Non-perturbation theory of electronic dynamic conductivity for two-barrier resonance tunnel nano-structure

The non-perturbation theory of electronic dynamic conductivity for open two-barrier resonance tunnel structure is established for the first time within the model of rectangular potentials and different effective masses of electrons in the elements of nano-structure and the wave function linear over the intensity of electromagnetic field. It is proven that the results of the theory of dynamic conductivity, developed earlier in weak signal approximation within the perturbation method, qualitatively and quantitatively correlate with the obtained results. The advantage of non-perturbation theory is that it can be extended to the case of electronic currents interacting with strong electromagnetic fields in open multi-shell resonance tunnel nano-structures, as active elements of quantum cascade lasers and detectors.Comment: 10 pages, 2 figure

Quasi-stationary states of electrons interacting with strong electromagnetic field in two-barrier resonance tunnel nano-structure

An exact solution of non-stationary Schrodinger equation is obtained for a one-dimensional movement of electrons in an electromagnetic field with arbitrary intensity and frequency. Using it, the permeability coefficient is calculated for a two-barrier resonance tunnel nano-structure placed into a high-frequency electromagnetic field. It is shown that a nano-structure contains quasi-stationary states the spectrum of which consists of the main and satellite energies. The properties of resonance and non-resonance channels of permeability are displayed.Comment: 8 pages, 3 figure

Energy spectrum of localized quasiparticles renormalized by multi-phonon processes at finite temperature

The theory of renormalized energy spectrum of localized quasi-particle interacting with polarization phonons at finite temperature is developed within the Feynman-Pines diagram technique. The created computer program effectively takes into account multi-phonon processes, exactly defining all diagrams of mass operator together with their analytical expressions in arbitrary order over the coupling constant. Now it is possible to separate the pole and non-pole mass operator terms and perform a partial summing of their main terms. The renormalized spectrum of the system is obtained within the solution of dispersion equation in the vicinity of the main state where the high- and low-energy complexes of bound states are observed. The properties of the spectrum are analyzed depending on the coupling constant and the temperature.Comment: 16 pages, 3 figures, 3 table

Optical properties of GaAs/Alx_{x}Ga1−x_{1-x}As/GaAs quantum dot with off-central impurity driven by electric field

The effect of a constant electric field and donor impurity on the energies and oscillator strengths of electron intraband quantum transitions in double-well spherical quantum dot GaAs/Al$_{x}$Ga$_{1-x}$As/GaAs is researched. The problem is solved in the framework of the effective mass approximation and rectangular potential wells and barriers model using the method of wave function expansion over a complete set of electron wave functions in nanostructure without electric field. It is shown that under the effect of electric field, the electron in the ground state tunnels from the inner potential well into the outer one. It also influences on the oscillator strengths of intraband quantum transition. The binding energy of an electron with ion impurity is obtained as a function of electric field intensity at a different location of impurity.Comment: 9 pages, 6 figure

Renormalized energy of ground and first excited state of Fr\"{o}hlich polaron in the range of weak coupling

Partial summing of infinite range of diagrams for the two-phonon mass operator of polaron described by Fr\"{o}hlich Hamiltonian is performed using the Feynman-Pines diagram technique. Renormalized spectral parameters of ground and first excited (phonon repeat) polaron state are accurately calculated for a weak electron-phonon coupling at $T=0$ K. It is shown that the stronger electron-phonon interaction shifts the energy of both states into low-energy region of the spectra. The ground state stays stationary and the excited one decays at a bigger coupling constant.Comment: 12 pages, 5 figure

Optimization of quantum cascade laser operation by geometric design of cascade active band in open and closed models

Using the effective mass and rectangular potential approximations, the theory of electron dynamic conductivity is developed for the plane multilayer resonance tunnel structure placed into a constant electric field within the model of open nanosystem, and oscillator forces of quantum transitions within the model of closed nanosystem. For the experimentally produced quantum cascade laser with four-barrier active band of separate cascade, it is proven that just the theory of dynamic conductivity in the model of open cascade most adequately describes the radiation of high frequency electromagnetic field while the electrons transport through the resonance tunnel structure driven by a constant electric field.Comment: 10 pages, 2 figure

Dynamic conductivity of symmetric three-barrier plane nanosystem in constant electric field

The theory of dynamic conductivity of nanosystem is developed within the model of rectangular potentials and different effective masses of electron in open three-barrier resonance-tunnel structure in a constant homogeneous electric field. The application of this theory for the improvement of operating characteristics of quantum cascade laser active region (for the experimentally investigated In$_{0.53}$Ga$_{0.47}$As/In$_{0.52}$Al$_{0.48}$As heterosystem) proves that for a certain geometric design of nanosystem there exists such minimal magnitude of constant electric field intensity, at which the electromagnetic field radiation power together with the density of current flowing through the separate cascade of quantum laser becomes maximal.Comment: 7 pages, 2 figure

Generalized method of Feynman-Pines diagram technique in the theory of energy spectrum of two-level quasiparticle renormalized due to multi-phonon processes at cryogenic temperature

Theory of the spectrum of localized two-level quasi-particle renormalized due to interaction with polarization phonons at cryogenic temperature is developed using the generalized method of Feynman-Pines diagram technique. Using the procedure of partial summing of infinite ranges of the main diagrams, mass operator is obtained as a compact branched chain fraction, which effectively takes into account multi-phonon processes. It is shown that multi-phonon processes and interlevel interaction of quasiparticle and phonons cardinally change the renormalized spectrum of the system depending on the difference of energies of two states, which either resonates with phonon energy or does not. The spectrum of non-resonant system contains renormalized energies of the main states and two similar infinite series of groups of phonon satellite levels. The spectrum of a resonant system contains a renormalized ground state and infinite series of satellite groups.Comment: 14 pages, 2 figures, 1 tabl

Analytic peculiarities of the polaron mass operator in the first two orders of the coupling constant

The exact analytic expression for the polaron mass operator in the second order of the coupling constant is established for the first time. It holds in the whole energy scale. The peculiarities of the mass operator are analysed. The renormalized polaron energy spectrum is obtained and analysed in this approximation.Вперше отримано точний аналітичний вираз для масового оператора полярона у другому порядку за константою зв’язку, справедливий для всієї області енергій. Проаналізовано особливості масового оператора. Знайдено і проаналізовано перенормований енергетичний спектр полярона у цьому наближенні