On depolarisation in 0D systems: Lamb-like level shift

An extremely quantized 0D system is studied for better understanding of an importance of many-body corrections to an one-electron spectrum. A new approach is proposed to describe the correction appearing as a depolarisation level shift of a (confined) electron moving within an electric field of a (confined) collective mode. For a quantum dot the correction diminishes at the size about 104−105 atoms, depending also on other system parameters. For a closed-shell carbon cluster the effect does not depend on the cluster size owing to stronger quantization and the one-electron estimation does not fit anywhere. For the semiconductor quantum dot system an experimental method to check the depolarisation model is proposed. In the paper we study an anomalous large level shift, resulted from the interaction of an electron in a 0D-system with zero-point oscillations of confined modes of the electric field. Of course, any complete many-body theory, taking into account all the Coulomb interaction, gives the correct value for the electron levels, though it is not known for present. We go to reveal an important correction treating the effect of valence electrons of a 0D object, which can be a spherical quantum dot and a closed-shell fullerene cluster, selfconsistently. Then the theory remains to be semi-classical while a nature of the effect is quantumelectrodynamical. This continues our consideration of C60 in frame of a simple quantum mechanical model of the spherical-shell quantum well (SSQW) [1]. The energy correction depends on the system radius. This size scaling of the depolarisation is computed within an approach proposed by Migdal [2] for a calculation of Lamb shift in a hydrogen-like atom. The shift of the one-electron level is quite predictable and we will show that its amount becomes very large for the quantized system. The closed-shell fullerene depolarisation is of the order of the bare energy and independent of the cluster radius while the shift in the quantum dot decreases with the increasing number of atoms. Between two examples — a fullerene carbon nanocluster and a semiconductor quantum dot structure — the latter has not only theoretical importance. The possible experimental manifestation of the depolarisation effect is proposed basing on the spectroscopy of the quantum dot levels for different matrix materials. 1. Theory for depolarisation level shift: C60 1. The use of the group of full rotations, SO(3), allows one to label the one-electron states and to get analytically the solution for the selfconsistent RPA response function of C60 [1]. A peak of a collective excitation shows up in this spectrum, resulting from fast coherent oscillations of a total electron density of valence states. This surface density oscillation can be thought as a confined electrical field mode or the surface plasmon. We have considered semiclassically the LS for an arbitrary shell object in [3], followed to Migdal [2]. The frequency of the zero-point fluctuations of the external field is much