Physical mechanisms for zero-bias conductance peaks in Majorana nanowires

Motivated by the need to understand and simulate the ubiquitous experimentally observed zero-bias conductance peaks in superconductor-semiconductor hybrid structures, we theoretically investigate the tunneling conductance spectra in one-dimensional nanowires in proximity to superconductors in a systematic manner taking into account several different physical mechanisms producing zero-bias conductance peaks. The mechanisms we consider are the presence of quantum dots, inhomogeneous potential, random disorder in the chemical potential, random fluctuations in the superconducting gap, and in the effective g factor with the self-energy renormalization induced by the parent superconductor in both short (L similar to 1 mu m) and long nanowires (L similar to 3 mu m). We classify all foregoing theoretical results for zero-bias conductance peaks into three types: the good, the bad, and the ugly, according to the physical mechanisms producing the zero-bias peaks and their topological properties. We find that, although the topological Majorana zero modes are immune to weak disorder, strong disorder (ugly) completely suppresses topological superconductivity and generically leads to trivial zero-bias peaks. Compared qualitatively with the extensive existing experimental results in the superconductor-semiconductor nanowire structures, we conclude that most current experiments are likely exploring trivial zero-bias peaks in the ugly situation dominated by strong disorder. We also study the nonlocal end-to-end correlation measurement in both the short and long wires, and point out the limitation of the nonlocal correlation in ascertaining topological properties particularly when applied to short wires. Although we present results for good and bad zero-bias peaks, arising respectively from topological Majorana bound states and trivial Andreev bound states, strictly for the sake of direct comparison with the ugly zero-bias conductance peaks arising from strong disorder, the main goal of the current work is to establish with a very high confidence level the real physical possibility that essentially all experimentally observed zero-bias peaks in Majorana nanowires are most likely ugly, i.e., purely induced by strong disorder, and are as such utterly nontopological. Our work clearly suggests that an essential prerequisite for any future observation of topological Majorana zero modes in nanowires is a substantialmaterials improvement of the semiconductor-superconductor hybrid systems leading to much cleaner wires.