Large spin-orbit coupling in carbon nanotubes

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. In solids, spin-orbit coupling has recently become a very active topic, in particular in the context of its role in a new class of materials with a non-trivial topological order[1, 2, 3], and its use to enable new control techniques in solid-state qubits based on manipulating spins with electric fields[4, 5]. Due to the low atomic number of the carbon nucleus, the spin-orbit interaction in carbon materials is, in general, weak. An example of this is flat graphene, in which intrinsic spin-orbit effects are expected to appear at energy scales of only 1 µeV (10 mK)[6, 7]. In carbon nanotubes, however, the curvature of the surface breaks a symmetry that is present in graphene. This broken symmetry enhances the intrinsic spin-orbit coupling in carbon nanotubes compared to flat graphene, with theoretical estimates predicting splittings on the order of 100 µeV, an energy scale easily accessible in transport measurements at dilution refrigerator temperatures, and recently observed 1 a