Spin exchange interaction with tunable range between graphene quantum dots

We study the spin exchange between two electrons localized in separate quantum dots in graphene. The electronic states in the conduction band are coupled indirectly by tunneling to a common continuum of delocalized states in the valence band. As a model, we use a two-impurity Anderson Hamiltonian which we subsequently transform into an effective spin Hamiltonian by way of a two-stage Schrieffer-Wolff transformation. We then compare our result to that from a Coqblin-Schrieffer approach as well as to fourth order perturbation theory.Comment: 8 pages, 3 figure

Quantum dots and spin qubits in graphene

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.Comment: 23 pages, 10 figures, topical review prepared for Nanotechnolog