  Quantum dots defined in carbon nanotubes are a platform for both basic
scientific studies and research into new device applications. In particular,
they have unique properties that make them attractive for studying the coherent
properties of single electron spins. To perform such experiments it is
necessary to confine a single electron in a quantum dot with highly tunable
barriers, but disorder has until now prevented tunable nanotube-based
quantum-dot devices from reaching the single-electron regime. Here, we use
local gate voltages applied to an ultra-clean suspended nanotube to confine a
single electron in both a single quantum dot and, for the first time, in a
tunable double quantum dot. This tunability is limited by a novel type of
tunnelling that is analogous to that in the Klein paradox of relativistic
quantum mechanics.
