Observation of the nonlinear Hall effect under time-reversal-symmetric conditions.

The electrical Hall effect is the production, upon the application of an electric field, of a transverse voltage under an out-of-plane magnetic field. Studies of the Hall effect have led to important breakthroughs, including the discoveries of Berry curvature and topological Chern invariants1,2. The internal magnetization of magnets means that the electrical Hall effect can occur in the absence of an external magnetic field2; this 'anomalous' Hall effect is important for the study of quantum magnets2-7. The electrical Hall effect has rarely been studied in non-magnetic materials without external magnetic fields, owing to the constraint of time-reversal symmetry. However, only in the linear response regime-when the Hall voltage is linearly proportional to the external electric field-does the Hall effect identically vanish as a result of time-reversal symmetry; the Hall effect in the nonlinear response regime is not subject to such symmetry constraints8-10. Here we report observations of the nonlinear Hall effect10 in electrical transport in bilayers of the non-magnetic quantum material WTe2 under time-reversal-symmetric conditions. We show that an electric current in bilayer WTe2 leads to a nonlinear Hall voltage in the absence of a magnetic field. The properties of this nonlinear Hall effect are distinct from those of the anomalous Hall effect in metals: the nonlinear Hall effect results in a quadratic, rather than linear, current-voltage characteristic and, in contrast to the anomalous Hall effect, the nonlinear Hall effect results in a much larger transverse than longitudinal voltage response, leading to a nonlinear Hall angle (the angle between the total voltage response and the applied electric field) of nearly 90 degrees. We further show that the nonlinear Hall effect provides a direct measure of the dipole moment10 of the Berry curvature, which arises from layer-polarized Dirac fermions in bilayer WTe2. Our results demonstrate a new type of Hall effect and provide a way of detecting Berry curvature in non-magnetic quantum materials.

Interventionism and Intelligibility: Why Depression Is Not (Always) a Brain Disease.

Major depressive disorder (MDD) is a serious condition with a large disease burden. It is often claimed that MDD is a "brain disease." What would it mean for MDD to be a brain disease? I argue that the best interpretation of this claim is as offering a substantive empirical hypothesis about the causes of the syndrome of depression. This syndrome-causal conception of disease, combined with the idea that MDD is a disease of the brain, commits the brain disease conception of MDD to the claim that brain dysfunction causes the symptoms of MDD. I argue that this consequence of the brain disease conception of MDD is false. It incorrectly rules out genuine instances of content-sensitive causation between adverse conditions in the world and the characteristic symptoms of MDD. Empirical evidence shows that the major causes of depression are genuinely psychological causes of the symptoms of MDD. This rules out, in many cases, the "brute" causation required by the brain disease conception. The existence of cases of MDD with non-brute causes supports the reinstatement of the old nosological distinction between endogenous and exogenous depression.

Control of Polarity in Kagome-NiAs Bismuthides.

A 2×2×1 superstructure of the P63/mmc NiAs structure is reported in which kagome nets are stabilized in the octahedral transition metal layers of the compounds Ni0.7Pd0.2Bi, Ni0.6Pt0.4Bi, and Mn0.99Pd0.01Bi. The ordered vacancies that yield the true hexagonal kagome motif lead to filling of trigonal bipyramidal interstitial sites with the transition metal in this family of "kagome-NiAs" type materials. Further ordering of vacancies within these interstitial layers can be compositionally driven to simultaneously yield kagome-connected layers and a net polarization along the c axes in Ni0.9Bi and Ni0.79Pd0.08Bi, which adopt Fmm2 symmetry. The polar and non-polar materials exhibit different electronic transport behaviour, reflecting the tuneability of both structure and properties within the NiAs-type bismuthide materials family.

One Site, Two Cations, Three Environments: s2 and s0 Electronic Configurations Generate Pb-Free Relaxor Behavior in a Perovskite Oxide.

The piezoelectric devices widespread in society use noncentrosymmetric Pb-based oxides because of their outstanding functional properties. The highest figures of merit reported are for perovskites based on the parent Pb(Mg1/3Nb2/3)O3 (PMN), which is a relaxor: a centrosymmetric material with local symmetry breaking that enables functional properties, which resemble those of a noncentrosymmetric material. We present the Pb-free relaxor (K1/2Bi1/2)(Mg1/3Nb2/3)O3 (KBMN), where the thermal and (di)electric behavior emerges from the discrete structural roles of the s0 K+ and s2 Bi3+ cations occupying the same A site in the perovskite structure, as revealed by diffraction methods. This opens a distinctive route to Pb-free piezoelectrics based on relaxor parents, which we demonstrate in a solid solution of KBMN with the Pb-free ferroelectric (K1/2Bi1/2)TiO3, where the structure and function evolve together, revealing a morphotropic phase boundary, as seen in PMN-derived systems. The detailed multiple-length-scale understanding of the functional behavior of KBMN suggests that precise chemical manipulation of the more diverse local displacements in the Pb-free relaxor will enhance performance.

Discovery of a Low Thermal Conductivity Oxide Guided by Probe Structure Prediction and Machine Learning.

We report the aperiodic titanate Ba10 Y6 Ti4 O27 with a room-temperature thermal conductivity that equals the lowest reported for an oxide. The structure is characterised by discontinuous occupancy modulation of each of the sites and can be considered as a quasicrystal. The resulting localisation of lattice vibrations suppresses phonon transport of heat. This new lead material for low-thermal-conductivity oxides is metastable and located within a quaternary phase field that has been previously explored. Its isolation thus requires a precisely defined synthetic protocol. The necessary narrowing of the search space for experimental investigation was achieved by evaluation of titanate crystal chemistry, prediction of unexplored structural motifs that would favour synthetically accessible new compositions, and assessment of their properties with machine-learning models.

Modular Design via Multiple Anion Chemistry of the High Mobility van der Waals Semiconductor Bi4O4SeCl2.

Making new van der Waals materials with electronic or magnetic functionality is a chemical design challenge for the development of two-dimensional nanoelectronic and energy conversion devices. We present the synthesis and properties of the van der Waals material Bi4O4SeCl2, which is a 1:1 superlattice of the structural units present in the van der Waals insulator BiOCl and the three-dimensionally connected semiconductor Bi2O2Se. The presence of three anions gives the new structure both the bridging selenide anion sites that connect pairs of Bi2O2 layers in Bi2O2Se and the terminal chloride sites that produce the van der Waals gap in BiOCl. This retains the electronic properties of Bi2O2Se while reducing the dimensionality of the bonding network connecting the Bi2O2Se units to allow exfoliation of Bi4O4SeCl2 to 1.4 nm height. The superlattice structure is stabilized by the configurational entropy of anion disorder across the terminal and bridging sites. The reduction in connective dimensionality with retention of electronic functionality stems from the expanded anion compositional diversity.

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.

Temperature-field phase diagram of extreme magnetoresistance.

The recent discovery of extreme magnetoresistance (XMR) in LaSb introduced lanthanum monopnictides as a new platform to study this effect in the absence of broken inversion symmetry or protected linear band crossing. In this work, we report XMR in LaBi. Through a comparative study of magnetotransport effects in LaBi and LaSb, we construct a temperature-field phase diagram with triangular shape that illustrates how a magnetic field tunes the electronic behavior in these materials. We show that the triangular phase diagram can be generalized to other topological semimetals with different crystal structures and different chemical compositions. By comparing our experimental results to band structure calculations, we suggest that XMR in LaBi and LaSb originates from a combination of compensated electron-hole pockets and a particular orbital texture on the electron pocket. Such orbital texture is likely to be a generic feature of various topological semimetals, giving rise to their small residual resistivity at zero field and subject to strong scattering induced by a magnetic field.

Rationalism, optimism, and the moral mind.

I welcome many of the conclusions of May's book, but I offer a suggestion - and with it what I take to be a complementary strategy - concerning the core commitments of rationalism across the domains of moral psychology in the hopes of better illuminating why a rationalist picture of the mind can deliver us from pessimism.

Bi2+2 nO2+2 nCu2-δSe2+ n-δXδ (X = Cl, Br): A Three-Anion Homologous Series.

Both layered multiple-anion compounds and homologous series are of interest for their electronic properties, including the ability to tune the properties by changing the nature or number of the layers. Here we expand, using both computational and experimental techniques, a recently reported three-anion material, Bi4O4Cu1.7Se2.7Cl0.3, to the homologous series Bi2+2 nO2+2 nCu2-δSe2+ n-δXδ (X = Cl, Br), composed of parent blocks that are well-studied thermoelectric materials. All of the materials show exceptionally low thermal conductivity (0.2 W/mK and lower) parallel to the axis of pressing of the pellets, as well as narrow band gaps (as low as 0.28 eV). Changing the number of layers affects the band gap, thermal conductivity, carrier type, and presence of a phase transition. Furthermore, the way in which the different numbers of layers are accessed, by tuning the compensating Cu vacancy concentration and halide substitution, represents a novel route to homologous series. This homologous series shows tunable properties, and the route explored here could be used to build new homologous series out of known structural blocks.

Bi4O4Cu1.7Se2.7Cl0.3: Intergrowth of BiOCuSe and Bi2O2Se Stabilized by the Addition of a Third Anion.

Layered two-anion compounds are of interest for their diverse electronic properties. The modular nature of their layered structures offers opportunities for the construction of complex stackings used to introduce or tune functionality, but the accessible layer combinations are limited by the crystal chemistries of the available anions. We present a layered three-anion material, Bi4O4Cu1.7Se2.7Cl0.3, which adopts a new structure type composed of alternately stacked BiOCuSe and Bi2O2Se-like units. This structure is accessed by inclusion of three chemically distinct anions, which are accommodated by aliovalently substituted Bi2O2Se0.7Cl0.3 blocks coupled to Cu-deficient Bi2O2Cu1.7Se2 blocks, producing a formal charge modulation along the stacking direction. The hypothetical parent phase Bi4O4Cu2Se3 is unstable with respect to its charge-neutral stoichiometric building blocks. The complex layer stacking confers excellent thermal properties upon Bi4O4Cu1.7Se2.7Cl0.3: a room-temperature thermal conductivity (κ) of 0.4(1) W/mK was measured on a pellet with preferred crystallite orientation along the stacking axis, with perpendicular measurement indicating it is also highly anisotropic. This κ value lies in the ultralow regime and is smaller than those of both BiOCuSe and Bi2O2Se. Bi4O4Cu1.7Se2.7Cl0.3 behaves like a charge-balanced semiconductor with a narrow band gap. The chemical diversity offered by the additional anion allows the integration of two common structural units in a single phase by the simultaneous and coupled creation of charge-balancing defects in each of the units.

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.

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.

Synthesis, Structure, and Basic Magnetic and Thermoelectric Properties of the Light Lanthanide Aurobismuthides.

We report the crystal structures and elementary properties of the new aurobismuthides La3Au3Bi4, Ce3Au3Bi4, Pr3Au3Bi4, Nd3Au3Bi4, Sm3Au3Bi4, and Gd3Au3Bi4. These ternary compounds are found only for the large lanthanides and crystallize in the cubic Y3Au3Sb4 structure type, which is a stuffed Th3P4-type derivative. The compounds are electron-precise, leading to semiconducting behavior, and display magnetic properties arising from localized lanthanide f states. Resistivity data, Seebeck coefficient measurements, and electronic structure calculations suggest that these phases are heavily doped, p-type semiconductors. Nd3Au3Bi4 and Sm3Au3Bi4 have Seebeck coefficients of 105 and 190 µV/K at 350 K, respectively, making them worthy of further thermoelectric studies.

Gold-gold bonding: the key to stabilizing the 19-electron ternary phases LnAuSb (Ln = La-Nd and Sm).

We report a new family of ternary 111 hexagonal LnAuSb (Ln = La-Nd, Sm) compounds that, with a 19 valence electron count, has one extra electron compared to all other known LnAuZ compounds. LaAuSb, CeAuSb, PrAuSb, NdAuSb, and SmAuSb crystallize in the YPtAs-type structure, and have a doubled unit cell compared to other LnAuZ phases as a result of the buckling of the Au-Sb honeycomb layers to create interlayer Au-Au dimers. The dimers accommodate the one excess electron per Au and thus these new phases can be considered Ln2(3+)(Au-Au)(0)Sb2(3-). Band structure, density of states, and crystal orbital calculations confirm this picture, which results in a nearly complete band gap between full and empty electronic states and stable compounds; we can thus present a structural stability phase diagram for the LnAuZ (Z = Ge, As, Sn, Sb, Pb, Bi) family of phases. Those calculations also show that LaAuSb has a bulk Dirac cone below the Fermi level. The YPtAs-type LnAuSb family reported here is an example of the uniqueness of gold chemistry applied to a rigidly closed shell system in an unconventional way.

Landau quantization and quasiparticle interference in the three-dimensional Dirac semimetal Cd3As2.

Condensed-matter systems provide a rich setting to realize Dirac and Majorana fermionic excitations as well as the possibility to manipulate them for potential applications. It has recently been proposed that chiral, massless particles known as Weyl fermions can emerge in certain bulk materials or in topological insulator multilayers and give rise to unusual transport properties, such as charge pumping driven by a chiral anomaly. A pair of Weyl fermions protected by crystalline symmetry effectively forming a massless Dirac fermion has been predicted to appear as low-energy excitations in a number of materials termed three-dimensional Dirac semimetals. Here we report scanning tunnelling microscopy measurements at sub-kelvin temperatures and high magnetic fields on the II-V semiconductor Cd3As2. We probe this system down to atomic length scales, and show that defects mostly influence the valence band, consistent with the observation of ultrahigh-mobility carriers in the conduction band. By combining Landau level spectroscopy and quasiparticle interference, we distinguish a large spin-splitting of the conduction band in a magnetic field and its extended Dirac-like dispersion above the expected regime. A model band structure consistent with our experimental findings suggests that for a magnetic field applied along the axis of the Dirac points, Weyl fermions are the low-energy excitations in Cd3As2.

p-type CuRhO2 as a self-healing photoelectrode for water reduction under visible light.

Polycrystalline CuRhO2 is investigated as a photocathode for the splitting of water under visible irradiation. The band edge positions of this material straddle the water oxidation and reduction redox potentials. Thus, photogenerated conduction band electrons are sufficiently energetic to reduce water, while the associated valence band holes are energetically able to oxidize water to O2. Under visible illumination, H2 production is observed with ~0.2 V underpotential in an air-saturated solution. In contrast, H2 production in an Ar-saturated solution was found to be unstable. This instability is associated with the reduction of the semiconductor forming Cu(s). However, in the presence of air or O2, bulk Cu(s) was not detected, implying that CuRhO2 is self-healing when air is present. This property allows for the stable formation of H2 with ca. 80% Faradaic efficiency.

Experimental realization of a three-dimensional Dirac semimetal.

We report the direct observation of the three-dimensional (3D) Dirac semimetal phase in cadmium arsenide (Cd(3)As(2)) by means of angle-resolved photoemission spectroscopy. We identify two momentum regions where electronic states that strongly disperse in all directions form narrow conelike structures, and thus prove the existence of the long sought 3D Dirac points. This electronic structure naturally explains why Cd(3)As(2) has one of the highest known bulk electron mobilities. This realization of a 3D Dirac semimetal in Cd(3)As(2) not only opens a direct path to a wide spectrum of applications, but also offers a robust platform for engineering topologically nontrivial phases including Weyl semimetals and quantum spin Hall systems.

The crystal and electronic structures of Cd(3)As(2), the three-dimensional electronic analogue of graphene.

The structure of Cd3As2, a high-mobility semimetal reported to host electrons that act as Dirac particles, is reinvestigated by single-crystal X-ray diffraction. It is found to be centrosymmetric rather than noncentrosymmetric as previously reported. It has a distorted superstructure of the antifluorite (M2X) structure type with a tetragonal unit cell of a = 12.633(3) and c = 25.427(7) Å in the centrosymmetric I41/acd space group. The antifluorite superstructure can be envisioned as consisting of distorted Cd6□2 cubes (where □ = an empty cube vertex) in parallel columns, stacked with opposing chirality. Electronic structure calculations performed using the experimentally determined centrosymmetric structure are similar to those performed with the inversion symmetry absent but with the important implication that Cd3As2 is a three-dimensional (3D)-Dirac semimetal with no spin splitting; all bands are spin degenerate and there is a 4-fold degenerate bulk Dirac point at the Fermi energy along Γ-Z in the Brillouin zone. This makes Cd3As2 a 3D electronic analogue of graphene. Scanning tunneling microscopy experiments identify a 2 × 2 surface reconstruction in the (112) cleavage plane of single crystals; needle crystals grow with a [110] long axis direction.