Geometry-Induced Topological Superconductivity and Majorana Zero Modes in Carbon Nanotubes

The mechanisms responsible for generation of Majorana zero modes in carbon nanotubes proximately represented by an s-wave superconductor and placed in a uniform axial magnetic field are theoretically and numerically analyzed. An effective 1D low-energy model is built on the basis of the Dirac description of electronic states of graphene taking into account the rolled-up structure geometry. It is shown that the quantization of transverse motion, the orbital contribution of a magnetic field (the Aharonov–Bohm effect), and the curvature-induced spin–orbit coupling jointly form a topologically nontrivial superconducting state. In the appropriate parametric mode, the effective Hamiltonian is reduced to a known 1D model with all its parameters expressed directly through the geometric characteristics of a nanotube and the value of an external magnetic field, without introducing phenomenological assumptions. The Majorana modes emerging at the nanotube edges are nonlocal quantum states protected by the superconducting gap, which makes them promising for implementing topological qubits. The analytical results are confirmed by the numerical simulation within the Bogoliubov–de Gennes Hamiltonian, which demonstrates the energy gap closing and reopening and the emergence of localized edge states.