Topological phases and Majorana states in screened interacting quantum wires

TL;DR

This paper investigates how long-range and on-site Coulomb interactions influence topological phases and Majorana states in spin-orbit-coupled quantum wires, revealing interaction-induced modifications to phase boundaries and transport properties.

Contribution

It provides a self-consistent analysis of Coulomb interactions' effects on topological phases, highlighting enhanced regimes and altered phase boundaries in quantum wires with superconductors.

Findings

Coulomb interactions enhance topological regimes.

Charge accumulates at wire edges affecting phases.

Majorana zero-bias peaks are influenced by interactions.

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 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.