Quality factor for the quantization of zero-bias conductance peaks in Majorana nanowire*

A zero-bias conductance peak (ZBCP) with a nearly quantized height of 2e²/h is one of the most direct and unique signatures of a topological Majorana zero mode. However, despite recent experimental progress in observing large zero bias peaks, theoretical work has raised questions about the uniqueness of quantized ZBCPs as a signature for Majorana modes. On the other hand, the ZBCPs associated with Majorana modes are predicted, to be robustly quantized even as the tunnel barrier is pinched off to vanishingly low conductance. In this work we compare the robustness of the quantization of ZBCPs associated with Majorana modes, quasi-Majoranas and disorder to variations of the tunnel barrier and Zeeman field. By defining a quality factor associated with the variation of the tunnel barier and Zeeman field for each type of ZBCP, we find that Majoranas are significantly more robust compared to non-Majorana ZBCPs in the ideal low temperature limit. However the distinction between Majoranas and non-topological ZBCPs is reduced at more practical temperatures such as 20mK. Based on the quality factors calculated over a wide range of parameters and models we conclude that the observation of a tunnel barrier quality factor over a threshold value of two might be considered a strong evidence of Majorana modes.