  We propose carbon nanotubes (CNTs) with magnetic impurities as a versatile
platform to achieve unconventional Kondo physics, where the CNT bath is gapped
by the spin-orbit interaction and surface curvature. While the strong-coupling
phase is inaccessible for the special case of half-filled impurities in neutral
armchair CNTs, the system in general can undergo quantum phase transitions to
the Kondo ground state. The resultant position-specific phase diagrams are
investigated upon variation of the CNT radius, chirality, and carrier doping,
revealing several striking features, e.g., the existence of a maximal radius
for nonarmchair CNTs to realize phase transitions, and an interference-induced
suppression of the Kondo screening. We show that by tuning the Fermi energy via
electrostatic gating, the quantum critical region can be experimentally
accessed.
