  It has recently been recognized that the strong spin-orbit interaction
present in solids can lead to new phenomena, such as materials with non-trivial
topological order. Although the atomic spin-orbit coupling in carbon is weak,
the spin-orbit coupling in carbon nanotubes can be significant due to their
curved surface. Previous works have reported spin-orbit couplings in reasonable
agreement with theory, and this coupling strength has formed the basis of a
large number of theoretical proposals. Here we report a spin-orbit coupling in
three carbon nanotube devices that is an order of magnitude larger than
measured before. We find a zero-field spin splitting of up to 3.4 meV,
corresponding to a built-in effective magnetic field of 29 T aligned along the
nanotube axis. While the origin of the large spin-orbit coupling is not
explained by existing theories, its strength is promising for applications of
the spin-orbit interaction in carbon nanotubes devices.
