Observation of Josephson harmonics in tunnel junctions.

Approaches to developing large-scale superconducting quantum processors must cope with the numerous microscopic degrees of freedom that are ubiquitous in solid-state devices. State-of-the-art superconducting qubits employ aluminium oxide (AlOx) tunnel Josephson junctions as the sources of nonlinearity necessary to perform quantum operations. Analyses of these junctions typically assume an idealized, purely sinusoidal current-phase relation. However, this relation is expected to hold only in the limit of vanishingly low-transparency channels in the AlOx barrier. Here we show that the standard current-phase relation fails to accurately describe the energy spectra of transmon artificial atoms across various samples and laboratories. Instead, a mesoscopic model of tunnelling through an inhomogeneous AlOx barrier predicts percent-level contributions from higher Josephson harmonics. By including these in the transmon Hamiltonian, we obtain orders of magnitude better agreement between the computed and measured energy spectra. The presence and impact of Josephson harmonics has important implications for developing AlOx-based quantum technologies including quantum computers and parametric amplifiers. As an example, we show that engineered Josephson harmonics can reduce the charge dispersion and associated errors in transmon qubits by an order of magnitude while preserving their anharmonicity.

Atomic Diffusion-Induced Polarization and Superconductivity in Topological Insulator-Based Heterostructures.

The proximity effect at a highly transparent interface of an s-wave superconductor (S) and a topological insulator (TI) provides a promising platform to create Majorana zero modes in artificially designed heterostructures. However, structural and chemical issues pertinent to such interfaces have been poorly explored so far. Here, we report the discovery of Pd diffusion-induced polarization at interfaces between superconductive Pd1+x(Bi0.4Te0.6)2 (xPBT, 0 ≤ x ≤ 1) and Pd-intercalated Bi2Te3 by using atomic-resolution scanning transmission electron microscopy. Our quantitative image analysis reveals that nanoscale lattice strain and QL polarity synergistically suppress and promote Pd diffusion at the normal and parallel interfaces, formed between Te-Pd-Bi triple layers (TLs) and Te-Bi-Te-Bi-Te quintuple layers (QLs), respectively. Further, our first-principles calculations unveil that the superconductivity of the xPBT phase and topological nature of the Pd-intercalated Bi2Te3 phase are robust against the broken inversion symmetry. These findings point out the necessity of considering the coexistence of electric polarization with superconductivity and topology in such S-TI systems.

Antiferromagnetic topological insulator with selectively gapped Dirac cones.

Antiferromagnetic (AF) topological materials offer a fertile ground to explore a variety of quantum phenomena such as axion magnetoelectric dynamics and chiral Majorana fermions. To realize such intriguing states, it is essential to establish a direct link between electronic states and topology in the AF phase, whereas this has been challenging because of the lack of a suitable materials platform. Here we report the experimental realization of the AF topological-insulator phase in NdBi. By using micro-focused angle-resolved photoemission spectroscopy, we discovered contrasting surface electronic states for two types of AF domains; the surface having the out-of-plane component in the AF-ordering vector displays Dirac-cone states with a gigantic energy gap, whereas the surface parallel to the AF-ordering vector hosts gapless Dirac states despite the time-reversal-symmetry breaking. The present results establish an essential role of combined symmetry to protect massless Dirac fermions under the presence of AF order and widen opportunities to realize exotic phenomena utilizing AF topological materials.

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.

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.

Two-Dimensional-Dirac Surface States and Bulk Gap Probed via Quantum Capacitance in a Three-Dimensional Topological Insulator.

BiSbTeSe2 is a 3D topological insulator (3D-TI) with Dirac type surface states and low bulk carrier density, as donors and acceptors compensate each other. Dominating low-temperature surface transport in this material is heralded by Shubnikov-de Haas oscillations and the quantum Hall effect. Here, we experimentally probe and model the electronic density of states (DOS) in thin layers of BiSbTeSe2 by capacitance experiments both without and in quantizing magnetic fields. By probing the lowest Landau levels, we show that a large fraction of the electrons filled via field effect into the system ends up in (localized) bulk states and appears as a background DOS. The surprisingly strong temperature dependence of such background DOS can be traced back to Coulomb interactions. Our results point at the coexistence and intimate coupling of Dirac surface states with a bulk many-body phase (a Coulomb glass) in 3D-TIs.

Uniaxial-strain control of nematic superconductivity in SrxBi2Se3.

Nematic states are characterized by rotational symmetry breaking without translational ordering. Recently, nematic superconductivity, in which the superconducting gap spontaneously lifts the rotational symmetry of the lattice, has been discovered. In nematic superconductivity, multiple superconducting domains with different nematic orientations can exist, and these domains can be controlled by a conjugate external stimulus. Domain engineering is quite common in magnets but has not been achieved in superconductors. Here, we report control of the nematic superconductivity and their domains of SrxBi2Se3, through externally-applied uniaxial stress. The suppression of subdomains indicates that it is the Δ4y state that is most favoured under compression along the basal Bi-Bi bonds. This fact allows us to determine the coupling parameter between the nematicity and lattice distortion. These results provide an inevitable step towards microscopic understanding and future utilization of the unique topological nematic superconductivity.

Generalized Anderson's theorem for superconductors derived from topological insulators.

A well-known result in unconventional superconductivity is the fragility of nodal superconductors against nonmagnetic impurities. Despite this common wisdom, Bi2Se3-based topological superconductors have recently displayed unusual robustness against disorder. Here, we provide a theoretical framework that naturally explains what protects Cooper pairs from strong scattering in complex superconductors. Our analysis is based on the concept of superconducting fitness and generalizes the famous Anderson's theorem into superconductors having multiple internal degrees of freedom with simple assumptions such as the Born approximation. For concreteness, we report on the extreme example of the Cu x (PbSe)5(BiSe3)6 superconductor. Thermal conductivity measurements down to 50 mK not only give unambiguous evidence for the existence of nodes but also reveal that the energy scale corresponding to the scattering rate is orders of magnitude larger than the superconducting energy gap. This provides the most spectacular case of the generalized Anderson's theorem protecting a nodal superconductor.

Conversion of a conventional superconductor into a topological superconductor by topological proximity effect.

Realization of topological superconductors (TSCs) hosting Majorana fermions is a central challenge in condensed-matter physics. One approach is to use the superconducting proximity effect (SPE) in heterostructures, where a topological insulator contacted with a superconductor hosts an effective p-wave pairing by the penetration of Cooper pairs across the interface. However, this approach suffers a difficulty in accessing the topological interface buried deep beneath the surface. Here, we propose an alternative approach to realize topological superconductivity without SPE. In a Pb(111) thin film grown on TlBiSe2, we discover that the Dirac-cone state of substrate TlBiSe2 migrates to the top surface of Pb film and obtains an energy gap below the superconducting transition temperature of Pb. This suggests that a Bardeen-Cooper-Schrieffer superconductor is converted into a TSC by the topological proximity effect. Our discovery opens a route to manipulate topological superconducting properties of materials.

Nanomosaic of Topological Dirac States on the Surface of Pb5Bi24Se41 Observed by Nano-ARPES.

We have performed scanning angle-resolved photoemission spectroscopy with a nanometer-sized beam spot (nano-ARPES) on the cleaved surface of Pb5Bi24Se41, which is a member of the (PbSe)5(Bi2Se3)3 m homologous series (PSBS) with m = 4 consisting of alternate stacking of the topologically trivial insulator PbSe bilayer and four quintuple layers (QLs) of the topological insulator Bi2Se3. This allows us to visualize a mosaic of topological Dirac states at a nanometer scale coming from the variable thickness of the Bi2Se3 nanoislands (1-3 QLs) that remain on top of the PbSe layer after cleaving the PSBS crystal, because the local band structure of topological origin changes drastically with the thickness of the Bi2Se3 nanoislands. A comparison of the local band structure with that in ultrathin Bi2Se3 films on Si(111) gives us further insights into the nature of the observed topological states. This result demonstrates that nano-ARPES is a very useful tool for characterizing topological heterostructures.

Observation of Chiral Fermions with a Large Topological Charge and Associated Fermi-Arc Surface States in CoSi.

Topological semimetals materialize a new state of quantum matter where massless fermions protected by a specific crystal symmetry host exotic quantum phenomena. Distinct from well-known Dirac and Weyl fermions, structurally chiral topological semimetals are predicted to host new types of massless fermions characterized by a large topological charge, whereas such exotic fermions are yet to be experimentally established. Here, by using angle-resolved photoemission spectroscopy, we experimentally demonstrate that a transition-metal silicide CoSi hosts two types of chiral topological fermions, a spin-1 chiral fermion and a double Weyl fermion, in the center and corner of the bulk Brillouin zone, respectively. Intriguingly, we found that the bulk Fermi surfaces are purely composed of the energy bands related to these fermions. We also find the surface states connecting the Fermi surfaces associated with these fermions, suggesting the existence of the predicted Fermi-arc surface states. Our result provides the first experimental evidence for the chiral topological fermions beyond Dirac and Weyl fermions in condensed-matter systems, and paves the pathway toward realizing exotic electronic properties associated with unconventional chiral fermions.

Observation of Room-Temperature Photoluminescence Blinking in Armchair-Edge Graphene Nanoribbons.

By enhancing the photoluminescence from aligned seven-atom wide armchair-edge graphene nanoribbons using plasmonic nanoantennas, we are able to observe blinking of the emission. The on- and off-times of the blinking follow power law statistics. In time-resolved spectra, we observe spectral diffusion. These findings together are a strong indication of the emission originating from a single quantum emitter. The room temperature photoluminescence displays a narrow spectral width of less than 50 meV, which is significantly smaller than the previously observed ensemble line width of 0.8 eV. From spectral time traces, we identify three optical transitions, which are energetically situated below the lowest bulk excitonic state E11 of the nanoribbons. We attribute the emission to transitions involving Tamm states localized at the end of the nanoribbon. The photoluminescence from a single ribbon is strongly enhanced when its end is in the antenna hot spot resulting in the observed single molecule characteristics of the emission. Our findings illustrate the essential role of the end termination of graphene nanoribbons in light emission and allow us to construct a model for photoluminescence from nanoribbons.

Anomalous Fraunhofer Patterns in Gated Josephson Junctions Based on the Bulk-Insulating Topological Insulator BiSbTeSe2.

One-dimensional Majorana modes are predicated to form in Josephson junctions based on three-dimensional topological insulators (TIs). While observations of supercurrents in Josephson junctions made on bulk-insulating TI samples have been reported recently, the Fraunhofer patters observed in such TI-based Josephson junctions, which sometimes present anomalous features, are still not well-understood. Here, we report our study of highly gate-tunable TI-based Josephson junctions made of one of the most bulk-insulating TI materials, BiSbTeSe2, and Al. The Fermi level can be tuned by gating across the Dirac point, and the high transparency of the Al-BiSbTeSe2 interface is evinced by a high characteristic voltage and multiple Andreev reflections, with peak indices reaching 12. Anomalous Fraunhofer patterns with missing lobes were observed in the entire range of gate voltage. We found that, by employing an advanced fitting procedure to use the maximum entropy method in a Monte Carlo algorithm, the anomalous Fraunhofer patterns are explained as a result of inhomogeneous supercurrent distributions on the TI surface in the junction. Besides establishing a highly promising fabrication technology, this work clarifies one of the important open issues regarding TI-based Josephson junctions.

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.

Gigantic negative magnetoresistance in the bulk of a disordered topological insulator.

With the recent discovery of Weyl semimetals, the phenomenon of negative magnetoresistance (MR) is attracting renewed interest. Large negative MR is usually related to magnetism, but the chiral anomaly in Weyl semimetals is a rare exception. Here we report a mechanism for large negative MR which is also unrelated to magnetism but is related to disorder. In the nearly bulk-insulating topological insulator TlBi0.15Sb0.85Te2, we observed gigantic negative MR reaching 98% in 14 T at 10 K, which is unprecedented in a nonmagnetic system. Supported by numerical simulations, we argue that this phenomenon is likely due to the Zeeman effect on a barely percolating current path formed in the disordered bulk. Since disorder can also lead to non-saturating linear MR in Ag2+δSe, the present finding suggests that disorder engineering in narrow-gap systems is useful for realizing gigantic MR in both positive and negative directions.

Topological superconductors: a review.

This review elaborates pedagogically on the fundamental concept, basic theory, expected properties, and materials realizations of topological superconductors. The relation between topological superconductivity and Majorana fermions are explained, and the difference between dispersive Majorana fermions and a localized Majorana zero mode is emphasized. A variety of routes to topological superconductivity are explained with an emphasis on the roles of spin-orbit coupling. Present experimental situations and possible signatures of topological superconductivity are summarized with an emphasis on intrinsic topological superconductors.

Dual-gated topological insulator thin-film device for efficient Fermi-level tuning.

Observations of novel quantum phenomena expected for three-dimensional topological insulators (TIs) often require fabrications of thin-film devices and tuning of the Fermi level across the Dirac point. Since thin films have both top and bottom surfaces, an effective control of the surface chemical potential requires dual gating. However, a reliable dual-gating technique for TI thin films has not yet been developed. Here we report a comprehensive method to fabricate a dual-gated TI device and demonstrate tuning of the chemical potential of both surfaces across the Dirac points. The most important part of our method is the recipe for safely detaching high-quality, bulk-insulating (Bi(1-x)Sb(x))2Te3 thin films from sapphire substrates and transferring them to Si/SiO2 wafers that allow back gating. Fabrication of an efficient top gate by low-temperature deposition of a SiN(x) dielectric complements the procedure. Our dual-gated devices are shown to be effective in tuning the chemical potential in a wide range encompassing the Dirac points on both surfaces.