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We study coherent transport through a semiconductor nanowire in the presenceof spin-orbit coupling and Zeeman splitting due to an applied magnetic field.By employing analytical and numerical techniques we develop a theory for theJosephson effect in the superconductor-semiconductor nanowire-superconductorstructure. We show that Josephson current through the clean semiconductornanowire exhibits a number of interesting features due to the interplay betweenthe Zeeman splitting and spin-orbit coupling. We also study effect how disorderin the nanowire affects Andreev bound-state energy spectrum and calculate localdensity of states at the junction.

Josephson Current through a Semiconductor Nanowire: effect of strong spin-orbit coupling and Zeeman splitting