Reentrant topological order in a strongly correlated nanowire due to Rashba spin-orbit coupling

The effect of the Rashba spin-orbit coupling (RSOC) on the topological properties of the one-dimensional (1D) extended $s$-wave superconducting Hamiltonian, in the presence of strong electron-electron correlation, is investigated. It is found that a nonzero RSOC increases the periodicity of the effective Hamiltonian, which results in the folding of the Brillouin zone (BZ) and consequently in the emergence of an energy gap at the boundary of the BZ. Essentially, the initial single band is divided into a number of subbands. If the chemical potential lies inside the energy gaps (subbands), then the phase is topologically trivial (nontrivial). This is the origin of the reentrant nature of the existent topological properties. The emergence of subbands allows us to drive the system in and out of the topological phase by the proper tuning of the chemical potential. A heterostructure involving van der Waals materials and a 1D moir\'e pattern for an investigation of the predicted effect has also been proposed. We also discuss how in-plane magnetic field can be used to control the RSOC coupling and induced periodicity in depleted InAs nanowire in which evidence of strong electron-electron correlation has been found.