How to infer non-Abelian statistics and topological invariants from tunneling conductance properties of realistic Majorana nanowires

TL;DR

This paper links tunneling conductance measurements in Majorana nanowires to their topological nature by defining a topological visibility, showing that non-Abelian statistics can manifest even with non-ideal conductance peaks.

Contribution

It introduces the concept of topological visibility derived from tunneling conductance and scattering matrix properties, connecting experimental measurements with topological invariants in realistic nanowires.

Findings

Non-ideal zero bias peaks can still indicate non-Abelian statistics.

Large superconducting gaps and small peak splitting are crucial for braiding.

Half-quantized conductance values may suffice for non-Abelian behavior.

Abstract

We consider a simple conceptual question with respect to Majorana zero modes in semiconductor nanowires: Can the measured non-ideal values of the zero-bias-conductance-peak in the tunneling experiments be used as a characteristic to predict the underlying topological nature of the proximity induced nanowire superconductivity? In particular, we define and calculate the topological visibility, which is a variation of the topological invariant associated with the scattering matrix of the system as well as the zero-bias-conductance-peak heights in the tunneling measurements, in the presence of dissipative broadening, using realistic nanowire parameters to connect the topological invariants with the zero bias tunneling conductance values. This dissipative broadening is present in both (the existing) tunneling measurements and also (any future) braiding experiments as an inevitable consequence of a finite braiding time. The connection between the topological visibility and the conductance allows us to obtain the visibility of realistic braiding experiments in nanowires, and to conclude that the current experimentally accessible systems with non-ideal zero bias conductance peaks may indeed manifest (with rather low visibility) non-Abelian statistics for the Majorana zero modes. In general, we find that large (small) superconducting gap (Majorana peak splitting) is essential for the manifestation of the non-Abelian braiding statistics, and in particular, a zero bias conductance value of around half the ideal quantized Majorana value should be sufficient for the manifestation of non-Abelian statistics in experimental nanowires.