Nanoscale physics

Spectrum of localized quasiparticle renormalized due to the interaction with three-mode phonons
Tkach M.V., Seti Ju.O., Hutiv V.V., Voitsekhivska O.M.
Department of Theoretical Physics and Computer Simulation, Yuriy Fedkovych Chernivtsi National University, 2, Kotsyubinsky Str., 58012, Chernivtsi, Ukraine,
E-mail: hutiv.vasyl@chnu.edu.ua
Intensive development of nano scale physics during the last decades have been revealed the new physical properties of low-dimensional structures and stimulated the growth of different multi-layered nano heterostructures: quantum dots, wires, rings, etc. Also, it caused the experimental appearance of new unique nano devices which are widely used in medicine, ecology, communication and space, military, scientific investigation.
From the physical considerations, nano heterostructures are principally different with respect to 3D structures just due to the nano size of their composing elements. The effect of size quantization is always present in nano structures. It causes the multi-band spectra of quasiparticles (electrons, holes, excitons) and multi-mode spectra of polarization phonons.
It is well known that in order to optimize the operating parameters of modern nano devices functioning in infrared range, one should deeply understand the physical processes in multi-layered heterostructures, being their main elements.  The quantum theory of photon- and phonon-assisted tunneling, being developed now, will provide this knowledge. The main problem of the theoretical investigation is to take into account the multi-phonon processes, which essentially renormalize the quasiparticles spectra. This cannot be done in the framework of perturbation method.
Consistently solving the complicated problem of renormalized spectrum of multi-level quasiparticle interacting with multi-mode polarization phonons, we have been modified the method of Feynman-Pines diagram technique and in the recent papers, using the Frohlich-like Hamiltonian, obtained the renormalized spectrum of multi-level quasiparticle interacting with one-mode phonons.
In the proposed paper, we solve the problem of renormalized energy spectrum of one-level quasiparticle interacting with three-mode phonons (for example, one mode of confined phonons and two modes of interface phonons). It is shown that depending on the characteristics of the model, this spectrum contains the bound states with all possible combinations of frequencies or complicated bands of energies, corresponding to the super-positions between states of quasiparticle and phonon modes.