We theoretically investigate the emergence of Jackiw-Rebbi zero modes and their conductance signature in non-uniform topological insulator nano-wires. We modelled the non-uniform nano-wires as junction between two cylindrical nano-wires with different radius. In the limit of wire length being much larger than its radius, the surface state of the nanowire splits into one dimensional Dirac modes propagating along the axis of the cylinder owing to radial confinement. The sign of the mass gap in each of these Dirac mode is decided by angular momentum quantum number corresponding to the rotational motion of the electron about the axis of the cylindrical. Application of an external magnetic flux through the cylindrical nanowires enables us to tune the mass gap from positive to negative value across the junction. Due to this flux tunable band inversion, controlled by the external magnetic filed, Jackiw-Rebbi zero modes can be made to appear or disappear at the junction. We compute differential conductance of our topological insulator nanowire junction and show that a quantized conductance peak appears at zero-energy (zero-bias) in the presence of the Jackiw-Rebbi mode.
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