The ground and the first excited states of an electron in a multidimensional polar semiconductor quantum dot: an all-coupling variational approach

Abstract

A variational calculation is performed to obtain the polaronic corrections to the ground and the first-excited-state energies of an electron in a parabolic quantum dot of a polar semiconductor for the entire range of the electron-phonon coupling constant and the confinement length. The number of virtual phonons, the size of the polaron and the polarization potential in the polaron ground state are also calculated. The theory is applied to both two- and three-dimensional GaAs quantum dots and it is shown that both the ground and the first-excited-state polaronic corrections in these dots can be considerably large if the dot sizes are of the order a few nanometres.

Temperature Dependence of Polaronic Correction to the Ground State Energy in a GaAs Parabolic Quantum Dot

“…If l 0 exceeds a certain value the polaronic corrections vary rather slowly with l 0 , assuming asymptotically a constant value, essentially independent of the size of the dot. This result is in consistent with that obtained by Wang et al [34] and Mukhopadhyay and Chatterjee [35]. Figures 1 and 2 also show that as the size of the QDs becomes small, the change in the polaronic corrections with temperature will be obvious.…”

Bipolaronic phase in polar semiconductor quantum dots: An all-coupling approach

“…To determine the bipolaron binding energy we need to obtain the single polaron energy within the same approximation. The ground state polaron energy for a three-dimensional quantum dot with parabolic confinement calculated using the LLPH method is given by [13]…”

A Comprehensive Study of the Thermal and Magnetic Properties of Two-Harmonically Interacting Electrons Confined in a Parabolic GaAs Quantum Dot in a Magnetic Field

“…Unfortunately, multi-electrons QD problem with the e-e interaction does not recognize exactly theoretical solution. Thus, many analytical methods and numerical approximations have been adopted to explore and study a multi-electrons QD problem (Beenakker, 1991;Oaknin, Palacios, Brey, & Tejedor, 1994;Johnson & Reina, 1992;Reusch & Grabert, 2003;Emperador, Lipparini, & Serra, 2006;McEuen, Foxman, Kinaret, Meirav, Kastner, Wingreen, & Wind, 1992;Harju, Sverdlov, Nieminen, & Halonen, 1999;Ferconi & Vignale, 1994;Cipriani, Rosa-Clot, & Taddei, 2000;Mukhopadhyay & Chatterjee, 2000;Harju, Sverdlov, Barbiellini, & Nieminen, 1998;Mukhopadhyay & Chatterjee, 1999a, 1999bLiu et al, 2017). While a portion of these techniques are excessively shortsighted, making it impossible to catch the fundamental features of QDs, some are limited just to the ground energy levels, some ignore to incorporate the correlation and exchange effects legitimately, some are unable to manage and work with high electron density and large magnetic field.…”