Properties of the electron spectrum of a closed two-well spherical quantum dot and evolution of the spectrum with the outer-well width

Abstract

The theory of the electron spectrum of a closed three-sphere two-well spherical quantum dot is developed and the evolution of the spectrum under variations in the width of the outer spherical well from zero (the steady-state spectrum of a simple closed spherical quantum dot) to infinity (quasi-steady-state spectrum of a simple open spherical quantum dot) is studied. The mechanism of damping of electron states in a closed two-well spherical quantum dot due to the increase in the width of the outer spherical well is considered for the first time. It is established that the physical cause of the transformation of the steady-state spectrum into the quasi-steady-state spectrum is the redistribution of the probabilities that an electron excited to the resonance state of the spherical quantum dot is found in the energy states of the quasi-steady-state band in the entire space of the nanosystem. It is shown that the basic properties of an electron in a simple open spherical quantum dot can be reproduced to any specified accuracy in the model of a closed two-well spherical quantum dot with a sufficiently large width of the outer well. The approach developed here is based on the mathematical formulation of the quantum field theory (the Green’s function method). The approach can serve as a basis for the development of the still lacking theory of quasi-steady-state spectra and the theory of interaction of quasiparticles (electrons, holes) with each other (exciton), as well as with quantum fields (photons) in open multilayered nanosystems.