Conductance spectroscopy of topological superconductor wire junctions

We study the zero-temperature transport properties of one-dimensional normal metal-superconductor (NS) junctions with topological superconductors across their topological transitions. Working within the Blonder-Tinkham-Klapwijk (BTK) formalism generalized for topological NS junctions, we analytically calculate the differential conductance for tunneling into two models of a topological superconductor: a spinless intrinsic $p$-wave superconductor and a spin-orbit-coupled $s$-wave superconductor in a Zeeman field. The zero-bias conductance takes nonuniversal values in the nontopological phase while it is robustly quantized at $2e^2/h$ in the topological regime. Despite this quantization at zero voltage, the zero-bias conductance only develops a peak (or a local maximum) as a function of voltage for sufficiently large interfacial barrier strength, or certain parameter regimes of spin-orbit coupling strength. Our calculated BTK conductance also shows that the conductance is finite inside the superconducting gap region because of the finite barrier transparency, providing a possible mechanism for the observed “soft gap” feature in the experimental studies.