Abstract:
We investigate how the strain-induced nuclear quadrupole interaction influences the degree of nuclear spin polarization in self-assembled quantum dots. Our calculation shows that the achievable nuclear spin polarization in In_{x}Ga_{1-x}As quantum dots is related to the concentration of indium and the resulting strain distribution in the dots. The interplay between the nuclear quadrupole interaction and Zeeman splitting leads to interesting features in the magnetic field dependence of the nuclear spin polarization. Our results are in qualitative agreement with measured nuclear spin polarization by various experimental groups.

Abstract:
We explore the static longitudinal and dynamic transverse spin susceptibilities in quantum dots and nanoparticles within the framework of the Hamiltonian that extends the universal Hamiltonian to the case of uniaxial anisotropic exchange. For the limiting cases of Ising and Heisenberg exchange interactions we ascertain how fluctuations of single-particle levels affect the Stoner instability in quantum dots. We reduce the problem to the statistics of extrema of a certain Gaussian process. We prove that, in spite possible strong randomness of the single-particle levels, the spin susceptibility and all its moments diverge simultaneously at the point which is determined by the standard criterion of the Stoner instability involving the mean level spacing only.

Abstract:
This is a review on graphene quantum dots and their use as a host for spin qubits. We discuss the advantages but also the challenges to use graphene quantum dots for spin qubits as compared to the more standard materials like GaAs. We start with an overview of this young and fascinating field and will then discuss gate-tunable quantum dots in detail. We calculate the bound states for three different quantum dot architectures where a bulk gap allows for confinement via electrostatic fields: (i) graphene nanoribbons with armchair boundary, (ii) a disc in single-layer graphene, and (iii) a disc in bilayer graphene. In order for graphene quantum dots to be useful in the context of spin qubits, one needs to find reliable ways to break the valley-degeneracy. This is achieved here, either by a specific termination of graphene in (i) or in (ii) and (iii) by a magnetic field, without the need of a specific boundary. We further discuss how to manipulate spin in these quantum dots and explain the mechanism of spin decoherence and relaxation caused by spin-orbit interaction in combination with electron-phonon coupling, and by hyperfine interaction with the nuclear spin system.

Abstract:
We study spectral and transport properties of interacting quantum dots with spin. Two particular model systems are investigated: Lateral multilevel and two parallel quantum dots. In both cases different paths through the system can give rise to interference. We demonstrate that this strengthens the multilevel Kondo effect for which a simple two-stage mechanism is proposed. In parallel dots we show under which conditions the peak of an interference-induced orbital Kondo effect can be split.

Abstract:
The conditions for a spontaneous spin polarization in a quantum wire positioned in a zero magnetic field are analyzed under weak population of one-dimensional subbands that gives rise to the efficient quenching of the kinetic energy by the exchange energy of carriers. The critical linear concentration of carriers above which the quasi one-dimensional gas undergoes a complete spin depolarization is determined by the Hartree-Fock approximation. The dependence of the critical linear concentration on the concentration of carriers is defined to reveal the interplay of the spin depolarization with the evolution of the 0.7 (2e2/h) feature in the quantum conductance staircase from the e2/h to 3/2 (e2/h) values. This dependence is used to study the effect of the hole concentration on the 0.7 (2e2/h) feature in the quantum conductance staircase of the quantum wire prepared inside the p-type silicon quantum well using the split-gate technique. The 1D channel is demonstrated to be spin-polarized at the linear concentration of holes lower than the critical linear concentration, because the 0.7 (2e2/h) feature is close to the value of 0.5 (2e2/h) that indicates the spin degeneracy lifting for the first step of the quantum conductance staircase. The 0.7 (2e2/h) feature is found to take however its normal magnitude when the linear concentration of holes attains the critical value corresponding to the spin depolarization. The variations in the height of the 0.7 (2e2/h) feature observed in the hole quantum conductance staircase that is revealed by the p-type silicon quantum wire seem to be related to the evidences of the quantum conductance staircase obtained by varying the concentration of electrons in the 1D channel prepared inside the GaAs-AlGaAs heterojunction.

Abstract:
We review progress on the spintronics proposal for quantum computing where the quantum bits (qubits) are implemented with electron spins. We calculate the exchange interaction of coupled quantum dots and present experiments, where the exchange coupling is measured via transport. Then, experiments on single spins on dots are described, where long spin relaxation times, on the order of a millisecond, are observed. We consider spin-orbit interaction as sources of spin decoherence and find theoretically that also long decoherence times are expected. Further, we describe the concept of spin filtering using quantum dots and show data of successful experiments. We also show an implementation of a read out scheme for spin qubits and define how qubits can be measured with high precision. Then, we propose new experiments, where the spin decoherence time and the Rabi oscillations of single electrons can be measured via charge transport through quantum dots. Finally, all these achievements have promising applications both in conventional and quantum information processing.

Abstract:
The spin relaxation time due to the electron-acoustic phonon scattering in GaAs quantum dots is studied after the exact diagonalization of the electron Hamiltonian with the spin-orbit coupling. Different effects such as the magnetic field, the quantum dot size, the temperature as well as the electric field on the spin relaxation time are investigated in detail. Moreover, we show that the perturbation method widely used in the literature is inadequate in accounting for the electron structure and therefore the spin relaxation time.

Abstract:
Andreev quantum dot (AQD) is a superconducting junction where Bogolyubov quasiparticles can be trapped in discrete Andreev levels. We investigate the feasibility of manipulating individual spin in an AQD. We show that AQD can be brought into spin-1/2 state. The coupling between spin and superconducting current facilitate manipulation and measurement of this state in comparison with common semiconductor quantum dots. We demonstrate that AQD's coupled inductively can serve as a solid-state base for universal quantum computing.

Abstract:
We propose how to form spin qubits in graphene. A crucial requirement to achieve this goal is to find quantum dot states where the usual valley degeneracy in bulk graphene is lifted. We show that this problem can be avoided in quantum dots based on ribbons of graphene with semiconducting armchair boundaries. For such a setup, we find the energies and the exact wave functions of bound states, which are required for localized qubits. Additionally, we show that spin qubits in graphene can not only be coupled between nearest neighbor quantum dots via Heisenberg exchange interaction but also over long distances. This remarkable feature is a direct consequence of the quasi-relativistic spectrum of graphene.

Abstract:
We investigate heavy-hole spin relaxation and decoherence in quantum dots in perpendicular magnetic fields. We show that at low temperatures the spin decoherence time is two times longer than the spin relaxation time. We find that the spin relaxation time for heavy holes can be comparable to or even longer than that for electrons in strongly two-dimensional quantum dots. We discuss the difference in the magnetic-field dependence of the spin relaxation rate due to Rashba or Dresselhaus spin-orbit coupling for systems with positive (i.e., GaAs quantum dots) or negative (i.e., InAs quantum dots) $g$-factor.