Topological phases and transport properties of screened interacting quantum wires

Abstract

We study theoretically the effects of long-range and on-site Coulomb interactions on the topological phases and transport properties of spin–orbit-coupled quasi-one-dimensional quantum wires imposed on a s-wave superconductor. The distributions of the electrostatic potential and charge density are calculated self-consistently within the Hartree approximation. Due to the finite width of the wires and charge repulsion, the potential and density distribute inhomogeneously in the transverse direction and tend to accumulate along the lateral edges where the hard-wall confinement is assumed. This result has profound effects on the topological phases and the differential conductance of the interacting quantum wires and their hybrid junctions with superconductors. Coulomb interactions renormalize the gate voltage and alter the topological phases strongly by enhancing the topological regimes and producing jagged boundaries. Moreover, the multicritical points connecting different topological phases are modified remarkably in striking contrast to the predictions of the two-band model. We further suggest the possible non-magnetic topological phase transitions manipulated externally with the aid of long-range interactions. Finally, the transport properties of normal–superconductor junctions are further examined, in particular, the impacts of Coulomb interactions on the zero-bias peaks related to the Majorana fermions and near zero-energy peaks.