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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 s0K+and s2Bi3+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.

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 Bi2O2layers 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 Bi4O4SeCl2to 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.

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 effect10in electrical transport in bilayers of the non-magnetic quantum material WTe2under time-reversal-symmetric conditions. We show that an electric current in bilayer WTe2leads 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 moment10of 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.

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+2nO2+2nCu2−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.

Recent experimental evidence for the quantum spin Hall (QSH) state in monolayer WTe2has linked the fields of two-dimensional materials and topological physics1–7. This two-dimensional topological crystal also displays unconventional spin–torque8and gate-tunable superconductivity7. Whereas the realization of the QSH has demonstrated the nontrivial topology of the electron wavefunctions of monolayer WTe2, the geometrical properties of the wavefunction, such as the Berry curvature9, remain unstudied. Here we utilize mid-infrared optoelectronic microscopy to investigate the Berry curvature in monolayer WTe2. By optically exciting electrons across the inverted QSH gap, we observe an in-plane circular photogalvanic current even under normal incidence. The application of an out-of-plane displacement field allows further control of the direction and magnitude of the photocurrent. The observed photocurrent reveals a Berry curvature dipole that arises from the nontrivial wavefunctions near the inverted gap edge. The Berry curvature dipole and strong electric field effect are enabled by the inverted band structure and tilted crystal lattice of monolayer WTe2. Such an electrically switchable Berry curvature dipole may facilitate the observation of a wide range of quantum geometrical phenomena such as the quantum nonlinear Hall10,11, orbital-Edelstein12and chiral polaritonic effects13,14. Optoelectronic experiments show that a monolayer of WTe2is a material that simultaneously has topological electronic states and electron wavefunctions with a dipole in their Berry curvature.

Research in topological matter has expanded to include the Dirac and Weyl semimetals1–10, which feature three-dimensional Dirac states protected by symmetry. Zirconium pentatelluride has been of recent interest as a potential Dirac or Weyl semimetal material. Here, we report the results of experiments performed by in situ three-dimensional double-axis rotation to extract the full 4π solid angular dependence of the transport properties. A clear anomalous Hall effect is detected in every sample studied, with no magnetic ordering observed in the system to the experimental sensitivity of torque magnetometry. Large anomalous Hall signals develop when the magnetic field is rotated in the plane of the stacked quasi-two-dimensional layers, with the values vanishing above about 60 K, where the negative longitudinal magnetoresistance also disappears. This suggests a close relation in their origins, which we attribute to the Berry curvature generated by the Weyl nodes. Magnetotransport measurements show that ZrTe5exhibits an anomalous Hall effect without magnetic ordering, a signature of Berry curvature introduced by Weyl nodes. This indicates that ZrTe5may be a Weyl semimetal, even though this was not predicted.

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 αxxof 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.