Quantitative estimation of exchange interaction energy using two-electron vertical double quantum dots

Single-particle and collective excitations in quantum wires made up of vertically stacked quantum dots: zero magnetic field

We report on the theoretical investigation of the elementary electronic excitations in a quantum wire made up of vertically stacked self-assembled InAs/GaAs quantum dots. The length scales (of a few nanometers) involved in the experimental setups prompt us to consider an infinitely periodic system of two-dimensionally confined (InAs) quantum dot layers separated by GaAs spacers. The resultant quantum wire is characterized by a two-dimensional harmonic confining potential in the x-y plane and a periodic (Kronig-Penney) potential along the z (or the growth) direction within the tight-binding approximation. Since the wells and barriers are formed from two different materials, we employ the Bastard's boundary conditions in order to determine the eigenfunctions along the z direction. These wave functions are then used to generate the Wannier functions, which, in turn, constitute the legitimate Bloch functions that govern the electron dynamics along the direction of periodicity. Thus, the Bloch functions and the Hermite functions together characterize the whole system. We then make use of the Bohm-Pines' (full) random-phase approximation in order to derive a general nonlocal, dynamic dielectric function. Thus, developed theoretical framework is then specified to work within a (lowest miniband and) two-subband model that enables us to scrutinize the single-particle as well as collective responses of the system. We compute and discuss the behavior of the eigenfunctions, band-widths, density of states, Fermi energy, single-particle and collective excitations, and finally size up the importance of studying the inverse dielectric function in relation with the quantum transport phenomena. It is remarkable to notice how the variation in the barrier- and well-widths can allow us to tailor the excitation spectrum in the desired energy range. Given the advantage of the vertically stacked quantum dots over the planar ones and the foreseen applications in the single-electron devices and in the quantum computation, it is quite interesting and important to explore the electronic, optical, and transport phenomena in such systems.