Nonlinear Transport due to Magnetic-Field-Induced Flat Bands in the Nodal-Line Semimetal ZrTe_{5}.

The Dirac material ZrTe_{5} at very low carrier density was recently found to be a nodal-line semimetal, where ultraflat bands are expected to emerge in magnetic fields parallel to the nodal-line plane. Here, we report that in very low carrier-density samples of ZrTe_{5}, when the current and the magnetic field are both along the crystallographic a axis, the current-voltage characteristics presents a pronounced nonlinearity which tends to saturate in the ultra quantum limit. The magnetic-field dependence of the nonlinear coefficient is well explained by the Boltzmann theory for flat-band transport, and we argue that this nonlinear transport is likely due to the combined effect of flat bands and charge puddles; the latter appear due to very low carrier densities.

Trivial Andreev Band Mimicking Topological Bulk Gap Reopening in the Nonlocal Conductance of Long Rashba Nanowires.

We consider a one-dimensional Rashba nanowire in which multiple Andreev bound states in the bulk of the nanowire form an Andreev band. We show that, under certain circumstances, this trivial Andreev band can produce an apparent closing and reopening signature of the bulk band gap in the nonlocal conductance of the nanowire. Furthermore, we show that the existence of the trivial bulk reopening signature in nonlocal conductance is essentially unaffected by the additional presence of trivial zero-bias peaks in the local conductance at either end of the nanowire. The simultaneous occurrence of a trivial bulk reopening signature and zero-bias peaks mimics the basic features required to pass the so-called "topological gap protocol." Our results therefore provide a topologically trivial minimal model by which the applicability of this protocol can be benchmarked.

Top-Down Fabrication of Bulk-Insulating Topological Insulator Nanowires for Quantum Devices.

In a nanowire (NW) of a three-dimensional topological insulator (TI), the quantum confinement of topological surface states leads to a peculiar sub-band structure that is useful for generating Majorana bound states. Top-down fabrication of TINWs from a high-quality thin film would be a scalable technology with great design flexibility, but there has been no report on top-down-fabricated TINWs where the chemical potential can be tuned to the charge neutrality point (CNP). Here we present a top-down fabrication process for bulk-insulating TINWs etched from high-quality (Bi1-xSbx)2Te3 thin films without degradation. We show that the chemical potential can be gate-tuned to the CNP, and the resistance of the NW presents characteristic oscillations as functions of the gate voltage and the parallel magnetic field, manifesting the TI-sub-band physics. We further demonstrate the superconducting proximity effect in these TINWs, preparing the groundwork for future devices to investigate Majorana bound states.

Gigantic Magnetochiral Anisotropy in the Topological Semimetal ZrTe_{5}.

Topological materials with broken inversion symmetry can give rise to nonreciprocal responses, such as the current rectification controlled by magnetic fields via magnetochiral anisotropy. Bulk nonreciprocal responses usually stem from relativistic corrections and are always very small. Here we report our discovery that ZrTe_{5} crystals in proximity to a topological quantum phase transition present gigantic magnetochiral anisotropy, which is the largest ever observed to date. We argue that a very low carrier density, inhomogeneities, and a torus-shaped Fermi surface induced by breaking of inversion symmetry in a Dirac material are central to explain this extraordinary property.

Giant magnetochiral anisotropy from quantum-confined surface states of topological insulator nanowires.

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.

Quantum confinement of the Dirac surface states in topological-insulator nanowires.

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.

Spin liquid mediated RKKY interaction.

We propose an RKKY-type interaction that is mediated by a spin liquid. If a spin liquid exists such an interaction could leave a fingerprint by ordering underlying localised moments such as nuclear spins. This interaction has a unique phenomenology that is distinct from the RKKY interaction found in fermionic systems; most notably the lack of a Fermi surface and absence of the requirement for itinerant electrons, since most spin liquids are insulators. We demonstrate that the interaction is predominately shaped by the lattice symmetries of the underlying spin liquid. As a working example we investigate the possible ordering of nuclear spins that interact through an underlying lattice of the two-dimensional spin-1/2 kagome antiferromagnet (KHAF), although the treatment remains general and can be extended to other spin liquids and dimensions. We find that several different nuclear spin orderings minimise the RKKY-type energy induced by the KHAF but are unstable due to a zero-energy flat magnon band in linear spin-wave theory. Despite this we show that a small magnetic field is able to gap out this magnon spectrum resulting in an intricate nuclear magnetism.

Planar Hall effect from the surface of topological insulators.

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-x Sb x Te3 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.