet portion of the spectrum, the latter end of which had not yet been studied. These calculations are performed in the velocity gauge and directly address the components of the conductivity tensor. In the velocity gauge, the radiation field is represented by a power series…
We devise a theory of adsorption of low-energy atoms on suspended graphene membranes maintained at 10 K based on a model of atom-acoustic phonon interactions. Our primary technique includes a non-perturbative method which treats the dynamics of the multiple phonons in an exact manner within the purview of the Independent Boson Model. We present a study on the effects of the phonons assisting the renormalization as well as decay of the incident atom propagator and discuss results for the many-body adsorption rates for atomic hydrogen on graphene micromembranes. Additionally, we report similarit…
Graphene as a zero-bandgap two-dimensional semiconductor with a linear electron band dispersion near the Dirac points has the potential to exhibit very interesting nonlinear optical properties. In particular, third harmonic generation of terahertz radiation should occur due to the nonlinear relationship between the crystal momentum and the current density. In this work, we investigate the terahertz nonlinear response of graphene inside a parallel-plate waveguide. We optimize the plate separation and Fermi energy of the graphene to maximize third harmonic generation, by maximizing the nonlinear…
The field theoretic renormalization study of reduced quantum electrodynamics (QED) is performed up to two loops. In the condensed matter context, reduced QED constitutes a very natural effective relativistic field theory describing (planar) Dirac liquids, e.g., graphene and graphene-like materials, the surface states of some topological insulators and possibly half-filled fractional quantum Hall systems. From the field theory point of view, the model involves an effective (reduced) gauge field propagating with a fractional power of the d'Alembertian in marked contrast with usual QEDs. The use …
Due to its linear dispersion, monolayer graphene is expected to generate a third harmonic response at terahertz frequencies. There have been a variety of different models of this effect and recently it has been experimentally observed. However, there is still considerable uncertainty as to the role of scattering on harmonic generation in graphene. In this work, we model third-harmonic generation in doped monolayer graphene at THz frequencies by employing a nearest-neighbour tight-binding model in the length gauge. We include optical phonon and neutral impurity scattering at the microscopic lev…
Hot electrons dominate the ultrafast ($\sim$fs-ps) optical and electronic properties of metals and semiconductors and they are exploited in a variety of applications including photovoltaics and photodetection. We perform power-dependent third harmonic generation measurements on gated single-layer graphene and detect a significant deviation from the cubic power-law expected for a third harmonic generation process. We assign this to the presence of hot electrons. Our results indicate that the performance of nonlinear photonics devices based on graphene, such as optical modulators and frequency c…
An approach that has been given promising results concerning investigations on the physics of graphene is the so-called reduced quantum electrodynamics. In this work we consider the natural generalization of this formalism to curved spaces. We employ the local momentum space representation. We discuss the validity of the Ward identity and study one-loop diagrams in detail. We show that the one-loop beta function is zero. As an application, we calculate the one-loop optical conductivity of graphene by taking into account curvature effects which can be incorporated locally. In addition, we demon…
We use an on-chip superconducting resonator as a sensitive meter to probe the properties of graphene double quantum dots at microwave frequencies. Specifically, we investigate the charge dephasing rates in a circuit quantum electrodynamics architecture. The dephasing rates strongly depend on the number of charges in the dots, and the variation has a period of four charges, over an extended range of charge numbers. Although the exact mechanism of this fourfold periodicity in dephasing rates is an open problem, our observations hint at the fourfold degeneracy expected in graphene from its spin a…
Graphene is an atomically thin two-dimensional material demonstrating strong optical nonlinearities including harmonics generation, four wave mixing, Kerr and other nonlinear effects. In this paper we theoretically analyze the optical heterodyne detection (OHD) technique of measuring the optical Kerr effect (OKE) in two-dimensional crystals and show how to relate the quantities measured in such experiments with components of the third-order conductivity tensor $σ^{(3)}_{αβγδ}(ω_1,ω_2,ω_3)$ of the two-dimensional crystal. Using results of a recently developed quantum theory of the third-order n…
A manifestation of electron-hole pairing in nonlinear electromagnetic response of a double layer graphene system is studied. It is shown that the pairing causes the appearance of a number of peaks in the frequency dependence of the intensity of the third harmonic generation (THG). The highest peak corresponds to \hbarω= (2/3)Δ, where ω is the incident wave frequency, and Δ is the order parameter of the electron-hole pairing. The absolute value of the THG intensity in the systems with electron-hole pairing is in several orders of magnitude greater than the THG intensity in the unpaired state. I…
