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Abstract

Topological insulator nanowires with uniform cross section, combined
with a magnetic flux, can host both a perfectly transmitted mode and
Majorana zero modes. Here we consider nanowires with rippled surfaces-
specifically, wires with a circular cross section with a radius varying
along its axis-and we calculate their transport properties. At zero
doping, chiral symmetry places the clean wires (no impurities) in the
AIII symmetry class, which results in a Z topological classification. A
magnetic flux threading the wire tunes between the topologically
distinct insulating phases, with perfect transmission obtained at the
phase transition. We derive an analytical expression for the exact flux
value at the transition. Both doping and disorder break the chiral
symmetry and the perfect transmission. At finite doping, the interplay
of surface ripples and disorder with the magnetic flux modifies quantum
interference such that the amplitude of Aharonov-Bohm oscillations
reduces with increasing flux, in contrast to wires with uniform surfaces
where it is flux-independent.