Study on the tunneling spectroscopy of $N-pS$ junction and $N-hS$ junction

We study the complete tunneling spectroscopy of a normal metal/$p$-wave superconductor junction ($N-pS$) and normal metal/heterostructure superconductor junction ($N-hS$) by Blonder-Tinkham-Klapwijk (BTK) method. We find that, for $p$-wave superconductor with non-trivial topology, there exists a quantized zero-bias conductance peak stably, for heterostructure superconductor with non-trivial topology, the emerging zero-bias conductance peak is non-quantized and usually has a considerable gap to the quantized value. Furthermore, it is sensitive to parameters, especially to spin-orbit coupling and the $s$-wave pairing potential. Results obtained suggest that the observation of a small zero-bias conductance peak, instead of a quantized zero-bias conductance peak, in current tunneling experiments can be a natural result if the spin-orbit coupling turns out to be several times smaller than the reported one. Results obtained also suggest that both a stronger spin-orbit coupling and proximity $s$-wave superconductor with relative weaker pairing potential can produce a much more striking zero-bias conductance peak (compared to the experiments), even an almost quantized one. As $s$-wave superconductors are common in nature, the prediction can be verified within current experiment ability.

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