Spin coherence in carbon-based nanodevices

The scope of this thesis is the coherence of spins in carbon-based nanodevices. The motivation for this study are the promising spin-related properties of carbon-based materials, such as weak spin-orbit and hyperfine interaction, which are advantageous for achieving long spin coherence times. In addition, carbon based materials such as graphene and carbon nanotubes have a low mass density and high stiffness which make them well-suited for building nanomechanical devices. This thesis consists of three parts. The first part is an introduction to spin-based quantum computing. We give an overview of the prerequisites for quantum computing in general and discuss basic concepts of spin quantum dots, both in conventional semiconductors and in carbon-based devices. In the second part we study stationary quantum dots made of graphene. In particular we investigate a gate tunable single-layer graphene quantum dot. We calculate the spin-relaxation time T1 of an electron confined to the quantum dot. We find a behavior markedly different from the known results from quantum dots in conventional semiconductors such as GaAs. The presence of two independent K-valleys in graphene results in an effective breaking of time-reversal symmetry of the electronic states in the quantum dot. This leads to an absence of the so-called Van Vleck cancellation even for a vanishing magnetic field. As a result the spin-relaxation time depends only weakly on the magnetic field for low field strengths. At higher fields a cross over to 1/T1 ∝ B and 1/T1 ∝ B is predicted. A novel direct spin-phonon coupling involving the out-of-plane phonons in graphene is found to be an important contribution to the spin-relaxation. We also study the coupling of non-neighboring quantum dots in an array of dots in a graphene nanoribbon. The electronic states in the conduction band are coupled indirectly via tunneling to a common continuum of delocalized states in the valence band. We model the system with a two-impurity Anderson Hamiltonian which is transformed into an effective spin Hamiltonian with the help of a two-stage Schrieffer-Wolff transformation. The result is compared to that from a calculation using a Coqblin-Schrieffer approach