  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 an s-wave
superconductor. The electrostatic potential and charge density distributions
are computed self-consistently within the Hartree approximation. Due to the
finite width of the wires and the 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 chemical potential, and
alter the topological phases strongly by enhancing the topological regimes and
producing jagged boundaries. Moreover, the multicritical points connecting
different topological phases from high-index subbands 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 also examined and interaction
impacts on the emergence of Majorana fermions and the strength of Majorana
zero-bias peaks are revealed.
