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We investigate the ground-state energy and spin of disordered quantum dots using spin-density-functional theory. Fluctuations of addition energies (Coulomb-blockade peak spacings) do not scale with average addition energy but remain proportional to level spacing. With increasing interaction strength, the even-odd alternation of addition energies disappears, and the probability of non-minimal spin increases, but never exceeds 50%. Within a two-orbital model, we show that the off-diagonal Coulomb matrix elements help stabilize a ground state of minimal spin.
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We consider an impurity with a spin degree of freedom coupled to a finite reservoir of non-interacting electrons, a system which may be realized by either a true impurity in a metallic nano-particle or a small quantum dot coupled to a large one. We show how the physics of such a spin impurity is revealed in the many-body spectrum of the entire finite-size system; in particular, the evolution of the spectrum with the strength of the impurity-reservoir coupling reflects the fundamental many-body correlations present. Explicit calculation in the strong and weak coupling limits shows that the spectrum and its evolution are sensitive to the nature of the impurity and the parity of electrons in the reservoir. The effect of the finite size spectrum on two experimental observables is considered. First, we propose an experimental setup in which the spectrum may be conveniently measured using tunneling spectroscopy. A rate equation calculation of the differential conductance suggests how the many-body spectral features may be observed. Second, the finite-temperature magnetic susceptibility is presented, both the impurity susceptibility and the local susceptibility. Extensive quantum Monte-Carlo calculations show that the local susceptibility deviates from its bulk scaling form. Nevertheless, for special assumptions about the reservoir -- the clean Kondo box model -- we demonstrate that finite-size scaling is recovered. Explicit numerical evaluations of these scaling functions are given, both for even and odd parity and for the canonical and grand-canonical ensembles.
We quantify the contributions of hyperfine and spin-orbit mediated singlet-triplet mixing in weakly coupled InAs quantum dots by electron transport spectroscopy in the Pauli spin blockade regime. In contrast to double dots in GaAs, the spin-orbit coupling is found to be more than two orders of magnitudes larger than the hyperfine mixing energy. It is already effective at magnetic fields of a few mT, where deviations from hyperfine mixing are observed.
Using the exactly solvable excitation spectrum of two-electron quantum dots with parabolic potential, we show that the inclusion of the vertical extension of the quantum dot provides a consistent description of the experimental findings of Nishi et al. [Phys.Rev.B75, 121301(R) (2007)]. We found that the second singlet-triplet transition in the ground state is a vanishing function of the lateral confinement in the three-dimensional case, while it always persists in the two-dimensional case. We show that a slight decrease of the lateral confinement leads to a formation of the Wigner molecule at low magnetic fields.
Quantum dots (QDs) can act as convenient hosts of two-level quantum szstems, such as single electron spins, hole spins or excitons (bound electron-hole pairs). Due to quantum confinement, the ground state of a single hole confined in a QD usually has dominant heavy-hole (HH) character. For this reason light-hole (LH) states have been largely neglected, despite the fact that may enable the realilzation of coherent photon-to-spin converters or allow for faster spin manipulation compared to HH states. In this work, we use tensile strains larger than 0.3% to switch the ground state of excitons confined in high quality GaAs/AlGaAs QDs from the conventional HH- to LH-type. The LH-exciton fine structure is characterized by two in-plane-polarized lines and, ~400 micro-eV above them, by an additional line with pronounced out-of-plane oscillator strength, consistent with theoretical predictions based on atomistic empirical pseudopotential calculations and a simple mesoscopic model.
We present a new method for calculating ground state properties of quantum dots in high magnetic fields. It takes into account the equilibrium positions of electrons in a Wigner cluster to minimize the interaction energy in the high field limit. Assuming perfect spin alignment the many-body trial function is a single Slater determinant of overlapping oscillator functions from the lowest Landau level centered at and near the classical equilibrium positions. We obtain an analytic expression for the ground state energy and present numerical results for up to N=40.
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