  We show that shaped topological insulator (TI) nanowires, i.e. such that
their cross-section radius varies along the wire length, can be tuned into a
number of different transport regimes when immersed in a homogeneous coaxial
magnetic field. This is in contrast with widely studied tubular nanowires with
constant cross-section, and is due to magnetic confinement of Dirac surface
carriers. In flat 2D systems such a confinement requires non-homogeneous
magnetic fields, while for shaped nanowires of standard size homogeneous fields
of the order of $B\sim\,1$T are sufficient. We put recent work [Kozlovsky et
al., Phys. Rev. Lett. 124, 126804 (2020)] into broader context and extend it to
deal with axially symmetric wire geometries with arbitrary radial profile. A
dumbbell-shaped TI nanowire is used as a paradigmatic example for transport
through a constriction and shown to be tunable into five different transport
regimes: (i) conductance steps, (ii) resonant transmission, (iii) current
suppression, (iv) Coulomb blockade, and (v) transport through a triple quantum
dot. Switching between regimes is achieved by modulating the strength of a
coaxial magnetic field and does not require strict axial symmetry of the wire
cross-section. As such, it should be observable in TI nanowires fabricated with
available experimental techniques.
