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S. A. Mikhailov

Publications and source records attributed to S. A. Mikhailov.

At least 19 recordsLinked to original sources
arXiv2024

Toward a new theory of the fractional quantum Hall effect

The fractional quantum Hall effect was experimentally discovered in 1982. It was observed that the Hall conductivity $σ_{yx}$ of a two-dimensional electron system is quantized, $σ_{yx}=e^2/3h$, in the vicinity of the Landau level filling factor $ν=1/3$. In 1983, Laughlin proposed a trial many-body wave function, which he claimed described a ``new state of matter'' -- a homogeneous incompressible liquid with fractionally charged quasiparticles. Here I develop an exact diagonalization theory that allows calculation of the energy and other physical properties of the ground and excited states of a system of $N$ two-dimensional Coulomb interacting electrons in a strong magnetic field. I analyze the energies, electron densities, and other physical properties of the systems with $N\le 7$ electrons, continuously as a function of magnetic field in the range $1/4\lesssimν<1$. The results show that both the ground and excited states of the system resemble a sliding Wigner crystal, whose parameters are influenced by the magnetic field. Energy gaps in the many-particle spectra appear and disappear as the magnetic field changes. I also calculate the physical properties of the $ν=1/3$ Laughlin state for $N\le 8$ and show that neither this state nor its fractionally charged excitations describe the physical reality. The results obtained shed new light on the nature of the ground and excited states in the fractional quantum Hall effect.

cond-mat.mes-hall↗
arXiv2023

Theory of the in-plane photoelectric effect in quasi-one-dimensional electron systems

The in-plane photoelectric (IPPE) effect is a recently discovered [Sci. Adv. \textbf{8}, eabi8398 (2022)] quantum phenomenon which enables efficient detection of terahertz (THz) radiation in semiconductor structures with a two-dimensional (2D) electron gas. Here we develop a theory of the IPPE effect in quasi-one-dimensional electron systems in which the width of the 2D conducting channel is so small that the transverse quantization energy is larger than the thermal energy. We calculate the THz photoresponse of such a system, as a function of the THz frequency, control gate voltages, and geometrical parameters of the detector. We show that the transverse quantization of the electron motion manifests itself in oscillating gate-voltage dependences of the photocurrent, if the THz photon energy is less than the one-dimensional quantization energy. Results of the theory are applicable to any semiconductor systems with 2D electron gases, including III-V structures, silicon-based field effect transistors, and the novel 2D layered, graphene-related materials.

cond-mat.mes-hall↗
arXiv2022

Theory of the in-plane photoelectric effect in two-dimensional electron systems

A new photoelectric phenomenon, the in-plane photoelectric (IPPE) effect, has been recently discovered at terahertz (THz) frequencies in a GaAs/Al$_x$Ga$_{1-x}$As heterostructure with a two-dimensional (2D) electron gas (W. Michailow et al., Sci. Adv. \textbf{8}, eabi8398 (2022)). In contrast to the conventional PE phenomena, the IPPE effect is observed at normal incidence of radiation, the height of the in-plane potential step, which electrons overcome after absorption of a THz photon, is electrically tunable by gate voltages, and the effect is maximal at a negative electron ``work function'', when the Fermi energy lies above the potential barrier. Based on the discovered phenomenon, efficient detection of THz radiation has been demonstrated. In this work we present a detailed theory of the IPPE effect providing analytical results for the THz wave generated photocurrent, the quantum efficiency, and the internal responsivity of the detector, in dependence on the frequency, the gate voltages, and the geometrical parameters of the detector. The calculations are performed for macroscopically wide samples at zero temperature. Results of the theory are applicable to any semiconductor systems with 2D electron gases, including III-V structures, silicon-based field effect transistors, and the novel 2D layered, graphene-related materials.

cond-mat.mes-hall↗
arXiv2021

Nonperturbative quasiclassical theory of graphene photoconductivity

We present a nonperturbative quasi-classical theory of graphene photoconductivity. We consider the influence of low-frequency (microwave, terahertz, mid-infrared) radiation on the static conductivity of a uniform graphene layer and calculate its photoconductivity as a function of frequency, polarization and strength of the external ac electric field, as well as on the material properties (electron density, scattering time) and temperature. The theory is valid at frequencies $\hbarω\lesssim 2E_F$ and at arbitrarily strong ac electric fields. We compare our results with those of the third-order perturbation theory and determine the applicability range of the perturbative solutions.

cond-mat.mes-hall↗
arXiv2019

Theory of the strongly nonlinear electrodynamic response of graphene: A hot electron model

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 as of the ratio $τ_ε/τ_{\rm rec}$ of the intra-band energy relaxation time $τ_ε$ to the recombination time $τ_{\rm rec}$. The influence of the radiation intensity on the absorption coefficient $A$ at low ($\hbarω\lesssim 2|μ_0|$, $dA/dI>0$) and high ($\hbarω\gtrsim 2|μ_0|$, $dA/dI<0$) frequencies is studied. The results are shown to be in good agreement with recent experimental data.

cond-mat.mes-hall↗
arXiv2019

Equations of macroscopic electrodynamics for two-dimensional crystals

The electrodynamics of two-dimensional (2D) dielectric and conducting layers cannot be described by such three-dimensional macroscopic quantities as the dielectric constant $ε$ or the refractive index $n$. By means of the proper averaging of the microscopic Maxwell equations we derive general macroscopic electrodynamic equations for 2D crystals and discuss some of their consequences.

cond-mat.mes-hall↗
arXiv2018

Nonlinear Electrodynamics and Optics of Graphene

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.

cond-mat.mes-hall↗
arXiv2018

Graphene for Emission of Terahertz Radiation

Graphene is a two-dimensional crystal consisting of a monatomic layer of carbon atoms. Electrons and holes in graphene behave as quasi-relativistic particles with zero effective mass and large (as compared to semiconductors) Fermi velocity. These unique physical properties can be used for designing detectors, emitters and modulators of terahertz radiation. Here we discuss several ideas of using graphene based structures for emission of terahertz radiation.

cond-mat.mes-hall↗
arXiv2018

Negative dynamic conductivity of a current driven array of graphene nanoribbons

We consider a periodic array of graphene nanoribbons under the action of a strong dc electric field $E_0$ and an external electromagnetic excitation with the frequency $ω$ and the lateral wave vector $q$. Solving the quasi-classical Boltzmann kinetic equation and calculating the surface dynamic conductivity $σ_{2D}(q,ω,E_0)$ and the absorption coefficient of such a system we show that the real part of the conductivity and the absorption coefficient may become negative under certain conditions. Physically this corresponds to the amplification of the electromagnetic waves at the expense of the energy of the direct current source. The results are discussed in connection with experiments on the surface acoustic waves and on the Smith-Purcell-type graphene-based terahertz emitter.

cond-mat.mes-hall↗
arXiv2018

Nonperturbative quasi-classical theory of the nonlinear electrodynamic response of graphene

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 radiation and of the ratio of the radiative to scattering damping rates. We show that the optical bistability effect, predicted in Phys. Rev. B 90, 125425 (2014) on the basis of a perturbative approach, disappears when the problem is solved exactly. We show that, under the action of a high-power radiation ($\gtrsim 100$ kW/cm$^2$) both the reflection and absorption coefficients strongly decrease and the layer becomes transparent.

cond-mat.mes-hall↗
arXiv2018

Optical Kerr Effect in Graphene: Theoretical Analysis of the Optical Heterodyne Detection Technique

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 nonlinear electrodynamic response of graphene we analyze the frequency, charge carrier density, temperature and other dependencies of the OHD-OKE response of this material. We compare our results with a recent OHD-OKE experiment in graphene and find good agreement between the theory and experiment.

cond-mat.mes-hall↗
arXiv2017

Influence of optical nonlinearities on plasma waves in graphene

A theory of the nonlinear plasma waves in graphene is developed in the nonperturbative regime. The influence of strong electric fields on the position and linewidth of plasma resonances in the far-infrared transmission experiments, as well as on the wavelength and the propagation length in the scanning near-field optical microscopy experiments is studied. The theory shows that the fields of order of a few to a few tens of kV/cm should lead to a red shift and broadening of plasma resonances in the first type and to a reduction of the wavelength and the propagation length in the second type of experiments.

cond-mat.mes-hall↗
arXiv2017

Electrically Tunable Optical Nonlinearities in Graphene-Covered SiN Waveguides Characterized by Four-Wave Mixing

We present a degenerate four-wave mixing experiment on a silicon nitride (SiN) waveguide covered with gated graphene. We observe strong dependencies on signal-pump detuning and Fermi energy, i.e. the optical nonlinearity is demonstrated to be electrically tunable. In the vicinity of the interband absorption edge ($2|E_F|\approx \hbarω$) a peak value of the waveguide nonlinear parameter of $\approx$ 6400 m$^{-1}$W$^{-1}$, corresponding to a graphene nonlinear sheet conductivity $|σ_s^{(3)}|\approx4.3\cdot 10^{-19}$ A m$^2$V$^{-3}$ is measured.

physics.optics↗
arXiv2017

Giant microwave-induced $B$-periodic magnetoresistance oscillations in a two-dimensional electron gas with a bridged-gate tunnel point contact

We have studied the magnetoresistance of the quantum point contact fabricated on the high mobility two-dimensional electron gas (2DEG) exposed to microwave irradiation. The resistance reveals giant $B$-periodic oscillations with the relative amplitude $ΔR/R$ of up to $700$\% resulting from the propagation and interference of the edge magnetoplasmons (EMPs) in the sample. This giant photoconductance is attributed to the considerably large local electron density modulation in the vicinity of the point contact. We have also analyzed the oscillation periods $ΔB$ of the resistance oscillations and, comparing the data with the EMP theory, extracted the EMP interference length $L$. We have found that the length $L$ substantially exceeds the distance between the contact leads but rather corresponds to the distance between metallic contact pads measured along the edge of the 2DEG. This resolves existing controversy in the literature and should help to properly design highly sensitive microwave and terahertz spectrometers based on the discussed effect.

cond-mat.mes-hall↗
arXiv2016

Third harmonic generation from graphene lying on different substrates: Optical-phonon resonances and interference effects

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 side. In some frequency intervals, the presence of the polar dielectric substrate compensates the strongly decreasing with $ω$ frequency dependence of the third-order conductivity of graphene making the response almost frequency independent.

cond-mat.mes-hall↗
arXiv2016

Quantum theory of the third-order nonlinear electrodynamic effects in graphene

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.

cond-mat.mes-hall↗
arXiv2015

Giant enhancement of the third harmonic in graphene integrated in a layered structure

Graphene was shown to have strongly nonlinear electrodynamic properties. In particular, being irradiated by an electromagnetic wave with the frequency $ω$, it can efficiently generate higher frequency harmonics. Here we predict that in a specially designed structure "graphene -- dielectric -- metal" the third-harmonic ($3ω$) intensity can be increased by more than two orders of magnitude as compared to an isolated graphene layer.

cond-mat.mes-hall↗