Interplay between magnetic gap and quasi-particle lifetime in topological insulator ferromagnet/f-wave superconductor junctions

Abstract

Using the modified Blonder–Tinkham–Klapwijk (BTK) theory, the interplay between the lifetime of quasi particles and the magnetic gap in a topological insulator-based ferromagnet/f-wave superconductor (TI-based FM/f–wave SC) tunnel structure is theoretically studied. Two symmetries of f1 and f2 waves are considered for superconducting pairing states. The results indicate that reducing the finite quasi-particle lifetime will induce a transformation of energy-gap peaks into a zero-bias peak in tunneling conductance spectrum, as well as a transformation of energy-gap dips into a zero-bias dip in shot noise spectrum, ultimately resulting in the smoothing of the zero-bias conductance peak and the zero-bias shot noise dip. An increase in magnetic gap will suppress the tunnel conductance and shot noise when the conventional Andreev retro-reflection dominates, but will enhance them when the specular Andreev reflection is dominant. Both specular Andreev reflection and conventional Andreev retro-reflection will be enhanced as the quasi-particle lifetime increases. When Fermi energy equals the magnetic gap, shot noise and tunneling conductance vanish across all energy ranges. These findings not only contribute to a better understanding of specular Andreev reflection in the FM/f–wave SC junction based on TIs but also provide insights for experimentally determining the f-wave pairing symmetry.