  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.
