Electrical and superconducting transport in topological insulator nanoribbons

In this chapter, we present recent progress in electrical and phase coherent superconducting transport in topological insulators (TIs) with an emphasis on TI nanoribbons (TINRs). We first overview signatures of topological transport in the surface states by analysing the temperature and axial magnetic field dependence of the electrical conductance in the TINRs. In particular, the Aharonov–Bohm effect is studied in more detail as it may provide insight into the exact quantisation of surface modes in one dimension. Finally, we discuss how topological surface states affect superconducting transport across a Josephson junction. We present the temperature and phase dependence of the critical current as powerful probes to investigate topological superconductivity and study the quantum interference patterns of the supercurrent in the axial magnetic field.