Tunneling conductance in ferromagnet/superconductor junctions with time-reversal symmetry breaking

The tunneling conductance of two kinds of tunnel junctions with time-reversal symmetry breaking, normal metal/insulator/ferromagnetic metal/ d x 2 − y 2 + i s -wave superconductor (NM/I/FM/ d x 2 − y 2 + i s -wave SC) and NM/I/FM/ d x 2 − y 2 + i d x y -wave SC, is calculated using the extended Blonder–Tinkham–Klapwijk theoretical method. The ratio of the subdominant s-wave and d x y -wave components to the dominant d x 2 − y 2 -wave component is expressed by Δ s Δ D and Δ d Δ D , respectively. Results show that for NM/I/FM/ d x 2 − y 2 + i s -wave SC tunnel junctions, the splitting of the zero-bias conductance peak (ZBCP) is obtained and the splitting peaks appear at e V Δ 0 = ± Δ s Δ D with eV the applied bias voltage and Δ 0 the zero temperature energy gap of SC. For NM/I/FM/ d x 2 − y 2 + i d x y -wave SC tunnel junctions, there are also conductance peaks at e V Δ 0 = ± Δ d Δ D , but the ZBCP does not split. For the two types of tunnel junctions, the completely reversed tunnel conductance spectrum indicates that when the exchange energy in FM is increased to a certain value, the proximity effect transforms the tunnel junctions from the ‘0 state’ to the ‘π state’. The shortening of the transport quasiparticle lifetime can weaken the proximity effect to smooth out the dips and peaks in the tunnel spectrum. This is considered a possible reason that the ZBCP splitting was not observed in some previous experiments. It is expected that these analysis results can serve as a guide for future experiments and the relevant conclusions can be confirmed.