Ilya Belopolski

By sidestepping the intractable calculations of many-body wave functions, density functional theory has revolutionized the prediction of ground states of materials. However, predicting nonlinear responses-critical for next-generation quantum devices-still relies heavily on explicit wave functions, limiting computational efficiency. In this Letter, using the circular photogalvanic effect in Weyl semimetals as a representative example, we realize a 1000-fold computational speedup by eliminating the explicit dependence on wave functions. Our approach leverages the one-to-one correspondence between free parameters of Weyl fermions and the associated responses to obtain precise wave-function-free formulations. Applying our methodology, we systematically investigated known Weyl semimetals and revealed that Ta_{3}S_{2} exhibits photocurrents an order of magnitude greater than those observed in TaAs, with potential for an additional order-of-magnitude enhancement under strain. To further demonstrate the generality of our approach, we obtained a wave-function-free formula for the Berry-curvature dipole in Weyl semimetals. Our Letter paves the way for substantially more efficient screening and optimization of nonlinear electromagnetic properties in topological quantum materials.

The emergent properties of materials are governed by the symmetries of their underlying atomic, spin and charge order. Therefore, intrinsic material properties usually constrain the exploration of symmetry-breaking effects. Focused ion beam (FIB) fabrication now enables the structuring of bulk crystals into ultraprecise transport devices, allowing the study of geometrical symmetry breaking on mesoscopic length scales. Here we extend FIB nanostructuring into three-dimensional, curvilinear geometries. Using single crystals of the high-mobility, centrosymmetric magnetic Weyl semimetal Co₃Sn₂S₂, we sculpt helices with lengths of 3–14 μm, diameters of 1–4 μm and pitches ranging from 500 nm to 2 μm. Lock-in measurements on the helical devices at temperatures between 10 K and 190 K show that the combination of imposed inversion symmetry-breaking geometry and ferromagnetism yields non-reciprocal electron transport—or diode effect—at zero applied magnetic field, exceeding classical self-field expectations by orders of magnitude at low temperatures. We attribute this behaviour to the quasi-ballistic motion of carriers as the mean free path approaches the length scale of the chiral device geometry. Finally, we show that current pulses can switch the magnetization of the device. These results highlight the potential of FIB nanosculpting to engineer symmetry and functionality beyond conventional device geometries.

Molecular beam epitaxy enables the growth of thin film materials with novel properties and functionalities. Typically, the lattice constants of films and substrates are designed to match to minimise disorders and strains. However, significant lattice mismatches can result in higher-order epitaxy, where commensurate growth occurs with a period defined by integer multiples of the lattice constants. Despite its potential, higher-order epitaxy is rarely used to enhance material properties or induce emergent phenomena. Here, we report single-crystalline FeTe films grown via 6:5 commensurate higher-order epitaxy on CdTe(001) substrates. Scanning transmission electron microscopy reveals self-organised periodic interstitials near the interface, arising from higher-order lattice matching. Synchrotron x-ray diffraction shows that the tetragonal-to-monoclinic structural transition in bulk FeTe is strongly suppressed. Remarkably, these films exhibit substrate-selective two-dimensional superconductivity, likely due to suppressed monoclinic distortion. These findings demonstrate the potential of higher-order epitaxy as a tool to control materials and inducing emergent phenomena.

Antiferromagnetic states with a spin-split electronic structure give rise to spintronic, magnonic and electronic phenomena despite (near-)zero net magnetization^{1,2,3,4,5,6,7}. The simplest odd-parity spin splitting—p wave—was originally proposed to emerge from a collective instability in interacting electron systems^8,9,10,11,12. Recent theory has identified a distinct route to realize p-wave spin-split electronic bands without strong correlations^13,14, termed p-wave magnetism. Here we demonstrate an experimental realization of a metallic p-wave magnet. The odd-parity spin splitting of delocalized conduction electrons arises from their coupling to an antiferromagnetic texture of localized magnetic moments: a coplanar spin helix whose magnetic period is an even multiple of the chemical unit cell, as revealed by X-ray scattering experiments. This texture breaks space-inversion symmetry but approximately preserves time-reversal symmetry up to a half-unit-cell translation—thereby fulfilling the symmetry conditions for p-wave magnetism. Consistent with theoretical predictions, our p-wave magnet shows a characteristic anisotropy in the electronic conductivity^13,14,15. Relativistic spin–orbit coupling and a tiny spontaneous net magnetization further break time-reversal symmetry, resulting in a giant anomalous Hall effect (Hall conductivity >600 S cm⁻¹, Hall angle >3%), for an antiferromagnet. Our model calculations show that the spin-nodal planes found in the electronic structure of p-wave magnets are readily gapped by a small perturbation to induce the anomalous Hall effect. We establish metallic p-wave magnets as an ideal platform to explore the functionality of spin-split electronic states in magnets, superconductors, and in spintronic devices.

Implementing and tuning chirality is fundamental in physics, chemistry, and materials science. Chiral charge density waves (CDWs), where chirality arises from correlated charge orders, are attracting intense interest due to their exotic transport and optical properties. However, a general framework for predicting chiral CDW materials is lacking, primarily because the underlying mechanisms remain elusive. Here, we address this challenge by developing the first comprehensive predictive framework, systematically identifying chiral CDW materials via first-principles calculations. The key lies in the previously overlooked phase difference of the CDW Q-vectors between layers, which is linked to opposite collective atomic displacements across different layers. This phase difference induces a spiral arrangement of the Q-vectors, ultimately giving rise to a chiral structure in real space. We validate our framework by applying it to the kagome lattice AV$_{3}$Sb$_{5}$ (A = K, Rb, Cs), successfully predicting emergent structural chirality. To demonstrate the generality of our approach, we extend it to predict chiral CDWs in the triangular-lattice NbSe$_{2}$. Beyond material predictions, our theory uncovers a universal and unprecedented Hall effect in chiral CDW materials, occurring without external magnetic fields or intrinsic magnetization. Our experiments on CsV$_{3}$Sb$_{5}$ confirm this prediction, observing a unique signature where the Hall conductivity's sign reverses when the input current is reversed, a phenomenon distinct from known Hall effects. Our findings elucidate the mechanisms behind chiral CDWs and open new avenues for discovering materials with unconventional quantum properties, with potential applications in next-generation electronic and spintronic devices.

Quantum materials governed by emergent topological fermions have become a cornerstone of physics. Dirac fermions in graphene form the basis for moiré quantum matter and Dirac fermions in magnetic topological insulators enabled the discovery of the quantum anomalous Hall (QAH) effect^1,2,3. By contrast, there are few materials whose electromagnetic response is dominated by emergent Weyl fermions^4,5,6. Nearly all known Weyl materials are overwhelmingly metallic and are largely governed by irrelevant, conventional electrons. Here we theoretically predict and experimentally observe a semimetallic Weyl ferromagnet in van der Waals (Cr,Bi)₂Te₃. In transport, we find a record bulk anomalous Hall angle of greater than 0.5 along with non-metallic conductivity, a regime that is strongly distinct from conventional ferromagnets. Together with symmetry analysis, our data suggest a semimetallic Fermi surface composed of two Weyl points, with a giant separation of more than 75% of the linear dimension of the bulk Brillouin zone, and no other electronic states. Using state-of-the-art crystal-synthesis techniques, we widely tune the electronic structure, allowing us to annihilate the Weyl state and visualize a unique topological phase diagram exhibiting broad Chern insulating, Weyl semimetallic and magnetic semiconducting regions. Our observation of a semimetallic Weyl ferromagnet offers an avenue towards new correlated states and nonlinear phenomena, as well as zero-magnetic-field Weyl spintronic and optical devices.