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It has been recently pointed out that the use of a superconducting (SC) leadinstead of a normal metal lead can suppress the thermal broadening effects intunneling conductance from Majorana fermions, helping reveal the quantizedconductance of $2e^2/h$. In this paper we discuss the specific case oftunneling conductance with SC leads of spin-orbit coupledsemiconductor-superconductor (SM-SC) heterostructures in the presence of aZeeman field, a system which has been extensively studied both theoreticallyand experimentally using a metallic lead. We examine the $dI/dV$ spectra usinga SC lead for different sets of physical parameters including temperature,tunneling strength, wire length, magnetic field, and induced SC pairingpotential in the SM nanowire. We conclude that in a finite wire the Majoranasplitting energy $\Delta E$, which has non-trivial dependence on these physicalparameters, remains responsible for the $dI/dV$ peak broadening, even when thetemperature broadening is suppressed by the SC gap in the lead. In a finitewire the signatures of Majorana fermions with a SC lead are oscillations ofquasi-Majorana peaks about bias $V=\pm\Delta_{\text{lead}}$, in contrast to thecase of metallic leads where such oscillations are about zero bias. Our resultswill be useful for analysis of future experiments on SM-SC heterostructuresusing SC leads.

Tunneling conductance for Majorana fermions in spin-orbit coupled semiconductor-superconductor heterostructures using superconducting leads