Spin-orbital polarization of Majorana edge states in oxide nanowires

We investigate a paradigmatic case of topological superconductivity in a one-dimensional nanowire with $d$-orbitals and a strong interplay of spin-orbital degrees of freedom due to the competition of the orbital Rashba interaction, atomic spin-orbit coupling, and structural distortions. We demonstrate that the resulting electronic structure exhibits an orbital-dependent magnetic anisotropy which affects the topological phase diagram and the character of the Majorana bound states (MBSs). The inspection of the electronic component of the MBSs reveals that the spin-orbital polarization generally occurs along the direction of the applied Zeeman magnetic field, and transverse to the magnetic and orbital Rashba fields. The competition of symmetric and antisymmetric spin-orbit coupling remarkably leads to a misalignment of the spin and orbital moments transverse to the orbital Rashba fields, whose manifestation is essentially orbital dependent. The behavior of the spin-orbital polarization along the applied Zeeman field reflects the presence of multiple Fermi points with inequivalent orbital character in the normal state. Additionally, the spin and spatially resolved density of states leads to distinctive fingerprints of the topological phase, especially when comparing the character of the MBS with the energy excitation close to the gap edge. These findings unveil novel paths to single out hallmarks relevant for the experimental detection of MBSs.