A prominent feature of topological insulators (TIs) is the surface states comprising of spin-nondegenerate massless Dirac fermions. Recent technical advances have made it possible to address the surface transport properties of TI thin films by tuning the Fermi levels of both top and bottom surfaces. Here we report our discovery of a novel planar Hall effect (PHE) from the TI surface, which results from a hitherto-unknown resistivity anisotropy induced by an in-plane magnetic field. This effect is observed in dual-gated devices of bulk-insulating Bi2−xSbxTe3 thin films, where the field-induced anisotropy presents a strong dependence on the gate voltage with a characteristic two-peak structure near the Dirac point. The origin of PHE is the peculiar time-reversal-breaking effect of an in-plane magnetic field, which anisotropically lifts the protection of surface Dirac fermions from backscattering. The observed PHE provides a useful tool to analyze and manipulate the topological protection of the TI surface.

Nuclear magnetic resonance (NMR) and transport measurements have been performed at high magnetic fields and low temperatures in a series of n-type Bi2Se3 crystals. In low density samples, a complete spin polarization of the electronic system is achieved, as observed from the saturation of the isotropic component of the 209 Bi NMR shift above a certain magnetic field. The corresponding spin splitting, defined in the phenomenological approach of a 3D electron gas with a large (spinorbit-induced) effective g-factor, scales as expected with the Fermi energy independently determined by simultaneous transport measurements. Both the effective electronic g-factor and the "contact" hyperfine coupling constant are precisely determined. The magnitude of this latter reveals a non negligible s-character of the electronic wave function at the bottom of the conduction band. Our results show that the bulk electronic spin polarization can be directly probed via NMR and pave the way for future NMR investigations of the electronic states in Bi-based topological insulators. Bismuth selenide, Bi 2 Se 3 , known for years as a narrow gap semiconductor, has recently appeared as one of the first examples of "3D topological insulators"[1-3]. As such unique state of matter, it is characterized by the coexistence of 2-dimensional conducting surface states with an insulating bulk material. The charge carriers at the surface behave as massless relativistic particles (Dirac fermions) with a spin locked to their translational momentum. These so-called "helical Dirac fermions", which promise applications in the field of spintronic [4] and quantum computation [5], have recently raised a considerable interest (see Ref. 6 for a review). As a matter of fact, the existence of gapless states at the boundary of the material is related to a well-defined change in the bulk band structure. In Bi 2 Se 3 , this originates from a parity inversion of the valence and conduction band in the presence of a large spin-orbit coupling [1].In an effort to deepen our understanding of the spin properties of topological insulators, a characterization of the coupling between the charge carriers and the nuclei in the Bi 2 Se 3 matrix is of high importance. Indeed, nuclear spins can inherently couple to the topologically protected electronic states and limit their coherence time. On the other hand, this hyperfine coupling can be efficiently exploited to probe the electronic system via NMR techniques. In particular, an electronic system bearing nonzero spin polarization acts as an effective local magnetic field which modifies the nuclei resonance frequency. This so-called "Knight shift" has previously been extensively studied to probe the electronic spin polarisation [7] as well as the spatial symmetry of the wave functions [8, 9] in some semiconductor-based bulk or low dimensional systems. A couple of recent works have investigated the NMR properties of Bi 2 Se 3 samples and revealed signatures of the bulk electronic states [10, 11]. These measurements were however l...

The non-trivial topology of three-dimensional topological insulators dictates the appearance of gapless Dirac surface states. Intriguingly, when made into a nanowire, quantum confinement leads to a peculiar gapped Dirac sub-band structure. This gap is useful for, e.g., future Majorana qubits based on TIs. Furthermore, these sub-bands can be manipulated by a magnetic flux and are an ideal platform for generating stable Majorana zero modes, playing a key role in topological quantum computing. However, direct evidence for the Dirac sub-bands in TI nanowires has not been reported so far. Here, using devices fabricated from thin bulk-insulating (Bi1−xSbx)2Te3 nanowires we show that non-equidistant resistance peaks, observed upon gate-tuning the chemical potential across the Dirac point, are the unique signatures of the quantized sub-bands. These TI nanowires open the way to address the topological mesoscopic physics, and eventually the Majorana physics when proximitized by an s-wave superconductor.

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Wireless technology relies on the conversion of alternating electromagnetic fields into direct currents, a process known as rectification. Although rectifiers are normally based on semiconductor diodes, quantum mechanical non-reciprocal transport effects that enable a highly controllable rectification were recently discovered1–9. One such effect is magnetochiral anisotropy (MCA)6–9, in which the resistance of a material or a device depends on both the direction of the current flow and an applied magnetic field. However, the size of rectification possible due to MCA is usually extremely small because MCA relies on inversion symmetry breaking that leads to the manifestation of spin–orbit coupling, which is a relativistic effect6–8. In typical materials, the rectification coefficient γ due to MCA is usually ∣γ∣ ≲ 1 A−1 T−1 (refs. 8–12) and the maximum values reported so far are ∣γ∣ ≈ 100 A−1 T−1 in carbon nanotubes13 and ZrTe5 (ref. 14). Here, to overcome this limitation, we artificially break the inversion symmetry via an applied gate voltage in thin topological insulator (TI) nanowire heterostructures and theoretically predict that such a symmetry breaking can lead to a giant MCA effect. Our prediction is confirmed via experiments on thin bulk-insulating (Bi1−xSbx)2Te3 (BST) TI nanowires, in which we observe an MCA consistent with theory and ∣γ∣ ≈ 100,000 A−1 T−1, a very large MCA rectification coefficient in a normal conductor.

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The critical current of a superconductor can depend on the direction of current flow due to magnetochiral anisotropy when both inversion and time-reversal symmetry are broken, an effect known as the superconducting (SC) diode effect. Here, we consider one-dimensional (1D) systems in which superconductivity is induced via the proximity effect. In both topological insulator and Rashba nanowires, the SC diode effect due to a magnetic field applied along the spin-polarization axis and perpendicular to the nanowire provides a measure of inversion symmetry breaking in the presence of a superconductor. Furthermore, a strong dependence of the SC diode effect on an additional component of magnetic field applied parallel to the nanowire as well as on the position of the chemical potential can be used to detect that a device is in the region of parameter space where the phase transition to topological superconductivity is expected to arise.