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Motivated by a recent experimental report[1] claiming the likely observationof the Majorana mode in a semiconductor-superconductor hybridstructure[2,3,4,5], we study theoretically the dependence of the zero biasconductance peak associated with the zero-energy Majorana mode in thetopological superconducting phase as a function of temperature, tunnel barrierpotential, and a magnetic field tilted from the direction of the wire forrealistic wires of finite lengths. We find that higher temperatures and tunnelbarriers as well as a large magnetic field in the direction transverse to thewire length could very strongly suppress the zero-bias conductance peak asobserved in Ref.[1]. We also show that a strong magnetic field along the wirecould eventually lead to the splitting of the zero bias peak into a doubletwith the doublet energy splitting oscillating as a function of increasingmagnetic field. Our results based on the standard theory of topologicalsuperconductivity in a semiconductor hybrid structure in the presence ofproximity-induced superconductivity, spin-orbit coupling, and Zeeman splittingshow that the recently reported experimental data are generally consistent withthe existing theory that led to the predictions for the existence of theMajorana modes in the semiconductor hybrid structures in spite of some apparentanomalies in the experimental observations at first sight. We also make severalconcrete new predictions for future observations regarding Majorana splittingin finite wires used in the experiments.

Zero bias conductance peak in Majorana wires made of semiconductor-superconductor hybrid structures