Quasiatomic Fine Structure and Selection Rules in Quantum Dots

Abstract

We probe the electronic shell structure of quasiatomic systems, realized in GaAs-AlGaAs quantum dots, by resonant Raman spectroscopy. We observe a series of discrete spin-density excitations, whose energies are very close to single-particle level spacings in a quantum dot. The combined information from experiments at different wave vectors in the lateral direction and from investigations with applied magnetic fields reveals a distinct set of Raman allowed transitions ͑Dn, Dm͒, where changes Dn and Dm are changes in radial and angular momentum quantum numbers, respectively.[S0031-9007(98)05571-9] PACS numbers: 73.20.Dx, 71.45.Gm, 73.20.Mf, 78.55.Cr Modern sophisticated growth techniques for semiconductor structures, such as molecular-beam epitaxy in combination with the technique of modulation doping have made it possible to realize nearly perfect two-dimensional (2D) electron gases in semiconductor heterostructures or quantum wells. Such structures are ideal starting points to fabricate systems with further reduced dimensionality, e.g., quantum wires and quasi-zero-dimensional (0D) dots. The latter can be considered as some kind of artificial atoms. The electronic excitations in these 0D systems can be probed advantageously by resonant Raman spectroscopy. In zinc blende-type semiconductors one can excite collective charge-density excitations (CDE, plasmons), which energies are renormalized with respect to single-particle energy spacings due to direct and exchange Coulomb interactions. One can also excite collective spin-density excitations (SDE) [1], which are affected only by exchange interaction and are therefore redshifted with respect to the corresponding singleparticle energies [2,3]. The CDE and SDE can be distinguished by polarization selection rules. CDE are observed if the polarizations of the incoming and scattered light are parallel to each other (polarized geometry) and SDE if the polarizations are perpendicular (depolarized geometry). There is a number of interesting Raman investigations of modulation-doped quantum-dot structures with [4] and without [3,5] external magnetic field. Lockwood et al. [4] recently found evidence for the shell structure in quantum dots by comparing single-particle excitations (SPE), so called since they occur in both polarization geometries [2], with a self-consistent Hartree calculation. We present in this Letter measurements on high-quality GaAs-AlGaAs quantum dots where we preserve polarization selection rules and can resolve in one and the same quantum-dot sample in addition to the SPE the spectrum of collective CDE and SDE in dependence on the transferred lateral wave vector q and magnetic field B. In contrast to the SPE, these excitations are very sharp and allow a fundamental investigation. At B 0, we find for large q a detailed fine structure in the spectrum of the SDE's. At B . 0, we observe a characteristic splitting of the lowest SDE mode, the SDE 1 . The low-frequency branch has a negative B dispersion and represents a collective edge-spin-density mode. The ...

Wave-vector dependence of spin and density multipole excitations in quantum dots

“…11 for an Nϭ200 electron quantum dot of radius Rϭ120 nm in GaAs-Al x Ga 1Ϫx As. We have modeled the confining potential by the Coulomb potential created by a positively charged jellium disk of the same radius.…”

“…It is worth to mention the application made by Wendler et al 32 to resonant Raman scattering in two electron quantum rings using a more general expression for the cross sections, of hopeless applicability to the N ϭ200 quantum dot described in Ref. 11, as well as the calculation by Steinebach et al 19 mentioned in the Introduction.…”

“…11 What makes this experiment especially appealing is that sharp spin and charge density excitations have been measured in conventional backwards geometry as a function of the applied magnetic field B and of the transferred lateral wave vector q. Previous studies were carried out at zero magnetic field, 8,10 or the experimental conditions were such that the spectra did not show a wave-vector conservation nor a clear polarization dependence, 9 hence it was not possible to resolve SDE and CDE from SPE, nor to record the spectra at predetermined q values. We attempt here a theoretical interpretation of these results based on the time-dependent local-spin densityfunctional theory ͑TDLSDFT͒, addressing the description of high multipolarity spin and charge density modes of a QD, and incorporating in a realistic way the on-plane wave-vector dependence of these collective excitations.…”

“…7 The situation is changing with the use of inelastic light scattering to study QD excitations. This experimental technique is nowadays recognized as one of the more powerful tools to study the elementary excitations of low-dimensional electronic nanostructures, [8][9][10][11][12][13] and it is contributing to a deeper understanding of the two-dimensional electron gas [14][15][16][17][18] ͑2DEG͒. Using polarization selection rules, it allows us to disentangle CDE from spin density ͑SDE͒ and singleparticle excitations ͑SPE͒, and to observe them all in the same sample.…”

Selection and jump rules in electronic Raman scattering fromGaAs∕AlxGa1−xAsDelgado1, Gonzalez2, Lockwood3 2005Phys. Rev. B5000View full textAdd to dashboardCite

“…Schüller et al 2,3 obtained Raman spectra dominated by collective excitations by illuminating the samples with lasers whose energy values were well (40 meV) above the effective band-gap of the dot. Two types of collective modes were found; the charge-density excitations (CDEs) and the spin-density excitations (SDEs) and these can be distinguished by polarization selection rules.…”