Majorana fermions in topological-insulator nanowires: From single superconducting nanowires to Josephson junctions

Signatures of Majorana-fermion bound states in one-dimensional topological-insulator (TI) nanowires with proximity-effect-induced superconductivity are studied. The phase diagram and energy spectra are calculated for single-TI nanowires, and it is shown that the nanowires can be in the topologically invariant phases of winding numbersW = 0,+/- 1, and +/- 2, corresponding to the cases with zero, one, and two pairs of Majorana fermions in the single-TI nanowires. It is also shown that the topological winding numbers, i.e., the numbers of pairs of Majorana fermions in the TI nanowires, can be extracted from the transport measurements of a Josephson-junction device made from two TI nanowires, while the sign in the winding numbers can be extracted using a superconducting quantum interference device setup.