  Magnetotransport through cylindrical topological insulator (TI) nanowires is
governed by the interplay between quantum confinement and geometric
(Aharonov-Bohm and Berry) phases. Here, we argue that the much broader class of
TI nanowires with varying radius -- for which a homogeneous coaxial magnetic
field induces a varying Aharonov-Bohm flux that gives rise to a non-trivial
mass-like potential along the wire -- is accessible by studying its simplest
member, a TI nanocone. Such nanocones allow to observe intriguing mesoscopic
transport phenomena: While the conductance in a perpendicular magnetic field is
quantized due to higher-order topological hinge states, it shows resonant
transmission through Dirac Landau levels in a coaxial magnetic field.
Furthermore, it may act as a quantum magnetic bottle, confining surface Dirac
electrons and leading to a largely interaction-dominated regime of Coulomb
blockade type. We show numerically that the above-mentioned effects occur for
experimentally accessible values of system size and magnetic field, suggesting
that TI nanocone junctions may serve as building blocks for Dirac electron
optics setups.
