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Dispersion equations are a common paradigm of collective excitation physics. However, in some systems, dispersion equations contain multivalued functions and their solutions are ambiguous. As an example, we consider graphene on a polar substrate where Dirac plasmons are coupled with surface optical phonons. The dispersion equation for this system contains square-root singularity. Using the initial value problem resolves this uncertainty and gives a unique solution. Particularly, we found that lower plasmon-phonon mode, which in terms of dispersion can have a good quality factor, is almost absent in excitation spectra. The physical reason and experimental evidence of the mode collapse are discussed., Comment: 6 pages, 3 figures, and supplemental material

A number of novel two-dimensional materials and nanostructures demonstrate complex single-electron energy dispersion, which is called the mexican-hat dispersion. In this paper, we analyze interaction of a pair of electrons with such an energy dispersion. We show that relative motion of the electron pair is of a very peculiar character. For example, the real space trajectories corresponding to electron-electron scattering can have three reversal points, reversal points at non-zero radial momentum and other unusual features. Despite the repulsive Coulomb interaction, two electrons can be coupled forming a composite quasi-particle - the bi-electron. The bi-electron corresponds to excited states of the two-electron system. Because the bi-electron coupled states exist in continuum of extended (free) states of the electron pair, these states are quasi-resonant and have finite times of life. We found that rotating bi-electron is a long-living composite quasi-particle. The rotating bi-electrons can be in motion. For slowly moving bi-electrons, we determined the kinetic energy and the effective mass. Due to strongly nonparabolic energy dispersion, the translational motion of the bi-electron is coupled to its internal motion. This results in effective masses dependent on quantum states of the bi-electron. In the paper, properties of the bi-electron are illustrated for the example of bigraphene in a transverse electric field., Comment: 13 pages, 4 figures

We investigate ultra-high frequency electrical properties of nanoscale $n^+$-$i$-$n^+$ diodes made of polar semiconductors. The calculations show that the coupling between optical vibrations of the lattice and the ballistic electrons strongly modifies and enhances the time-of-flight effects giving rise to narrow resonances of the diode impedance in the reststrahlen frequency range. Particularly, negative dynamic resistance is induced in close proximity to the optical phonon frequency. The resonant effects in the dynamic resistance of nanoscale GaAs and InP diodes are studied in detail. The obtained magnitudes of the negative dynamic resistance effect indicate that the nanoscale diodes are capable of generating electromagnetic radiation in far-infrared spectral range under electric pumping.

We studied the diffusion coefficient of hot electrons of GaN crystals in moderate electric (1...10 kV/cm) and magnetic (1...4 T) fields. Two configurations, parallel and crossed fields, are analysed. The study was carried out for compensated bulk-like GaN samples at different lattice temperatures (30...300 K) and impurity concentrations (10^16..10^17 cm^{-3}). We found that at low lattice temperatures and low impurity concentrations, electric-field dependencies of the transverse-to-current components of the diffusion tensor are non-monotonic for both configurations, while the diffusion processes are greatly controlled by the magnetic field. With an increase of the lattice temperature or the impurity concentration, the behaviour of the diffusion tensor becomes more monotonous and less affected by the magnetic field. We showed that such behaviour of the diffusion processes is due to the distinct kinetics of the hot electrons in polar semiconductors with strong electron-optical phonon coupling. We suggest that measurements of the diffusion coefficient of the electrons subjected to electric and magnetic fields facilitate the identification of features of different electron transport regimes and the development of more efficient devices and practical applications.

We present the analysis of high-frequency (dynamic) conductivity with the spatial dispersion, $\sigma (\omega, {\bf q})$, of two-dimensional electron gas subjected to a high electric field. We found that at finite wavevector, ${\bf q}$, and at high fields, the high-frequency conductivity shows following peculiarities: strong non-reciprocal dispersion; oscillatory behavior; a set of frequency regions with negative $\sigma'$; non-exponential decay of $\sigma'$ and $\sigma''$ with frequency (opposite to the Landau damping mechanism). We illustrate the general results by calculations of spectral characteristics of particular plasmonic heterostructures on the basis of III-V semiconductor compounds. We conclude that the detailed analysis of the spatial dispersion of the dynamic conductivity of 2DEG subjected to high electric fields is critically important for different THz applications.

We report the results of Monte Carlo simulation of electron dynamics in stationary and space- and time-dependent electric fields in compensated GaN samples. We have determined the frequency and wavevector dependencies of the dynamic conductivity, $\sigma_{\omega,q}$. We have found that the spatially dependent dynamic conductivity of the drifting electrons can be negative under stationary electric fields of moderate amplitudes, $2..5$ kV/cm. This effect is realized in a set of frequency windows. The low-frequency window with negative dynamic conductivity is due to the Cherenkov mechanism. For this case the time-dependent field induces a {\it traveling wave} of the electron concentration in real space and a {\it standing wave} in the energy/momentum space. The higher frequency windows of negative dynamic conductivity are associated with the optical phonon transient time resonances. For this case the time-dependent field is accompanied by oscillations of the electron distribution in the form of the {\it traveling} waves in both the real space and the energy/momentum space. We discuss the optimal conditions for the observation of these effects. We suggest that the studied negative dynamic conductivity can be used to amplify electromagnetic waves at the expense of energy of the stationary field and current.

We studied electric current and noise in planar GaN nanowires (NWs). The results obtained at low voltages provide us with estimates of the depletion effects in the NWs. For larger voltages, we observed the space-charge limited current (SCLC) effect. The onset of the effect clearly correlates with the NW width. For narrow NWs the mature SCLC regime was achieved. This effect has great impact on fluctuation characteristics of studied NWs. At low voltages, we found that the normalized noise level increases with decreasing NW width. In the SCLC regime, a further increase in the normalized noise intensity (up to 1E4 times) was observed, as well as a change in the shape of the spectra with a tendency towards slope -3/2. We suggest that the features of the electric current and noise found in the NWs are of a general character and will have an impact on the development of NW-based devices., Comment: 12 pages, 4 figures in Fluctuation and Noise Letters (2017)

We study theoretically wave-vector and frequency dispersion of the complex dynamic conductivity tensor (DCT), $\sigma_{lm}(\mathbf{k}, \omega)$, of doped monolayer graphene under a strong dc electric field. For a general analysis, we consider the weak ac field of arbitrary configuration given by two independent vectors, the ac field polarization and the wave vector $\mathbf{k}$. The high-field transport and linear response to the ac field are described on the base of the Boltzmann kinetic equation. We show that the real part of DCT, calculated in the collisionless regime, is not zero due to dissipation of the ac wave, whose energy is absorbed by the resonant Dirac quasiparticles effectively interacting with the wave. The role of the kinematic resonance at $\omega = v_F |{\bf k}|$ ($v_{F}$ is the Fermi velocity) is studied in detail taking into account deviation from the linear energy spectrum and screening by the charge carriers. The isopower-density curves and distributions of angle between the ac current density and field vectors are presented as a map which provides clear graphic representation of the DCT anisotropy. Also, the map shows certain ac field configurations corresponding to a negative power density, thereby it indicates regions of terahertz frequency for possible electrical (drift) instability in the graphene system., Comment: 32 pages, 9 figures, accepted to Physica E: Low-dimensional Systems and Nanostructures

Solving the initial value problem for semiclassical equations that describe two-dimensional electrons with the Dirac spectrum we found that collective excitations of the electrons are composed by a few distinct components of the oscillations. There always exist sustained plasma oscillations with well known plasmon frequency $\omega_{pl}(k)$. Additionally there are oscillations with the 'carrier frequency' $\omega = v_Fk$ slowly decaying in time according to a power law ($v_F$ and $k$ are the Fermi velocity and wavevector). The reason for onset of these oscillations has a fundamental character related to branching of the polarization function of the Dirac electrons. A strongly anisotropic initial disturbance of the electron distribution generates additional component of undamped oscillations in the form of an electron unidirectional beam which are van Kampen's modes in the Dirac plasma., Comment: 6 pages, 1 figure. Accepted for publication as a Rapid Communication in Physical Review B http://journals.aps.org/prb/accepted/c607bYa2P881f45478ef4333f007eada2f8fadc73

We have studied the high-frequency properties of the non-equilibrium electron gas in GaN samples subjected to electric and magnetic fields. Spectra of the complex tensor of the dynamical mobility have been calculated for THz frequency range. For the compensated GaN and low temperatures, in the intervals of electric fields of the few $kV/cm$ and magnetic fields of the few $T$ the existence of the cyclotron and optical phonon transit-time resonances has been identified. We have shown that interplay of two resonances gives rise to specific spectra of THz transmission and absorption (or gain). We suggest that experimental investigation of these effects will facilitate elaboration of field controlled devices for THz optoelectronics., Comment: 15 pages, 5 figures

We have analyzed low-temperature behavior of two-dimensional electron gas in polar heterostructures subjected to a high electric field. When the optical phonon emission is the fastest relaxation process, we have found existence of collective wave-like excitations of the electrons. These wave-like excitations are periodic in time oscillations of the electrons in both real and momentum spaces. The excitation spectra are of multi-branch character with considerable spatial dispersion. There are one acoustic-type and a number of optical-type branches of the spectra. Their small damping is caused by quasi-elastic scattering of the electrons and formation of relevant space charge. Also there exist waves with zero frequency and finite spatial periods - the standing waves. The found excitations of the electron gas can be interpreted as synchronous in time and real space manifestation of well-known optical-phonon-transient-time-resonance. Estimates of parameters of the excitations for two polar heterostructures, GaN/AlGaN and ZnO/MgZnO, have shown that excitation frequencies are in THz-frequency range, while standing wave periods are in sub-micrometer region., Comment: 26 pages and 6 figures

A hybrid system composed of an isotropic nanoparticle and a semiconductor heterostructure with a quantum well has been considered. The nanoparticle is supposed to be polarizable in an external electric field. A theoretical model of the hybrid system is substantiated and formulated. Exact solutions of the model equations are obtained. The frequencies of charge oscillations in the hybrid system and their damping owing to the dipole--plasmon interaction are found, the damping mechanism being similar to that of Landau damping. The space-time behavior of concentration perturbations in the two-dimensional electron gas is analyzed, and the polarization oscillations of a nanoparticle are studied. The induced polarization of a nanoparticle at nonzero electron drift velocities is found to have a complicated dynamics. In particular, the polarization vector circulates along elliptic trajectories for two of three frequency dispersion branches. If the electric current flows through the quantum well due to an applied electric field, the damping of oscillations in the hybrid system is replaced by their growth in time, which corresponds to the electric instability of the system. New phenomena in hybrid systems can be used to excite the emission of nanoparticles by an electric current and to electrically stimulate the emission in the terahertz spectral range., Comment: 14 pages, 12 figures

We studied the noise spectra of molecule-free and molecule-containing mechanically controllable break junctions. Both types of junctions revealed typical 1/ f noise characteristics at different distances between the contacts with square dependence of current noise power spectral density on current. Additional Lorentzian-shape (1/ f 2) noise components were recorded only when nanoelectrodes were bridged by individual 1,4 benzenediamine molecule. The characteristic frequency of the revealed 1/ f 2 noise related to a single bridging molecule correlates with the lock-in current amplitudes. The recorded behavior of Lorentzian-shape noise component as a function of current is interpreted as the manifestation of a dynamic reconfiguration of molecular coupling to the metal electrodes. We propose a phenomenological model that correlates the charge transport via a single molecule with the reconfiguration of its coupling to the metal electrodes. Experimentally obtained results are in good agreement with theoretical ones and indicate that coupling between the molecule metal electrodes is important aspect that should be taken into account., Comment: 15 pages, 7 figures

We report measurements of radiation transmission in the 0.220--0.325 THz frequency domain through GaN quantum wells grown on sapphire substrates at room and low temperatures. A significant enhancement of the transmitted beam intensity with the applied voltage on the devices under test is found. For a deeper understanding of the physical phenomena involved, these results are compared with a phenomenological theory of light transmission under electric bias relating the transmission enhancement to changes in the differential mobility of the two-dimensional electron gas.

We show that mismatch of the piezoelectric parameters between layers of multiple-quantum well structures leads to modification of the electron-phonon interaction. In particular, short-wavelength phonons propagating perpendicular to the layers with wavevector close to $2\pi n/d$, where $d$ is the period of the structure, induce a strong smoothly-varying component of the piezo-potential. As a result, they interact efficiently with 2D electrons. It is shown, that this property leads to emission of collimated quasi-monochromatic beams of high-frequency acoustic phonons from hot electrons in multiple-quantum well structures. We argue that this effect is responsible for the recently reported monochromatic transverse phonon emission from optically excited GaAs/AlAs superlattices, and provide additional experimental evidences of this., Comment: 6 pages, 7 figures

We consider an electron-acoustic phonon coupling mechanism associated with the dependence of crystal dielectric permittivity on the strain (the so-called Pekar mechanism) in nanostructures characterized by strong confining electric fields. The efficiency of Pekar coupling is a function of both the absolute value and the spatial distribution of the electric field. It is demonstrated that this mechanism exhibits a phonon wavevector dependence similar to that of piezoelectricity and must be taken into account for electron transport calculations in an extended field distribution. In particular, we analyze the role of Pekar coupling in energy relaxation in silicon inversion layers. Comparison with the recent experimental results is provided to illustrate its potential significance.

A novel device design is proposed for a strong enhancement of hole injection current in nitride-based light-emitting heterostructures. Preliminary calculations show orders of magnitude increase in injected hole current when using the proposed superlattice hole injector device based on the real-space transfer concept., Comment: This pdf-file contains 6 pages including 1 figure embedded into the text

To achieve a high-density electron-hole plasma in group-III nitrides for efficient light emission, we propose a planar two-dimensional (2D) p-i-n structure that can be created in selectively-doped superlattices and quantum wells. The 2D p-i-n structure is formed in the quantum well layers due to efficient activation of donors and acceptors in the laterally doped barriers. We show that strongly non-equilibrium 2D electron-hole plasma with density above $10^{12} cm^{-2}$ can be realized in the i-region of the laterally biased p-i-n structure, enabling the formation of interband population inversion and stimulated emission from such a LAteral Current pumped Emitter (LACE). We suggest that implementation of the lateral p-i-n structures provides an efficient way of utilizing potential-profile-enhanced doping of superlattices and quantum wells for electric pumping of nitride-based lasers., Comment: 10 pages, 1 table, 2 figures (3 actually submitted)

We investigate the current injection into a ballistic conductor under the space-charge limited regime, when the distribution function of injected carriers is an arbitrary function of energy F_c(epsilon). The analysis of the coupled kinetic and Poisson equations shows that the injected current fluctuations may be essentially suppressed by Coulomb correlations, and the suppression level is determined by the shape of F_c(epsilon). This is in contrast to the time-averaged quantities: the mean current and the spatial profiles are shown to be insensitive to F_c(epsilon) in the leading-order terms at high biases. The asymptotic high-bias behavior for the energy resolved shot-noise suppression has been found for an arbitrary (non-Poissonian) injection, which may suggest a new field of investigation on the optimization of the injected energy profile to achieve the desired noise-suppression level., Comment: extended version 4 -> 8 pages, examples and figure added

We analyze the Cerenkov emission of high-frequency confined acoustic phonons by drifting electrons in a quantum well. We find that the electron drift can cause strong phonon amplification (generation). A general formula for the gain coefficient, alpha, is obtained as a function of the phonon frequency and the structure parameters. The gain coefficient increases sharply in the short-wave region. For the example of a Si/SiGe/Si device it is shown that the amplification coefficients of the order of hundreds of 1/cm can be achieved in the sub-THz frequency range., Comment: 4 pages, 2 figures. Submitted to APL

A self-consistent theory of shot noise in ballistic two-terminal conductors under the action of long-range Coulomb correlations is presented. Analytical formulas for the electron distribution function and its fluctuation along the conductor, which account for the Coulomb correlations, have been derived. Based upon these formulas, the current-noise reduction factor has been obtained for biases ranging from thermal to shot-noise limits as dependent on two parameters: the ratio between the length of the sample and the Debye screening length \lambda=d/L_D and the applied voltage qU/k_BT. The difference with the formulas for a vacuum diode is discussed., Comment: 21 pages, 11 figs, minor changes

A general formula for current noise in a two-terminal ballistic nondegenerate conductor under the action of long-range Coulomb correlations has been derived. The noise reduction factor (in respect to the uncorrelated value) is obtained for biases ranging from thermal to shot noise limits, and it is related to spatial variations in transport characteristics. The contributions of different energy groups of carriers to the noise are found, that leads us to suggest an electron energy spectroscopy experiment to probe the Coulomb correlations in ballistic conductors., Comment: Results presented at XVI Sitges Conference "Statistical and dynamical aspects of mesoscopic systems", June 7-11, 1999, Sitges, Spain (4 pages, 2 figures, RevTex)

Electron scattering on a thin layer where the potential depends self-consistently on the wave function has been studied. When the amplitude of the incident wave exceeds a certain threshold, a soliton-shaped brightening (darkening) appears on the layer causing diffraction of the wave. Thus the spontaneously formed transverse pattern can be viewed as a self-induced nonlinear quantum screen. Attractive or repulsive nonlinearities result in different phase shifts of the wave function on the screen, which give rise to quite different diffraction patterns. Among others, the nonlinearity can cause self-focusing of the incident wave into a ``beam'', splitting in two ``beams'', single or double traces with suppressed reflection or transmission, etc., Comment: RevTex, 4 pages, epsf.sty to insert figures, to appear in Phys.Rev.B