Stable Majorana Modes in Spin-Polarized Wire with Strong Interactions
For the 1D Hubbard model with spin-orbit coupling and proximity-induced s-wave superconductivity, the damping rates of quasiparticles are studied in the framework of density-matrix renormalization group (DMRG) approach. It is shown that low-energy excitations belonging to the Hubbard bands are stable against strong electron interaction at the spin-polarized regime. In order to confirm this result analytically, the low-energy model of the strongly interacting spin-polarized nanowire was derived in the second order of perturbation theory. This model generalizes Kitaev chain, taking into account the hoppings and anomalous pairings in the secondary coordination spheres as well as terms describing charge correlations. The amplitudes of the latter ones are small, and the system can be effectively described by quadratic Hamiltonian supporting stable Majorana excitations, which confirms numerical calculations. The topological phase diagram of effective model is studied in the framework of mean-field approximation. The evolution of topological phase boundaries under increasing of charge correlations is studied, and the important role of the joint realization of different types of interactions is noted. The results obtained can be applied when describing the Al-EuS-InAs hybrid system, recently synthesized and studied in searching for Majorana bound states.