Investigation On The Modulation Of Topological Superconducting Quantum Wires And Rings

The studies of Majorana bound states with closely linked to electron spin-orbit coupling, superconductivity, Zeeman field became hotspot of the studies on semiconductor low-dimensional structure.Since the theoretical predictions that Majorana bound states obey the non-Abelian mathematical statistics, which makes it a great advantage in topological quantum computing. When there is induced superconductivity in semiconductor nanowires, interaction of the spin-orbit interaction and external Zeeman field can induce Majorana bound states. Many groups have reported the zero-bias peak of differential conductance appears in semiconductor nanowire junctions, which is a way to prove the existence of Majorana bound state. However, it is still controversy as to what the observed zerobias peak of differential conductance is the sign of the presence of Majorana bound states. This article hope through simulation calculate the wave functions of composite structures constitute of different quantum wires and quantum rings, to compare different wave functions of these structures to explore the emergence and disappearance of Majorana bound states. If Majorana bound state connects to an ordinary semiconductor nanowire, the Majorana bound state will leak out to the ordinary semiconductor nanowire. Based on it, we use a semiconductor quantum ring to replace the semiconductor nanowire, by adjusting the strength of Rashba spin-orbit interaction in quantum ring and the strength of the Zeeman field, through the Aharonov-Casher effect to modulate the wave function, makes Majorana bound state reappears.After studying the wave function, we investigate the dc Josephson effect in onedimensional junctions where a ring conductor is sandwiched between two semiconductor nanowires with proximity-induced superconductivity. Peculiar features of the Josephson effect arise due to the interplay of spin-orbit interaction and external Zeeman field where the wires can be in the topologically trivial or nontrivial phase. By tuning the Zeeman field orientation, the device can vary from 0 to π junction. More importantly, non-zero Josephson current is possible at zero phase difference across the junction.Although, this anomalous Josephson current is not relevant to the topological phase transition, its magnitude can be significantly enhanced when the nanowires become topological superconductors where Majorana bound states emerge. The topological phase transition can also leave signatures in the modulation of Josephson current due to Aharonov-Casher effect. Distinct modulation patterns are obtained for the semiconductor nanowires in the topologically trivial and non-trivial phases. These results are useful to probe the topological phase transition in semiconductor nanowire junctions via the dc Josephson effect.