Interacting multi-channel topological boundary modes in a quantum Hall valley system.

Symmetry and topology are central to understanding quantum Hall ferromagnets (QHFMs), two-dimensional electronic phases with spontaneously broken spin or pseudospin symmetry whose wavefunctions also have topological properties1,2. Domain walls between distinct broken-symmetry QHFM phases are predicted to host gapless one-dimensional modes-that is, quantum channels that emerge because of a topological change in the underlying electronic wavefunctions at such interfaces. Although various QHFMs have been identified in different materials3-8, interacting electronic modes at these domain walls have not been probed. Here we use a scanning tunnelling microscope to directly visualize the spontaneous formation of boundary modes at domain walls between QHFM phases with different valley polarization (that is, the occupation of equal-energy but quantum mechanically distinct valleys in the electronic structure) on the surface of bismuth. Spectroscopy shows that these modes occur within a topological energy gap, which closes and reopens as the valley polarization switches across the domain wall. By changing the valley flavour and the number of modes at the domain wall, we can realize different regimes in which the valley-polarized channels are either metallic or develop a spectroscopic gap. This behaviour is a consequence of Coulomb interactions constrained by the valley flavour, which determines whether electrons in the topological modes can backscatter, making these channels a unique class of interacting one-dimensional quantum wires. QHFM domain walls can be realized in different classes of two-dimensional materials, providing the opportunity to explore a rich phase space of interactions in these quantum wires.

Phase tuning of multiple Andreev reflections of Dirac fermions and the Josephson supercurrent in Al-MoTe2-Al junctions.

When an electron is incident on a superconductor from a metal, it is reflected as a hole in a process called Andreev reflection. If the metal N is sandwiched between two superconductors S in an SNS junction, multiple Andreev reflections (MARs) occur. We have found that, in SNS junctions with high transparency ([Formula: see text]) based on the Dirac semimetal MoTe2, the MAR features are observed with exceptional resolution. By tuning the phase difference [Formula: see text] between the bracketing Al superconductors, we establish that the MARs coexist with a Josephson supercurrent [Formula: see text]. As we vary the junction voltage V, the supercurrent amplitude [Formula: see text] varies in step with the MAR order n, revealing a direct relation between them. Two successive Andreev reflections serve to shuttle a Cooper pair across the junction. If the pair is shuttled coherently, it contributes to [Formula: see text]. The experiment measures the fraction of pairs shuttled coherently vs. V. Surprisingly, superconductivity in MoTe2 does not affect the MAR features.

A magnetic continuum in the cobalt-based honeycomb magnet BaCo2(AsO4)2.

Quantum spin liquids (QSLs) are topologically ordered states of matter that host fractionalized excitations. A particular route towards a QSL is via strongly bond-dependent interactions on the hexagonal lattice. A number of Ru- and Ir-based candidate Kitaev QSL materials have been pursued, but all have appreciable non-Kitaev interactions. Using time-domain terahertz spectroscopy, we observed a broad magnetic continuum over a wide range of temperatures and fields in the honeycomb cobalt-based magnet BaCo2(AsO4)2, which has been proposed to be a more ideal version of a Kitaev QSL. Applying an in-plane magnetic field of ~0.5 T suppresses the magnetic order, and at higher fields, applying the field gives rise to a spin-polarized state. Under a 4 T magnetic field that was oriented principally out of plane, a broad magnetic continuum was observed that may be consistent with a field-induced QSL. Our results indicate BaCo2(AsO4)2 is a promising QSL candidate.

Hexagonal Perovskites as Quantum Materials.

Hexagonal perovskites, in contrast to the more familiar perovskites, when oxides, allow for face-sharing of metal-oxygen octahedra or trigonal prisms within their structural frameworks. This results in dimers, trimers, tetramers, or longer fragments of chains of face-sharing octahedra in the crystal structures, and consequently in much shorter metal-metal distances and lower metal-oxygen-metal bond angles than are seen in the more familiar perovskites. The presence of the face-sharing octahedra can have a dramatic impact on magnetic properties of these compounds, and dimer-based materials, in particular, have been the subjects of many quantum-materials-directed studies in materials physics. Hexagonal oxide perovskites are also of contemporary interest due to their potential for geometrical frustration of the ordering of magnetic moments or orbital occupancies at low temperatures, which is especially relevant to their significance as quantum materials. As such, several hexagonal oxide perovskites have been identified as potential candidates for hosting the quantum-spin-liquid state at low temperatures. In our view, hexagonal oxide perovskites are fertile ground for finding new quantum materials. This review briefly describes the solid state chemistry of many of these materials.

Discovery of intrinsic ferromagnetism in two-dimensional van der Waals crystals.

The realization of long-range ferromagnetic order in two-dimensional van der Waals crystals, combined with their rich electronic and optical properties, could lead to new magnetic, magnetoelectric and magneto-optic applications. In two-dimensional systems, the long-range magnetic order is strongly suppressed by thermal fluctuations, according to the Mermin-Wagner theorem; however, these thermal fluctuations can be counteracted by magnetic anisotropy. Previous efforts, based on defect and composition engineering, or the proximity effect, introduced magnetic responses only locally or extrinsically. Here we report intrinsic long-range ferromagnetic order in pristine Cr2Ge2Te6 atomic layers, as revealed by scanning magneto-optic Kerr microscopy. In this magnetically soft, two-dimensional van der Waals ferromagnet, we achieve unprecedented control of the transition temperature (between ferromagnetic and paramagnetic states) using very small fields (smaller than 0.3 tesla). This result is in contrast to the insensitivity of the transition temperature to magnetic fields in the three-dimensional regime. We found that the small applied field leads to an effective anisotropy that is much greater than the near-zero magnetocrystalline anisotropy, opening up a large spin-wave excitation gap. We explain the observed phenomenon using renormalized spin-wave theory and conclude that the unusual field dependence of the transition temperature is a hallmark of soft, two-dimensional ferromagnetic van der Waals crystals. Cr2Ge2Te6 is a nearly ideal two-dimensional Heisenberg ferromagnet and so will be useful for studying fundamental spin behaviours, opening the door to exploring new applications such as ultra-compact spintronics.

Structural Diversity in Oxoiridates with 1D IrnO3(n+1) Chain Fragments and Flat Bands.

A previously unreported series of hexagonal-perovskite-based Rb-oxoiridates, Rb5Ir2O9, Rb7Ir3O12, and Rb12Ir7O24, have been synthesized and structurally analyzed via N2-protected single-crystal X-ray diffraction (SC-XRD). These materials exhibit different 1D IrnO3(n+1) chain fragments along their c axes. IrO6 octahedra and RbOx (x = 6, 8, and 10) polyhedra are their basic building blocks. The IrO6 octahedra are linked via face-sharing, forming Ir2O9 dimers, Ir3O12 trimers, and Ir7O24 heptamers. The nonmagnetic RbOx (x = 6, 8, and 10) polyhedra serve as both bridging units and spacers. Temperature-dependent SC-XRD shows all three to display positive thermal expansion and rules out structural transitions from their triangular symmetries down to 100 K. Density functional theory results suggest semiconducting-like behavior for the title compounds. The flatness of the electronic bands and our structural analysis are of potential interest for understanding and designing 1D quantum materials.

Hourglass fermions.

Spatial symmetries in crystals may be distinguished by whether they preserve the spatial origin. Here we study spatial symmetries that translate the origin by a fraction of the lattice period, and find that these non-symmorphic symmetries protect an exotic surface fermion whose dispersion relation is shaped like an hourglass; surface bands connect one hourglass to the next in an unbreakable zigzag pattern. These 'hourglass' fermions are formed in the large-gap insulators, KHgX (X = As, Sb, Bi), which we propose as the first material class whose band topology relies on non-symmorphic symmetries. Besides the hourglass fermion, another surface of KHgX manifests a three-dimensional generalization of the quantum spin Hall effect, which has previously been observed only in two-dimensional crystals. To describe the bulk topology of non-symmorphic crystals, we propose a non-Abelian generalization of the geometric theory of polarization. Our non-trivial topology originates from an inversion of the rotational quantum numbers, which we propose as a criterion in the search for topological materials.

K3Ir2O6 and K16.3Ir8O30, Low-Dimensional Iridates with Infinite IrO6 Chains.

A previously unreported 1D iridate, K3Ir2O6, has been grown by a flux method in O2-rich environment, and its crystal structure was determined via single crystal structural analysis. It exhibits straight chains of face-sharing [IrO6] octahedra, which are arranged along the crystallographic c axis, separated by nonmagnetic K ions. No magnetic transitions are observed during measured range, and the material is electrically insulating. Potentially interesting electronic behavior for K3Ir2O6 is supported by electronic structure calculations. A structurally related material, K16.3Ir8O30, which displays similar fundamental geometric units but in a different spatial arrangement-zigzag chains-based on edge and face sharing [IrO6] octahedra, is also reported. Both materials are of interest for probing the properties of a 1D system with strong spin-orbit coupling.

A gap-protected zero-Hall effect state in the quantum limit of the non-symmorphic metal KHgSb.

A recurring theme in topological matter is the protection of unusual electronic states by symmetry, for example, protection of the surface states in Z2 topological insulators by time-reversal symmetry1-3. Recently, interest has turned to unusual surface states in the large class of non-symmorphic materials4-12. In particular, KHgSb is predicted to exhibit double quantum spin Hall states10. Here we report measurements of the Hall conductivity in KHgSb in a strong magnetic field B. In the quantum limit, the Hall conductivity is observed to fall exponentially to zero, but the diagonal conductivity is finite. A large gap protects this unusual zero-Hall state. We theoretically propose that, in this quantum limit, the chemical potential drops into the bulk gap, intersecting equal numbers of right- and left-moving quantum spin Hall surface modes to produce the zero-Hall state. The zero-Hall state illustrates how topological protection in a non-symmorphic material with glide symmetry may lead to highly unusual transport phenomena.

Large, non-saturating magnetoresistance in WTe2.

Magnetoresistance is the change in a material's electrical resistance in response to an applied magnetic field. Materials with large magnetoresistance have found use as magnetic sensors, in magnetic memory, and in hard drives at room temperature, and their rarity has motivated many fundamental studies in materials physics at low temperatures. Here we report the observation of an extremely large positive magnetoresistance at low temperatures in the non-magnetic layered transition-metal dichalcogenide WTe2: 452,700 per cent at 4.5 kelvins in a magnetic field of 14.7 teslas, and 13 million per cent at 0.53 kelvins in a magnetic field of 60 teslas. In contrast with other materials, there is no saturation of the magnetoresistance value even at very high applied fields. Determination of the origin and consequences of this effect, and the fabrication of thin films, nanostructures and devices based on the extremely large positive magnetoresistance of WTe2, will represent a significant new direction in the study of magnetoresistivity.

Triangular Rare-Earth Lattice Materials RbBa R(BO3)2 ( R = Y, Gd-Yb) and Comparison to the KBa R(BO3)2 Analogs.

A previously unreported family of electrically insulating rare-earth borates, RbBa R(BO3)2 ( R = Y, Gd-Yb), was designed and then successfully obtained by traditional solid-state reaction. They crystallize in a monoclinic crystal system space group P21 /m (No. 11). They feature triangular planar rare-earth ( R) lattices, which are part of, for example, [Yb(BO3)2]3- infinite 2D layers. These R-based triangular lattices are stacked with layers of crystallographically ordered Rb and Ba atoms to build the 3D structures. Polycrystalline samples of RbBa R(BO3)2 were used to study the elementary magnetic properties, and millimeter-size RbBaYb(BO3)2 single crystals were grown by spontaneous nucleation for further anisotropic magnetic characterization. Antiferromagnetic spin interactions are observed for all magnetic compounds, and no long-range magnetic ordering is found down to 1.8 K. Our results suggest that this RbBa R(BO3)2 ( R = Gd-Yb) family may be of further interest both experimentally and theoretically as highly geometrically frustrated magnets.

Band Structure of the IV-VI Black Phosphorus Analog and Thermoelectric SnSe.

The success of black phosphorus in fast electronic and photonic devices is hindered by its rapid degradation in the presence of oxygen. Orthorhombic tin selenide is a representative of group IV-VI binary compounds that are robust and isoelectronic and share the same structure with black phosphorus. We measure the band structure of SnSe and find highly anisotropic valence bands that form several valleys having fast dispersion within the layers and negligible dispersion across. This is exactly the band structure desired for efficient thermoelectric generation where SnSe has shown great promise.

The chiral anomaly and thermopower of Weyl fermions in the half-Heusler GdPtBi.

The Dirac and Weyl semimetals are unusual materials in which the nodes of the bulk states are protected against gap formation by crystalline symmetry. The chiral anomaly, predicted to occur in both systems, was recently observed as a negative longitudinal magnetoresistance (LMR) in Na3Bi (ref. ) and in TaAs (ref. ). An important issue is whether Weyl physics appears in a broader class of materials. We report evidence for the chiral anomaly in the half-Heusler GdPtBi. In zero field, GdPtBi is a zero-gap semiconductor with quadratic bands. In a magnetic field, the Zeeman energy leads to Weyl nodes. We have observed a large negative LMR with the field-steering properties specific to the chiral anomaly. The chiral anomaly also induces strong suppression of the thermopower. We report a detailed study of the thermoelectric response function αxx of Weyl fermions. The scheme of creating Weyl nodes from quadratic bands suggests that the chiral anomaly may be observable in a broad class of semimetals.

Anomalous Nernst Effect in the Dirac Semimetal Cd_{3}As_{2}.

Dirac and Weyl semimetals display a host of novel properties. In Cd_{3}As_{2}, the Dirac nodes lead to a protection mechanism that strongly suppresses backscattering in a zero magnetic field, resulting in ultrahigh mobility (∼10^{7} cm^{2} V^{-1} s^{-1}). In an applied magnetic field, an anomalous Nernst effect is predicted to arise from the Berry curvature associated with the Weyl nodes. We report the observation of a large anomalous Nernst effect in Cd_{3}As_{2}. Both the anomalous Nernst signal and transport relaxation time τ_{tr} begin to increase rapidly at ∼50 K. This suggests a close relation between the protection mechanism and the anomalous Nernst effect. In a field, the quantum oscillations of bulk states display a beating effect, suggesting that the Dirac nodes split into Weyl states, allowing the Berry curvature to be observed as an anomalous Nernst effect.

Three-Dimensional Electronic Structure of the Type-II Weyl Semimetal WTe_{2}.

By combining bulk sensitive soft-x-ray angular-resolved photoemission spectroscopy and first-principles calculations we explored the bulk electron states of WTe_{2}, a candidate type-II Weyl semimetal featuring a large nonsaturating magnetoresistance. Despite the layered geometry suggesting a two-dimensional electronic structure, we directly observe a three-dimensional electronic dispersion. We report a band dispersion in the reciprocal direction perpendicular to the layers, implying that electrons can also travel coherently when crossing from one layer to the other. The measured Fermi surface is characterized by two well-separated electron and hole pockets at either side of the Γ point, differently from previous more surface sensitive angle-resolved photoemission spectroscopy experiments that additionally found a pronounced quasiparticle weight at the zone center. Moreover, we observe a significant sensitivity of the bulk electronic structure of WTe_{2} around the Fermi level to electronic correlations and renormalizations due to self-energy effects, previously neglected in first-principles descriptions.

Ultrahigh mobility and giant magnetoresistance in the Dirac semimetal Cd3As2.

Dirac and Weyl semimetals are 3D analogues of graphene in which crystalline symmetry protects the nodes against gap formation. Na3Bi and Cd3As2 were predicted to be Dirac semimetals, and recently confirmed to be so by photoemission experiments. Several novel transport properties in a magnetic field have been proposed for Dirac semimetals. Here, we report a property of Cd3As2 that was unpredicted, namely a remarkable protection mechanism that strongly suppresses backscattering in zero magnetic field. In single crystals, the protection results in ultrahigh mobility, 9 × 10(6) cm(2) V(-1) s(-1) at 5 K. Suppression of backscattering results in a transport lifetime 10(4) times longer than the quantum lifetime. The lifting of this protection by the applied magnetic field leads to a very large magnetoresistance. We discuss how this may relate to changes to the Fermi surface induced by the applied magnetic field.

Magneto-Optical Signature of Massless Kane Electrons in Cd_{3}As_{2}.

We report on optical reflectivity experiments performed on Cd_{3}As_{2} over a broad range of photon energies and magnetic fields. The observed response clearly indicates the presence of 3D massless charge carriers. The specific cyclotron resonance absorption in the quantum limit implies that we are probing massless Kane electrons rather than symmetry-protected 3D Dirac particles. The latter may appear at a smaller energy scale and are not directly observed in our infrared experiments.

Superconductivity in CaBi2.

Superconductivity is observed with critical temperature Tc = 2.0 K in self-flux-grown single crystals of CaBi2. This material adopts the ZrSi2 structure type with lattice parameters a = 4.696(1) Å, b = 17.081(2) Å and c = 4.611(1) Å. The crystals of CaBi2 were studied by means of magnetic susceptibility, specific heat and electrical resistivity measurements. The heat capacity jump at Tc is ΔC/γTc = 1.41, confirming bulk superconductivity; the Sommerfeld coefficient γ = 4.1 mJ mol(-1) K(-2) and the Debye temperature ΘD = 157 K. The electron-phonon coupling strength is λel-ph = 0.59, and the thermodynamic critical field Hc is low, between 111 and 124 Oe CaBi2 is a moderate coupling type-I superconductor. Results of electronic structure calculations are reported and charge densities, electronic bands, densities of states and Fermi surfaces are discussed, focusing on the effects of spin-orbit coupling and electronic property anisotropy. We find a mixed quasi-2D + 3D character in the electronic structure, which reflects the layered crystal structure of the material.

Transmission of topological surface states through surface barriers.

Topological surface states are a class of novel electronic states that are of potential interest in quantum computing or spintronic applications. Unlike conventional two-dimensional electron states, these surface states are expected to be immune to localization and to overcome barriers caused by material imperfection. Previous experiments have demonstrated that topological surface states do not backscatter between equal and opposite momentum states, owing to their chiral spin texture. However, so far there is no evidence that these states in fact transmit through naturally occurring surface defects. Here we use a scanning tunnelling microscope to measure the transmission and reflection probabilities of topological surface states of antimony through naturally occurring crystalline steps separating atomic terraces. In contrast to non-topological surface states of common metals (copper, silver and gold), which are either reflected or absorbed by atomic steps, we show that topological surface states of antimony penetrate such barriers with high probability. This demonstration of the extended nature of antimony's topological surface states suggests that such states may be useful for high current transmission even in the presence of atomic-scale irregularities-an electronic feature sought to efficiently interconnect nanoscale devices.

Gapped Surface States in a Strong-Topological-Insulator Material.

A three-dimensional strong-topological insulator or semimetal hosts topological surface states which are often said to be gapless so long as time-reversal symmetry is preserved. This narrative can be mistaken when surface state degeneracies occur away from time-reversal-invariant momenta. The mirror invariance of the system then becomes essential in protecting the existence of a surface Fermi surface. Here we show that such a case exists in the strong-topological-semimetal Bi(4)Se(3). Angle-resolved photoemission spectroscopy and ab initio calculations reveal partial gapping of surface bands on the Bi(2)Se(3) termination of Bi(4)Se(3)(111), where an 85 meV gap along Γ̅K̅ closes to zero toward the mirror-invariant Γ̅M̅ azimuth. The gap opening is attributed to an interband spin-orbit interaction that mixes states of opposite spin helicity.