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 coupli
ng 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.
We consider the effect of nonmagnetic and magnetic impurities on the superheating field $H_s$ in a type-II superconductor. We solved the Eilenberger equations, which take into account the nonlinear pairbreaking of Meissner screening currents, and cal
culated $H_s(T)$ for arbitrary temperatures and impurity concentrations in a single-band s-wave superconductor with a large Ginzburg-Landau parameter. At low temperatures nonmagnetic impurities suppress a weak maximum in $H_s(T)$ which has been predicted for the clean limit, resulting instead in a maximum of $H_s$ as a function of impurity concentration in a moderately clean limit. It is shown that nonmagnetic impurities weakly affect $H_s$ even in the dirty limit, while magnetic impurities suppress both $H_s$ and the critical temperature $T_c$. The density of quasiparticles states $N(epsilon)$ is strongly affected by an interplay of impurity scattering and current pairbreaking. We show that a clean superconductor at $H=H_s$ is in a gapless state, but a quasiparticle gap $epsilon_g$ in $N(epsilon)$ at $H=H_s$ appears as the concentration of nonmagnetic impurities increases. As the nonmagnetic scattering rate $alpha$ increases above $alpha_c=0.36$, the quasiparticle gap $epsilon_g(alpha)$ at $H=H_s$ increases, approaching $epsilon_gapprox 0.32Delta_0$ in the dirty limit $alphagg 1$, where $Delta_0$ is the superconducting gap parameter at zero field. The effects of impurities on $H_s$ can be essential for the nonlinear surface resistance and superconductivity breakdown by strong RF fields.
