Hyperfine interaction and electron-spin decoherence in graphene and carbon nanotube quantum dots

TL;DR

This paper analytically investigates hyperfine interactions and electron-spin decoherence in graphene and carbon nanotube quantum dots, revealing dependence on physical parameters and isotope composition, with implications for spin coherence times.

Contribution

It provides an analytical study of hyperfine interactions in graphene and nanotubes, highlighting the anisotropic Knight shift and dependence on curvature and isotope abundance.

Findings

Hyperfine coupling strength is less than 1 micro-eV.

Electron-spin decoherence times are tens of microseconds or longer.

Hyperfine-induced Knight shift is highly anisotropic.

Abstract

We analytically calculate the nuclear-spin interactions of a single electron confined to a carbon nanotube or graphene quantum dot. While the conduction-band states in graphene are p-type, the accordant states in a carbon nanotube are sp-hybridized due to curvature. This leads to an interesting interplay between isotropic and anisotropic hyperfine interactions. By using only analytical methods, we are able to show how the interaction strength depends on important physical parameters, such as curvature and isotope abundances. We show that for the investigated carbon structures, the 13C hyperfine coupling strength is less than 1 mu-eV, and that the associated electron-spin decoherence time can be expected to be several tens of microseconds or longer, depending on the abundance of spin-carrying 13C nuclei. Furthermore, we find that the hyperfine-induced Knight shift is highly anisotropic, both in graphene and in nanotubes of arbitrary chirality.