Spin coherence in carbon-based nanodevices

Abstract

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 ∝ B2 and 1/T1 ∝ B4 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 as well as to fourth-order perturbation theory. We discuss the ranges of validity of the different models and derive an expression for the long-distance coupling for the case of an array of quantum dots in a graphene nanoribbon.The second part of this thesis delves into the study of nanomechanics. We study the coupling of an electron spin to vibrational motion due to spin-orbit coupling in suspended carbon nanotube quantum dots. First we show that with current capabilities, a quantum dot with an odd number of electrons can serve as a realization of the Jaynes-Cummings model known from cavity quantum electrodynamics. Using realistic experimental parameters we argue that the strong-coupling regime can be reached. In the proposed setup, a quantized flexural mode of the suspended tube plays the role of the optical mode in cavity quantum electrodynamics and we identify two distinct two-level subspaces, at small and large magnetic field, which can be used as qubits in this setup. Using the quantum master equation we show how the coupling of spin and mechanical motion is imprinted in the amplitude of the stationary state of the nanotube.Furthermore we demonstrate how the spin of the electron in system described above can be read out by a charge sensing device in the vicinity of the charged nanotube. We calculate the response of the system to pulsed external driving of the mechanical motion using a Jaynes-Cummings model. We show how the spin can be read-out by measuring the current through the charge sensing device.