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Topological insulator nanowires with uniform cross section, combined with amagnetic flux, can host both a perfectly transmitted mode and Majorana zeromodes. Here we consider nanowires with rippled surfaces---specifically, wireswith a circular cross section with a radius varying along its axis---andcalculate their transport properties. At zero doping, chiral symmetry placesthe clean wires (no impurities) in the AIII symmetry class, which results in a$\mathbb{Z}$ topological classification. A magnetic flux threading the wiretunes between the topologically distinct insulating phases, with perfecttransmission obtained at the phase transition. We derive an analyticalexpression for the exact flux value at the transition. Both doping and disorderbreaks the chiral symmetry and the perfect transmission. At finite doping, theinterplay of surface ripples and disorder with the magnetic flux modifiesquantum interference such that the amplitude of Aharonov-Bohm oscillationsreduces with increasing flux, in contrast to wires with uniform surfaces whereit is flux-independent.

Perfect transmission and Aharanov-Bohm oscillations in topological insulator nanowires with nonuniform cross section