"Nanotechnology and nanomaterials"

Spectrum of localized three-level quasi-particle resonantly interacting with polarization phonons at cryogenic temperature
М. Ткаch, Ju. Seti, O. Pytiuk, О. Voitsekhivska, V. Gutiv 
Yuriy Fedkovych Chernivtsi National University, 2, Kotsyubinsky Str., 58012, Chernivtsi, Ukraine,
E-mail: email.of. corresponding_ olesya.pityuk@gmail.com

Physics of low-dimensional systems (in particular, nanophysics) is characterized by two fundamentally important factors that dramatically distinguish it from the physics of 3d systems. In the low-dimensional structures, due to the strong spatial confinement, the effect of size quantization is obligatory observed. It causes the multi-band, or multi-level quasi-particles spectra. The presence of hetero interfaces in such structures bring to the appearance of the new types of polarization phonons (confined, half-space, interface, propagating).
The rapid development of experimental nano-physics led not only to the discovery of new physical phenomena, but also to the creation of unique devices: quantum cascade lasers (QCL) and quantum cascade detectors (QCD), functioning at their basic. Interestingly, the multi-band structure of quasi-particles (electron) spectra inherent to nano-heterostructures, on the one hand, gives the possibility to create QCL and QCD that operate in the actual infrared range of frequencies at the inter-sub-band quantum transitions. On the other hand, it demands to create an adequate theory that would take into account multi-phonon processes in the cases of interaction between multi-band quasi-particles and variety of phonon modes. Such theory is only at the start of development.
In this paper, we develop the generalized method of Feynman-Pines diagram technique for the calculation of the Fourier-image of retarded Green’s function of the localized three-level quasi-particle interacting with polarization phonons at cryogenic temperature. The system is described by Frohlich Hamiltonian. The proposed approach of a sequential partial summing of the main diagrams yields a mass operator in the form of a continuous branched fraction, which effectively and in the same way takes into account the multi-phonon processes.
 It is shown that the obtained energy spectrum of the system can provide the mechanism of operation of the QCD, functioning in the near infrared range, with "torn phonon ladders".