We study the magnetotransport properties of patterned 3D topological insulator nanostructures with several leads, such as kinks or Y-junctions, near the Dirac point with analytical as well as numerical techniques. The interplay of the nanostructure geometry, the external magnetic field, and the spin-momentum locking of the topological surface states lead to a richer magnetoconductance phenomenology as compared to straight nanowires. Similar to straight wires, a quantized conductance with perfect transmission across the nanostructure can be realized across a kink when the input and output channels are pierced by a half-integer magnetic flux quantum. Unlike for straight wires, there is an additional requirement depending on the orientation of the external magnetic field. A right-angle kink shows a unique $\pi$-periodic magnetoconductance signature as a function of the in-plane angle of the magnetic field. For a Y-junction, the transmission can be perfectly steered to either of the two possible output legs by a proper alignment of the external magnetic field. These magnetotransport signatures offer new ways to explore topological surface states and could be relevant for quantum transport experiments on nanostructures which can be realized with existing fabrication methods.

In Josephson junctions, a supercurrent across a nonsuperconducting weak link is carried by electron-hole bound states. Because of the helical spin texture of nondegenerate topological surface states, gapless bound states are established in junctions with topological weak link. These have a characteristic 4π-periodic current phase relation (CΦR) that leads to twice the conventional Shapiro step separation voltage in radio frequency–dependent measurements. In this context, we identify an attenuated first Shapiro step in (Bi_0.06Sb_0.94)₂Te₃ (BST) Josephson junctions with AlO_x capping layer. We further investigate junctions on narrow, selectively deposited BST nanoribbons, where surface charges are confined to the perimeter of the nanoribbon. Within these junctions, previously identified signatures of gapless bound states are absent. Because of confinement, transverse momentum sub-bands are quantized and a topological gap opening is observed. Surface states within these quantized sub-bands are spin degenerate, which evokes bound states of conventional 2π-periodic CΦR within the BST nanoribbon weak link.

In this paper, in an in situ prepared three-terminal Josephson junction based on the topological insulator Bi${}_4$Te${}_3$ and the superconductor Nb the transport properties are studied. The differential resistance maps as a function of two bias currents reveal extended areas of Josephson supercurrent, including coupling effects between adjacent superconducting electrodes. The observed dynamics for the coupling of the junctions is interpreted using a numerical simulation of a similar geometry based on a resistively and capacitively shunted Josephson junction model. The temperature dependency indicates that the device behaves similar to prior experiments with single Josephson junctions comprising topological insulators’ weak links. Irradiating radio frequencies to the junction, we find a spectrum of integer Shapiro steps and an additional fractional step, which is interpreted with a skewed current–phase relationship. In a perpendicular magnetic field, we observe Fraunhofer-like interference patterns in the switching currents.

We succeeded in the fabrication of topological insulator (Bi_0.57Sb_0.43)₂Te₃ Hall bars as well as nanoribbons by means of selective-area growth using molecular beam epitaxy. By performing magnetotransport measurements at low temperatures information on the phase-coherence of the electrons is gained by analyzing the weak-antilocalization effect. Furthermore, from measurements on nanoribbons at different magnetic field tilt angles an angular dependence of the phase-coherence length is extracted, which is attributed to transport anisotropy and geometrical factors. For the nanoribbon structures universal conductance fluctuations were observed. By performing a Fourier transform of the fluctuation pattern a series of distinct phase-coherent closed-loop trajectories are identified. The corresponding enclosed areas can be explained in terms of nanoribbon dimensions and phase-coherence length. In addition, from measurements at different magnetic field tilt angles we can deduce that the area enclosed by the loops are predominately oriented parallel to the quintuple layers.

Three-dimensional topological insulators (TIs) host helical Dirac surface states at the interface with a trivial insulator. In quasi-one-dimensional TI nanoribbon structures the wave function of surface charges extends phase-coherently along the perimeter of the nanoribbon, resulting in a quantization of transverse surface modes. Furthermore, as the inherent spin-momentum locking results in a Berry phase offset of \pi π of self-interfering charge carriers an energy gap within the surface state dispersion appears and all states become spin-degenerate. We investigate and compare the magnetic field dependent surface state dispersion in selectively deposited Bi _2 2 Te _3 3 TI micro- and nanoribbon structures by analysing the gate voltage dependent magnetoconductance at cryogenic temperatures. While in wide microribbon devices the field effect mainly changes the amount of bulk charges close to the top surface we identify coherent transverse surface states along the perimeter of the nanoribbon devices responding to a change in top gate potential. We quantify the energetic spacing in between these quantized transverse subbands by using an electrostatic model that treats an initial difference in charge carrier densities on the top and bottom surface as well as remaining bulk charges. In the gate voltage dependent transconductance we find oscillations that change their relative phase by \pi π at half-integer values of the magnetic flux quantum applied coaxial to the nanoribbon, which is a signature for a magnetic flux dependent topological phase transition in narrow, selectively deposited TI nanoribbon devices.