Electron–Nuclear Interaction in $^{13}C$ Nanotube Double Quantum Dots

Abstract

For coherent electron spins, hyperfine coupling to nuclei in the host material can either be a dominant source of unwanted spin decoherence or, if controlled effectively, a resource enabling storage and retrieval of quantum information. To investigate the effect of a controllable nuclear environment on the evolution of confined electron spins, we have fabricated and measured gate-defined double quantum dots with integrated charge sensors made from single-walled carbon nanotubes with a variable concentration of $^{13}C$ (nuclear spin $(I=\frac{1}{2})$ among the majority zero-nuclear-spin $^{12}C$ atoms. We observe strong isotope effects in spin-blockaded transport, and from the magnetic field dependence estimate the hyperfine coupling in $^{13}C$ nanotubes to be of the order of $100 \mu eV$, two orders of magnitude larger than anticipated. $^{13}C$-enhanced nanotubes are an interesting system for spin-based quantum information processing and memory: the $^{13}C$ nuclei differ from those in the substrate, are naturally confined to one dimension, lack quadrupolar coupling and have a readily controllable concentration from less than one to $10^5$ per electron.Physic