A numerical solution to the problem of transient processes in a resonant tunneling diode featuring a current–voltage characteristic with hysteresis is found for the first time in the context of a coherent model (based on the coupled Schrödinger and Poisson equations) taking into account the Fermi distribution of electrons. The transitions from the high-current to the low-current state and vice versa, which result from the existence of hysteresis and are of great practical importance for ultrafast switches based on resonant tunneling diodes, are studied in detail. It is shown that the transition times for such processes initiated by the application of a small voltage can significantly exceed the characteristic time ℏ/Γ (where G is the width of the resonance level). It is established for the first time that the transition time can be reduced and made as short as the characteristic time ℏ/Γ by applying a sufficiently high voltage. For the parameters of the resonant-tunnelingdiode structure considered in this study, the required voltage is about 0.01 V.

A problem, which concerns the effect of the diamond heat-spreading layer on the temperature and voltage-current characteristics of gallium nitride (GaN) high-electron-mobility transistors (HEMTs) is solved for the first time in a hydrodynamic model (which includes the continuity equation, Poisson equation, and equations for electron and lattice temperatures). The mechanism of the occurrence of peak electron and lattice temperatures (hot spots) is analyzed. It is shown that introducing a heat spreader considerably reduces the maximum temperature (by 263 K for a sapphire substrate and by 163 K for a silicon carbide substrate) and improves the voltage-current characteristics. The effectiveness of the heat spreader is evaluated depending on its thickness, gate size, and substrate material to find the optimum design.

The impact of diamond and graphene heat spreading layers on the thermal and electrical characteristics of AlGaN/GaN high electron mobility transistors (HEMTs) has been investigated using numerical simulations in the hydrodynamic model. It is shown that the introduction of heat spreader significantly reduced maximum device temperature, increased the device lifetime, and improved current-voltage characteristics. The conditions under which the heat spreader works most effectively were found.

The first known numerical solution for the problem of transient processes in a resonant tunneling diode (RTD) in the presence of I-V curve hysteresis is found within a coherent model that incorporates a system of Schröbinger-Poisson equations with open boundary conditions. Transient currents are determined under various initial conditions and as functions of a wide range of parameters. The transition from the large-current state to the small-current one is analyzed in detail for the first time. This process assumes practical significance when RTDs are used as ultrafast switches. It is shown that the time of transition induced by a weak electric field may significantly exceed the expected -h/Γ, where Γ is the resonance level width. It is proven for the first time that the transition time may be reduced down to -h/Γ if a sufficiently strong field is applied.

The behavior of the higher harmonics of a resonant-tunneling diode is investigated experimentally and theoretically in the adiabatic limit. Within the framework of numerical solution of the time-dependent Schrodinger equation with open boundary conditions, the currents of the first three harmonics are calculated. It is shown that the behavior of the currents qualitatively agrees with the experimental data and the results of a simple model used by us previously. The possibility of the generation of an electromagnetic field at frequencies multiple to the harmonic number is shown.

The effect of strong electron-electron interaction on transient processes in a resonant tunneling diode (RTD) has been investigated. The transient current caused by instantaneously switching a bias voltage and switching on an incident flow has been calculated using a numerical solution of the Schrödinger equation within the Hartree approximation. The RTD transition from a high-current state to a low-current state is calculated in the presence of hysteresis. The behavior of the transition is analyzed and its duration is found. It is shown that, when the bias jump exceeds the level width Γ, the transition switching time is very short (on the order of 10−13 s) and the RTD can be used as an ultrafast switch. The transient periods of constructive interference in the quantum well and destructive interference in the emitter are found to be on the order of 5/Γ.

Director of the Division of Solid State Physics of the RAS Lebedev Physical Institute (FIAN in Russ. abbr.), Professor Yurii Vasil'evich Kopaev, died tragically on 24 December 2012 in a traffic accident. We lost a wonderful person loved by everyone, a physically and spiritually beautiful human being who lived and worked flamely and with enthusiasm, applying his extraordinary gift and invariably a grain of his soul to his every undertaking. The path that led this brilliant scientist to condensed matter physics is anything but typical. After graduating from a rural high school and a technical college of light industry (in 1956), Yu V Kopaev entered the Moscow Institute of Light Industry. It was there that he developed a keen interest in physics, mostly due to the influence of S S Vasil'ev, an excellent teacher, who took part in the early work on studying chain reactions. Yearning to do independent research work led YuV to transfer in 1959 to the Moscow Power Engineering Institute (MEI in Russ. abbr.). While still an MEI student, Kopaev indeed started independent research projects in the Department of Semiconductor Devices. On the recommendation of ProfessorKVShalimova (Head of the Department), L V Keldysh, then a young researcher at FIAN, agreed to supervise Kopaev's graduation thesis; this factor played a decisive role in Yu V Kopaev's scientific fate. Having graduated from MEI postgraduate studies in 1964 and after defending his PhD thesis (with LVKeldysh as his supervisor), he went to work in Zelenograd at the Research Institute ofMolecular Electronics. The young scientist immediately gained much authority already there: his special talent of actively generating fruitful ideas was obvious, and he generously shared them with colleagues. In 1970, Yu V Kopaev moved on to FIAN's Theoretical Physics Department, where he submitted and defended his Habilitation thesis for aDScdegree in 1972. In 1992,YuVKopaev rose to heading the Laboratory of Semiconductor Physics at the FIANDivision of Solid State Physics (OFTT), and in 1995 to directorship of the FIANOFTT. In 1964, Keldysh and Kopaev publish their famous paper on the theory of dielectric phase transitions (the Keldysh± Kopaev model), in which they showed that the modified Bardeen±Cooper±Schrieffer (BCS) formalism in the theory of superconductivity can be efficiently applied to describe metal±insulator phase transitions in solids. By analogy with the superconducting transition, the phase transition in the model can be interpreted as a Bose condensation of electron± hole pairs (excitons). Later on, the dielectric phase in the Keldysh±Kopaev model was given the name `exciton insulator', the term that is now commonly used. The Keldysh± Kopaev exciton insulator model gained the status of the standard method for description of interelectron correlations in the limit of weak interactions. Yu V Kopaev and his co-workers were able to show that the exciton insulatormodel describes a wide variety of experimentally observable states: charge and spin density waves (band antiferromagnetism), weak ferromagnetism of collectivized electrons, and the ferroelectric state in covalent crystals. They also studied various exotic states that arise in this model: states with spin and charge current waves (orbital antiferromagnetism). This last state is interesting in that under certain conditions it represents a qualitatively new type of ordered state in which the ordering parameter is the density of the toroidal dipole moment (toroidal moments form the third independent family of electromagnetic multipoles, along with the electric and magnetic moments). The hypothesis of spontaneous currents flowing in crystals is currently experiencing a genuine renaissance in connection with the discovery of a new class of solids known as topological insulators. In a topological insulator, spontaneous current (of electrons or spins) flows over the surface of the material. Uspekhi Fizicheskikh Nauk 183 (5) 557 ± 558 (2013) DOI: 10.3367/UFNr.0183.201305j.0557 Translated by V I Kisin PERSONALIA PACS number: 01.60.+q

In the present work, dynamics of vortex structure in the type-II superconductors with defects under a transport current has been studied using the time dependent Ginzburg-Landau equations. The vortex interactions with the pining centers in two-dimensional cases have been investigated. The model has been solved using ψU-method and finite element method. The defects are normal regions and it size was greater-than through influence of proximity effect. In our simulation, we have considered that using model agree well for description of vortices behavior in inhomogeneous sample under a transport current. We have considered defects influence and relative position on dynamics of vortices. Also we have calculated the values of critical current density at various configuration of sample.

Using the numerical solution to the Schrödinger equation, current-voltage characteristics of the resonant-tunneling diode with spacer layers were obtained. The dependences of the peak current of the resonant-tunneling diode on the emitter spacer width were plotted. It was shown that the peak current depends periodically on the emitter spacer width. The constructed electron density diagrams showed that the increase in the peak current is associated with the resonant level in the emitter spacer region.

The influence of the interelectronic interaction on the stationary characteristics of a resonant tunnel diode (RTD) with spacer layers (spacers) is investigated by means of a self-consistent solution to Schrödinger and Poisson equations. It is demonstrated that the interelectronic interaction influences significantly the RTD voltampere characteristics, in particular, it decreases the peak current density and displaces the position of maxima of the peak current dependence on the emitter spacer size. It is also demonstrated that the hysteresis of the RTD volt-ampere characteristics vanishes for definite spacer sizes.

Within the framework of multi-configurational self-consistent field (MCSCF) approximation, the ground and excited states of the N 4 (D 2H ) cluster of N 2 molecules are modeled from different initial states. The potential barriers to the cluster formation and dissociation are calculated. Investigations of the N 4 (D 2H ) electronic spectrum demonstrate that the most promising method of forming nitrogen nanostructures is compression of the excited triplet N 2 molecules.

The self-consistent solution for the Schrödinger and Poisson equations in the Hartree-Fock approximation is applied to the study of the effect of electron-electron interaction on the high-frequency characteristics for a double-well nanostructure. The response and the emission efficiency of the structure in a high or low alternating electromagnetic field are calculated. It is shown that the electron-electron interaction does not noticeably reduce the emission efficiency or change the resonance frequency.

On the basis of analytical and numerical solutions of the Schrödinger equation, the active polarization current and emission efficiency of double-well nanostructures were calculated in a wide range of amplitudes of alternating electromagnetic field. It is shown that generation in the important terahertz region with smooth frequency tuning and the highest efficiency are possible. The behavior of the coefficient of reflection of electrons from the structure is studied; this coefficient goes to zero under the conditions of maximum efficiency.

The features of the Meissner effect in superconductors with a finite pairing momentum are analyzed. Response to a weak magnetic field is calculated for various cases covering a pair momentum range from q ≪ Δ/ v 0 to q ∼ p 0 , including q = Δ 0 / v 0 ( v 0 is the velocity on the Fermi surface and Δ 0 is the order parameter at zero temperature; the system of units where ħ = 1 is used). The response of a superconductor carrying the transport current at a temperature close to the critical temperature T c is determined. It is shown that, at a certain critical momentum (current), the response parallel to the momentum vanishes and the London length is infinite. The response perpendicular to the momentum remains unchanged. The response of the superconductor in the current state at zero temperature is calculated. A new contribution to the paramagnetic current is found, and its mechanism is determined. This contribution can be large for high momenta q ∼ p 0 . The Meissner effect is analyzed in detail for the state proposed by Larkin and Ovchinnikov, Zh. Éksp. Teor. Fiz. 47 , 1136 (1964) [Sov. Phys. JETP 20 , 762 (1964)], as well as by Fulde and Ferrel, Phys. Rev. A 135 , 550 (1964). It is shown that the response parallel to the vector q is nonzero and diamagnetic. On the contrary, the response perpendicular to the momentum vanishes at the optimal momentum q 0 . The sensitivity of the Meissner effect to the fine features of the superconducting state such as the quasiparticle spectrum, coherent factors, etc. is demonstrated.

of the Russian Academy of Sciences (RAS), Director of the Solid State PhysicsDivision of theRASPNLebedev Physical Institute (FIAN), had his 70th birthday on 21 October 2007. Yurii Vasil'evich manifested his serious interest in physics while still a student. The paper that the student Yu VKopaev sent for publication was reviewed by a FIAN young research scientist L VKeldysh who wished to meet the juvenile author. Thismeeting and subsequent collaboration in research played a decisive role in the career of Yu V Kopaev. In 1964 Keldysh and Kopaev published the famous paper on the theory of insulator phase transitions (the Keldysh ± Kopaev model) in which they showed that the modified formalism of the BCS theory of superconductivity can be effectively used for a description of metal ± insulator phase transitions in solids. The phase transition arises in the model no matter how weak the interelectron interaction and, by analogy with the superconducting transition, can be interpreted as the Bose condensation of electron ± hole pairs (excitons). The insulator phase in the Keldysh ±Kopaev model was subsequently rechristened the `excitonic insulator' Ð the term that is now in general use. In fact, the Keldysh ±Kopaev excitonic insulator model became a standard way of describing interelectron correlations in the weak interaction limit. The importance of the exciton model of insulators follows largely from the fact that it describes (in a unified framework) an entire family of phase transitions with different types of symmetry of the ordered phase. The order parameter of the model characterizes the contribution of interelectron correlations to the self-consistent crystal potential. This potential has a complicated spin and phase structure that determines the type of ordering. Yu V Kopaev and coworkers showed that the excitonic insulator model describes a wide variety of experimentally observable states: charge and spin (band antiferromagnetism) density waves, weak ferromagnetism of collectivized electrons, and the ferroelectric state in nonionic crystals. Yu V Kopaev and his coworkers also studied various exotic states that arise in this model: states with spin and charge current (orbital antiferromagnetism). This last state is interesting in that under certain conditions it describes a qualitatively new type of ordered state in which the ordering parameter is the density of the toroidal dipole moment (toroidal moments are the third independent family, along with the electric and magnetic moments, of electromagnetic multipoles). It was also shown that microinhomogeneous toroidal orbital antiferromagnets can have anomalously high diamagnetism. Later, the ideas of Yu V Kopaev and his colleagues on ordered states with spontaneous currents were further developed in papers on strongly correlated states in connection with the problem of high-temperature superconductivity, where they are known as `flux phases'. In 1982 Yu V Kopaev, together with a team that submitted the completed project ``Prediction, detection and study of gapless semiconductors and exciton phases,'' received the USSR State Prize. A large series of papers written by Yu V Kopaev and coworkers is devoted to studying nonequilibrium phase transitions in semiconductors. In these papers the authors provide a reliable theoretical foundation to popular ideas of the analogy to laser generation phenomena and the phase transitions, and for the first time analyze them with mathematical rigor. Thus, Yu V Kopaev and his colleagues suggested and studied in detail the electron mechanism of laser annealing. The destruction of crystal structure connected with the formation of structural instability in response to the excitation of nonequilibrium charge carriers (nonequilibrium phase transition) is indeed observed in a number of semiconductors. This body of work, ``The discovery of the phenomenon of pulse-oriented crystallization in solids (laser annealing),'' received the USSR State Uspekhi Fizicheskikh Nauk 177 (11) 1251 ± 1252 (2007) DOI: 10.3367/UFNr.0177.200711g.1251 Translated by V I Kisin PERSONALIA PACS number: 01.60.+q

A theory of coherent resonance tunneling of electrons in a two-well nanostructure (TWNS) in the presence of a strong electromagnetic field is developed. The TWNS consists of two identical tunnel-coupled quantum wells to which a dc electric field is applied. Radiative transitions occur between two levels that arise due to the interwell interference and the dc electric field. The wavefunctions and polarization currents in the TWNS are found in the case of a strong electromagnetic field, and the oscillation power is determined as a function of the coherent pumping current and the parameters of the structure. It is shown that oscillations are possible in the relevant terahertz band, with fine frequency tuning by a dc field. It is found that the interference of electrons between quantum wells plays a crucial role. This interference significantly suppresses the effect of the electromagnetic field on the resonance tunneling and enhances the oscillation up to the highest possible level. It is proved that there exists an optimal regime of strong-field oscillations without inverse population and saturation, which are inherent in conventional lasers.

The existence of a metastable cluster He 4 * with total spin S = 2 is predicted. The cluster consists of two covalently bound excited spin-polarized triplet He 2 * molecules and is rectangular in shape. The electron wavefunctions, the dependence of the energy He 4 * system on the distance between the He 2 * triplet molecules, the atomic spacing, the frequency spectrum of natural oscillations of the cluster, and other characteristics are calculated from first principles. It is shown that the metastable state is formed if one of the excited He 2 * molecules is in the 3Σ u + state, while the other is in the 3Πg state. The radiation lifetime τ of the metastable cluster He 4 * is calculated; it is found to range from 100 to 200 s, which is much longer than the lifetime τ ≈ 20 s of the triplet molecule He 2 * (3Σ u + ). The height U ≈ 0.5 eV of the potential barrier preventing the departure from the local energy minimum is determined. The energy Eacc ≈ 9 eV/atom accumulated in the He 4 * cluster is calculated; this energy considerably exceeds the energy of known chemical energy carriers. It is shown that the accumulated energy is released virtually completely during decomposition of the He 4 * cluster into individual helium atoms. This means that helium clusters are a promising material with a high accumulated energy density (HEDM).

If the condition εσ(p)=ε−σ(−p+nI/vF) for magnetic nesting is fulfilled for the electron dispersion law with spin σ along a certain preferential direction n, ferromagnetism and the inhomogeneous superconducting state can coexist up to a very high magnetization I. This fact was used to explain the coexistence of ferromagnetism and superconductivity for layered cuprates of the RuSr2GdCu2O8 type, which possess a finite, though rather high, critical magnetization, because the conditions for magnetic nesting are fulfilled only approximately.

The effect of the electron-phonon interaction on resonant tunneling of electrons through a two-barrier nanostructure is investigated in the framework of a consistent quantum-mechanical model. The wave function is determined by solving the Schrödinger equation with correct boundary conditions in the semiclassical approximation in the electron-phonon interaction. The current calculated with the help of the wave function is averaged over the phonon subsystem with the help of the Bloch theorem. The analytic expressions derived for static and varying currents in a resonance tunnel diode taking into account the electron-phonon interaction formally coincide with the Mössbauer effect probability. In the adiabatic limit and for a strong electron-phonon interaction, the static current decreases in proportion to η, while the varying low-frequency current is proportional to η2. The shape of the resonance curve becomes Gaussian with a width of τ ph −1 . The fundamental result is that the properties inherent in coherent tunneling are preserved even in the limit η≪1 (which is often regarded as incoherent). The most striking effect (analogous to the Mössbauer effect) is the conservation of a narrow Lorentzian resonance curve in the limit η≪1, ωph≫Γ. This means that even for η≪1, the resonance current is due to coherent electrons (experiencing interference), but their fraction decreases in view of the electron-phonon interaction. It is concluded that the application of the rate equations and other approximate methods disregarding interference may lead to incorrect results. The expressions for the high-frequency and nonlinear responses are also derived. The quantum-mechanical regime is found to be less sensitive to the effect of phonons than the classical regime.