Topologically protected, correlated end spin formation in carbon nanotubes*

For most chiralities, semiconducting carbon nanotubes display topologically protected end states of multiple degeneracies. In the presence of interactions, these mid-gap states act as naturally formed quantum dots, half-filled for generic, neutral nanotubes. We demonstrate using density matrix renormalization group based quantum chemistry tools that the presence of Coulomb interactions induces the formation of massive end spins [C.P. Moca et al, Phys. Rev. Lett. 125, 056401 (2020)]. In the limit of infinite nanotube radius, these end spins transform into ferromagnetic graphene nanoribbon edge states. The interaction between the two ends is sensitive to the length of the nanotube, its dielectric constant, as well as the size of the spins: for S=1/2 end spins their interaction is antiferromagnetic, while for S>1/2 it changes from antiferromagnetic to ferromagnetic with increasing nanotube length. Controlling the exchange interaction by changing the dielectric constant of the environment provides a possible platform for two-spin quantum manipulations.