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 masslike 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 Coulomb blockade. 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.Electronic transport across phase-coherent structures has been a central topic of solid state research ever since the birth of mesoscopic physics some 40 years ago. While the complexity of mesoscopic setups has steadily increased, from the simple gate-defined quantum point contacts of the '80s [1] to elaborate present-day electron optics circuits in semiconductors [2] and graphene [3,4], their structure remains in the vast majority of cases planar -i.e. transport takes place in flat two-dimensional (2D) space. Exceptions to the 2D scenario are samples based on carbon nanotubes and 3D topological insulator (3DTI) nanowires [5][6][7][8]. 3DTIs are bulk band insulators hosting protected 2D surface metallic statesà la Dirac [9]. In mesoscopic nanostructures built out of 3DTIs low-temperature phase-coherent transport takes place on a 2D Dirac metal wrapped around an insulating 3D bulk. As such, it is strongly dependent on a peculiar conjunction of structural (real space) and spectral (reciprocal space) geometrical properties. This has remarkable consequences even for the possibly simplest setup, a topological insulator nanowire (TINW) with constant circular cross section in a coaxial magnetic field, shown in Fig. 2(a). The magnetoconductance of such an object is characterized by a non-trivial interplay between two fundamentals of mesoscopic physics: quantum confinement and geometric [Aharonov-Bohm (AB) and Berry] phases [6][7][8][10][11][12].

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Three-dimensional topological semimetals exhibit linear energy band crossing points that act as monopole sources of Berry curvature. Here, an alternative class of semimetals is introduced, featuring linear N -fold crossing points each of which acts as a source of a Berry dipole. Continuum and lattice models for such multifold Hopf semimetals (MHSMs) are proposed for N = 3, 4, 5. Weak field magnetotransport properties of MHSMs are revealed: a single Berry dipole generates not only an anomalous Hall effect, but also dissipative current contributions to linear order in B, similar to the axial anomaly, chiral magnetic, and magnetochiral effects familiar from a pair of coupled Weyl nodes. For strong B, the Landau level spectrum highlights the importance of quantum geometry: intraband corrections to the Onsager quantization condition crucially depend on the angle between B and the Berry dipole, and interband corrections reflect the strong coupling between degenerate orbits. Finally, it is shown that MHSMs mediate topological phase transitions between N -band Hopf insulators, suggesting them as an ideal playground to explore the physics of delicate topological semimetals and insulators.

Spin crossover (SCO) materials are potential building blocks for multifunctional hybrids. Mechanochemical processing appears as a promising tool to achieve bistable conducting composites with synergic magnetic and electrical bistability.

It is demonstrated 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 two-dimensional systems, such a confinement requires inhomogeneous magnetic fields, while for shaped nanowires of standard size homogeneous fields of the order of B ∼ 1 T are sufficient. We put recent work [R. 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.

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