Majorana mode stacking, robustness and size effect in cylindrical nanowires

Abstract

We discuss the robustness of Majorana edge modes in a finite quantum nanowire of cylindrical shape. The nanowire is modeled as a bidimensional cylindrical shell of semiconductor material with proximity-induced superconductivity and an intrinsic Rashba spin-orbit interaction. The latter is characterized by effective electric and magnetic fields in transverse direction of the nanowire. An applied external magnetic field pointing in an arbitrary orientation is also assumed. The numerical diagonalization of the Hamiltonian allows us to study the spectrum of the nanowire for different experimental configurations. The Majorana modes prove robust against tilting of the magnetic field away from the cylinder longitudinal axis, if the tilt direction is perpendicular to the effective spin-orbit magnetic field, but fragile otherwise. On the other hand, we find an increasing number of Majorana modes in the same cylinder edge for increasing values of the nanowire radius. We refer to this phenomenon as “stacking effect” and it occurs due to the orthogonality between Majorana mode wave functions. In this manner, different Majoranas take complementary positions on the nanowire surface.