We theoretically study the interaction of a heavy hole with nuclear spins in a quasi-two-dimensional III-V semiconductor quantum dot and the resulting dephasing of heavy-hole spin states. It has frequently been stated in the literature that heavy holes have a negligible interaction with nuclear spins. We show that this is not the case. In contrast, the interaction can be rather strong and will be the dominant source of decoherence in some cases. We also show that the form of the interaction is Ising-like, resulting in unique and interesting decoherence properties, which might provide a crucial advantage to using dot-confined hole spins for quantum information processing, as compared to electron spins.

We review our work on the dynamics and decoherence of electron and hole spins in single and double quantum dots. The first part, on electron spins, focuses on decoherence induced via the hyperfine interaction while the second part covers decoherence and relaxation of heavy-hole spins due to spin-orbit interaction as well as the manipulation of heavy-hole spin using electric dipole spin resonance.

We study spin relaxation and decoherence caused by electron-lattice and spin-orbit interaction and predict striking effects induced by magnetic fields B. For particular values of B, destructive interference occurs resulting in ultralong spin relaxation times T₁ exceeding tens of seconds. For small phonon frequencies ω, we find a 1/√ω spin-phonon noise spectrum -- a novel dissipation channel for spins in quantum dots -- which can reduce T₁ by many orders of magnitude. We show that nanotubes exhibit zero-field level splitting caused by spin-orbit interaction. This enables an all-electrical and phase-coherent control of spin.

We report the measurement of extremely slow hole spin relaxation dynamics in self-assembled InGaAs quantum dots. Individual spin orientated holes are optically created in the lowest orbital state of each dot and read out after a defined storage time using spin memory devices. The hole spin relaxation time (T_1h) is measured as a function of the external magnetic field and lattice temperature. As predicted by theory, hole spin relaxation can occur over remarkably long timescales in strongly confined quantum dots (up to T_1h ~270 \mus) comparable to the corresponding time for electrons. Our findings are supported by calculations that reproduce both the observed magnetic field and temperature dependencies. The results show that hole spin relaxation in strongly confined quantum dots is governed by spin-lattice interaction, in marked contrast to higher dimensional nanostructures where it is limited by spin-orbit coupling between valence bands.

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.

We propose and analyze a new method for manipulation of a heavy hole spin in a quantum dot. Due to spin-orbit coupling between states with different orbital momenta and opposite spin orientations, an applied rf electric field induces transitions between spin-up and spin-down states. This scheme can be used for detection of heavy-hole spin resonance signals, for the control of the spin dynamics in two-dimensional systems, and for determining important parameters of heavy-holes such as the effective g-factor, mass, spin-orbit coupling constants, spin relaxation and decoherence times.

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.

The spin-orbit splitting of the electron levels in a two-dimensional quantum dot in a perpendicular magnetic field is studied. It is shown that at the point of an accidental degeneracy of the two lowest levels above the ground state the Rashba spin-orbit coupling leads to a level anticrossing and to mixing of spin-up and spin-down states, whereas there is no mixing of these levels due to the Dresselhaus term. We calculate the relaxation and decoherence times of the three lowest levels due to phonons. We find that the spin relaxation rate as a function of a magnetic field exhibits a cusp-like structure for Rashba but not for Dresselhaus spin-orbit interaction.