The study on nano-hybrid superconducting quantum devices is recently of interest in the field of condensed matter physics. Such devices are working in the exotic quasiparticle state, so-called Majorana bound state (MBS), which follows non-Abelian statistics instead of those of bosons or fermions. Because the quasiparticle state is robust to the quantum decoherence, research on the topological quantum computer, based on MBS is actively in progress. MBS is predicted to be formed in one-dimensional semiconductor nanowires with strong spin-orbit interaction or topological insulators coupled with conventional s-wave superconductors. And the MBS in the topological Josephson junction would induce the supercurrent to be of non-trivial topological property. This topological supercurrent will play a crucial role in developing topologically-protected quantum information devices.

In the first part of this dissertation, we investigate the zero-bias conductance peak (ZBCP) in an InAs nanowire. The observed ZBCP due to reflectionless tunneling founded to be consistent with the theoretical expectation of phase-coherent electronic transport in terms of temperature, bias voltage, and magnetic field. The height of the ZBCP has a characteristic energy determined by the Thouless energy of nanowire and the phase coherence between electrons and retroreflected holes is preserved.

In the second part, we report on the fabrication and characterization of superconducting quantum interference devices (SQUIDs), made of topological insulator, Bi₂Se₃, nanoribbon (NR) contacted with PbIn superconducting electrodes. With a magnetic field being applied along the NR axis, NR exhibits Aharonov-Bohm oscillations due to one-dimensional subbands in the NR. And with a magnetic field being applied perpendicular to the SQUID plane, the critical current modulates periodically due to the flux quantization in SQUID.

In the third part, we report the fractional Josephson effect in topological Josephson junction based on Sb-doped Bi₂Se₃ NR. Under application of an external microwave, the fractional Josephson effect is conspicuously observed at n ＝ 1 step missing in Shapiro steps up to T ＝ 1 K. Moreover, the abnormal fractional AC Josephson effect is observed to be enhanced as the microwave frequency is lowered. This phenomenon is believed to be caused by the 4π-periodic topological supercurrent, mediated by MBS. Therefore, we propose that the topological insulator NR combined with s-wave superconductor provides a useful platform for the research and development of MBS-based topological quantum devices.