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Recent tunneling conductance measurements of Majorana nanowires show a strongvariation in the magnetic field dependence of the superconducting gap amongdifferent devices. Here, we theoretically study the magnetic field dependenceof the gap closing feature and establish that the degree of convexity (orconcavity) of the gap closing as a function of Zeeman field can providecritical constraints on the underlying microscopic parameters of thesemiconductor-superconductor hybrid system model. Specifically, we show thatthe gap closing feature is entirely concave only for strong spin-orbit couplingstrength relative to the chemical potential. Additionally, the non-linearity(i.e. concavity or convexity) of the gap closing as a function of magneticfield complicates the simple assignment of a constant effective $ g $-factor tothe states in the Majorana nanowire. We develop a procedure to estimate theeffective $ g $-factor from recent experimental data that accounts for thenon-linear gap closing resulting from the interplay between chemical potentialand spin-orbit coupling. Thus, measurements of the magnetic field dependence ofthe gap closure on the trivial side of the topological quantum phase transitioncan provide useful information on parameters that are critical to thetheoretical modeling of Majorana nanowires.

Curvature of gap closing features and the extraction of Majorana nanowire parameters