Magnetic-field dependence of hole levels in self-assembledInGaAsquantum dots

Abstract

Phys. Rev. Lett. 94, 026808 ͑2005͔͒ are interpreted by employing a multiband k · p Hamiltonian, which considers the interaction between heavy hole and light hole subbands explicitly. No need of invoking an incomplete energy shell filling is required within this model. The crucial role we ascribe to the heavy hole-light hole interaction is further supported by one-band local-spin-density functional calculations, which show that Coulomb interactions do not induce any incomplete hole shell filling and therefore cannot account for the experimental magnetic field dispersion. DOI: 10.1103/PhysRevB.72.233305 PACS number͑s͒: 73.21.La, 73.22.Ϫf, 73.23.Hk Knowledge of the electronic structure of semiconductor quantum dots ͑QDs͒ 1 is essential to understand and predict their physical properties. The energy structure of conduction band electrons confined in QDs has been thoroughly investigated using capacitance-voltage ͑C-V͒ 2 and far-infrared absorption spectroscopy. 3 However, direct and clear access to the energy structure of valence band holes has long been hindered by the high density of states arising from their larger effective mass. 4 Only very recent C-V spectroscopy experiments have succeeded in resolving a number of energy levels corresponding to holes confined in In͑Ga͒As selfassembled QDs. [5][6][7][8] Of particular interest are the results reported by Reuter et al.,7,8 which studied the energy dispersion of hole charging peaks in QDs with a magnetic field B applied along the growth direction. It was found that for QDs charged on average with one or two holes, the slope of the peaks dispersion was approximately zero. When the QDs were charged with three to six holes, the peaks shifted toward lower and higher energy in alternating fashion, the slope of the fifth and sixth peaks being about twice as strong as that of the third and fourth ones. By using a one-band effective mass Hamiltonian, such results were interpreted as a nonsequential shell filling, leading to highly spin-polarized ground states. 7 It was speculated that this phenomenon, which has no analogy in conduction band electrons, might be due to the Coulomb exchange interactions exceeding the rather small kinetic energy of holes.In this paper, we provide theoretical support for these experiments. First, we study the effect of Coulomb correlations on the electronic configuration of the hole ground state in self-assembled In͑Ga͒As QDs. To this end, we use a oneband local-spin-density functional ͑LSDF͒ model. We find that, even for a rather large QD and pure heavy hole effective mass, a sequential filling of the energy levels is predicted. It then follows that an explanation for the experimental magnetic field-induced dispersion of the charging peaks is unattainable within the one-band picture. Next, we study the role of heavy hole-light hole ͑HH-LH͒ coupling, using a fourband Luttinger-Kohn Hamiltonian. Our results show that HH-LH interaction, together with the spin Zeeman splitting, yield a plausible interpretation of the experimental data even at ...

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

“…The first vertically stacked self-assembled quantum dots were observed in InAs islands separated by GaAs spacer layers along the growth direction in 1995 [3]. What followed is a long list of experimental [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] and theoretical [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40] works dealing with the elastic, electrical, electronic, and optical phenomena which led the researchers to visualize a variety of solid-state devices [5].…”

The Coulomb-interaction-induced breaking of the Aufbau principle for the hole charging of InGaAs/GaAs quantum dots

“…Authors of Ref. 10 have shown that using the latter model for single hole -in form of the four-band KL Hamiltonian -leads to obtaining a set of three twofold Kramer degenerate shells. The shells correspond to absolute value of the total angular momentum of the holes |J z | equal to 3/2, 1/2 and 5/2, respectively.…”

“…This work is a continuation of the studies of the group of Planelles & Climente [see Refs. 10,[17][18][19]. It employs a model that is in several ways more precise than the one used by Ref.…”

“…It employs a model that is in several ways more precise than the one used by Ref. 10. Firstly spin-orbit split-off bands are included with six-band KL Hamiltonian instead of four-band one.…”

Hole and electron wave functions in self‐assembled InAs quantum dots: a comparison

“…Compared to electrons, the charging peaks for holes show a significantly different dispersion behavior in perpendicular (parallel to the growth direction) magnetic field and, within a simple effective mass model, a charging sequence with an incomplete shell filling was proposed to explain the observed dispersion behavior [6]. Recent theoretical work [7,8] discusses the use of the effective mass approximation for the hole system in InAs QDs critically and uses more sophisticated approaches to account for the experimental results given in [6].…”