Topological phases of strongly interacting time-reversal invariant topological superconducting chains under a magnetic field

Abstract

Using the density-matrix renormalization group, we determine the different topological phases and low-energy excitations of a time-reversal invariant topological superconducting (TRITOPS) wire with extended -wave superconductivity, Rashba spin-orbit coupling (SOC) and on-site repulsion , under an externally applied Zeeman field . For the case in which is perpendicular to the SOC, the model describes a chain of Shiba impurities on top of a superconductor with extended superconductor pairing. We identify the different topological phases of the model at temperature =0, and in particular we study the stability of the TRITOPS phase against the Zeeman field and the chemical potential , for different values of . In the case where the magnetic field is perpendicular to the SOC axis, the pair of Kramers degenerate Majorana zero modes at the edges of the system that exist for =0, remain degenerate until a critical value of the magnetic field is reached. For parallel to the SOC and up to moderate values of , the fractional spin projection ⟨⟩=1/4 at the ends, found for noninteracting wires at =0, is recovered. In addition, the analytic expression that relates ⟨⟩ with for finite noninteracting chains is shown to be universal up to moderate values of .