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

Theory of magnetotransport in shaped topological insulator nanowires