Quantum metric nonlinear Hall effect in a topological antiferromagnetic heterostructure.

The anomalous Hall effect in time-reversal symmetry broken systems is underpinned by the concept of Berry curvature in band theory. However, recent experiments reveal that the nonlinear Hall effect (NHE) can be observed in non-magnetic systems without applying an external magnetic field. The emergence of NHE under time-reversal symmetric conditions can be explained in terms of non-vanishing Berry curvature dipole (BCD) arising from inversion symmetry breaking. In this work, we availed realistic tight-binding models, first-principles calculations, and symmetry analyses to explore the combined effect of transverse electric field and strain, which leads to a giant BCD in the elemental buckled honeycomb lattices—silicene, germanene, and stanene. The external electric field breaks the inversion symmetry of these systems, while strain helps to attain an asymmetrical distribution of Berry curvature of a single valley. Furthermore, the topology of the electronic wavefunction switches from the band inverted quantum spin Hall state to normal insulating one at the gapless point. This band gap closing at the critical electric field strength is accompanied by an enhanced Berry curvature and concomitantly a giant BCD at the Fermi level. Our results predict the occurrence of an electrically switchable nonlinear electrical and thermal Hall effect in a new class of elemental systems that can be experimentally verified.

The interplay between charge density wave (CDW) formation and electron correlations can lead to the emergence of novel topological phases in materials. In quasi‐2D 1T‐TaS 2 , below approximately 150 K, the system transitions from a nearly commensurate (NC) to a commensurate (C) CDW phase. Here, it is shown that the NC‐CDW to C‐CDW phase transition is marked by the emergence of a finite planar Hall and nonlinear Hall effect, alongside sign changes in the ordinary Hall and thermoelectric signals, indicating the reconstruction of the Fermi surface in the C‐CDW phase. The theoretical calculations suggest that the C‐CDW phase, stabilized by specific layer stacking, breaks both mirror and inversion symmetries. This leads to finite Berry curvature and a substantial Berry curvature dipole, giving rise to the observed planar Hall and nonlinear Hall effect. This study highlights the nontrivial band geometry‐driven physics of 1T‐TaS 2 and opens new possibilities for developing innovative sensors.

Two-dimensional materials are a fertile ground for exploring quantum geometric phenomena, with Berry curvature and its first moment, the Berry curvature dipole, playing a central role in their electronic response. These geometric properties influence electronic transport and result in the anomalous and nonlinear Hall effects, and are typically controlled using static electric fields or strain. However, the possibility of modulating quantum geometric quantities in real-time remains unexplored. Here, we demonstrate the dynamic modulation of Berry curvature and its moments, as well as the generation of a pseudo-electric field and their coupling. By placing heterostructures on a membrane, we introduce oscillatory strain together with an in-plane AC electric field and measure Hall signals that are modulated at linear combinations of the frequencies of strain and electric field. We also present direct experimental and theoretical evidence for coupling between pseudo-electric field and quantum geometry that results in an unusual dynamic strain-induced Hall response. This approach opens up a new pathway for controlling quantum geometry on demand, moving beyond conventional static perturbations. The coupling of the pseudo-electric field with Berry curvature provides a framework for external electric field-free anomalous Hall response and opens new avenues for probing the topological properties.

The anomalous transverse transport properties, including the anomalous Hall and Nernst effects, are crucial for probing the topological band features in magnetic materials. In this study, we present a comprehensive investigation of the magnetic, electrical, and thermal transport, as well as the electronic band structure, of the noncollinear ferromagnet ${\mathrm{PrMn}}_{2}{\mathrm{Ge}}_{2}$. Our findings reveal that ${\mathrm{PrMn}}_{2}{\mathrm{Ge}}_{2}$ exhibits prominent anomalous Hall and Nernst effects. Scaling analysis suggests that the anomalous Hall effect is predominantly influenced by the intrinsic Berry curvature contribution. Additionally, the large anomalous Nernst signal exceeds the magnetization scaling relations observed in conventional ferromagnets, and the calculated anomalous Nernst conductivity exhibits a $T\text{ln}T$ relation. These observations align with the behavior seen in other magnetic topological materials, further suggesting a substantial intrinsic Berry curvature effect. Complemented by detailed theoretical calculations, we clarify the electronic band properties and confirm a substantial net Berry curvature near the Fermi level in this compound. Our work elucidates that the large anomalous Hall and Nernst effects of ${\mathrm{PrMn}}_{2}{\mathrm{Ge}}_{2}$ are dominated by an intrinsic mechanism and presents it as a probable magnetic topological material with a significant Berry phase effect in the momentum space.

Detection of interfacial spin accumulation induced by anomalous Hall effect in ferromagnets

Non-centrosymmetric topological material has attracted intense attention due to its superior characteristics as compared with the centrosymmetric one, although probing the local quantum geometry in non-centrosymmetric topological material remains challenging. The non-linear Hall (NLH) effect provides an ideal tool to investigate the local quantum geometry. Here, we report a non-centrosymmetric topological phase in ZrTe5, probed by using the NLH effect. The angle-resolved and temperature-dependent NLH measurement reveals the inversion and ab-plane mirror symmetries breaking at <30 K, consistently with our theoretical calculation. Our findings identify a new non-centrosymmetric phase of ZrTe5 and provide a platform to probe and control local quantum geometry via crystal symmetries.

The Hall effect occurs only in systems with broken time-reversal symmetry, such as materials under an external magnetic field in the ordinary Hall effect and magnetic materials in the anomalous Hall effect (AHE)1. Here we show a nonlinear AHE in a non-magnetic material under zero magnetic field, in which the Hall voltage depends quadratically on the longitudinal current2-6. We observe the effect in few-layer Td-WTe2, a two-dimensional semimetal with broken inversion symmetry and only one mirror line in the crystal plane. Our angle-resolved electrical measurements reveal that the Hall voltage maximizes (vanishes) when the bias current is perpendicular (parallel) to the mirror line. The observed effect can be understood as an AHE induced by the bias current, which generates an out-of-plane magnetization. The temperature dependence of the Hall conductivity further suggests that both the intrinsic Berry curvature dipole and extrinsic spin-dependent scatterings contribute to the observed nonlinear AHE.

We investigate aspects of the relation between the quantum geometry of the normal state (NS) and the superconducting phase, through the lens of nonlocality. By relating band theory to quantum estimation theory, we derive a direct momentum-dependent relation between quantum geometry and the quantum fluctuations of the position operator. We then investigate two effects of the NS quantum geometry on superconductivity. On the one hand, we present a physical interpretation of the conventional and geometric contributions to the superfluid weight in terms of two different movements of the normal state charge carriers forming the Cooper pairs. The first contribution stems from their center-of-mass motion while the second stems from their zero-point motion, thereby explaining its persistence in flat-band systems. On the other hand, we phenomenologically derive an emergent Darwin term driven by the NS quantum metric. We show its form in one and two-body problems, derive the effective pairing potential in $s$-wave superconductors, and explicit its form in the case of two-dimensional massive Dirac fermions. We thus show that the NS quantum metric screens the pairing interaction and weakens superconductivity, which could be tested experimentally by doping a superconductor. Our work reveals the ambivalent relationship between noninteracting quantum geometry and superconductivity, and possibly in other correlated phases.

As known, when a magnetic field is applied at right angles to the direction of an electric current or a thermal gradient, galvano- and thermo-magnetic effects appear in the material. In this paper, we shall show that if we study these effects in non-linear regime, the Thermodynamic Field Theory (TFT) foresees a new interesting effect: the Non Linear Hall effect. This prediction is herein submitted to experimental verification. In this paper, we shall analyse this new effect studying materials with weak thermo-electric power coefficients. We shall show the agreement between the theoretical predictions of the TFT and experiments. Expermental curves related to the non-linear Hall effect allow to determine the order of magnitude of the constant x introduced in the TFT.

We predict a nonlinear Hall effect in certain Weyl semimetals with broken inversion symmetry. When the energy dispersions about pairs of Weyl nodes are skewed -- the Weyl cones are "tilted" -- the concerted actions of the anomalous velocity and the chiral anomaly give rise to the nonlinear Hall effect. This Hall conductivity is linear in both electric and magnetic fields, and depends critically on the tilting of the Weyl cones. We also show that this effect does not rely on a finite Berry curvature dipole, in contrast to the intrinsic quantum nonlinear Hall effect that was recently observed in type-II Weyl semimetals.

We introduce the concept of quantum weight as a ground-state property of quantum many-body systems that is encoded in the static structure factor and characterizes density fluctuation at long wavelengths. The quantum weight carries a wealth of information about dielectric responses and optical properties of the system and is closely related to its quantum geometry. For systems with short-range interactions or low-dimensional Coulomb systems, we show that the many-body quantum metric (which measures the change of the ground state under twisted boundary conditions) can be determined directly from the quantum weight. Notably, the quantum weight is a property of a single ground state and independent of boundary conditions in the thermodynamic limit. Our finding thus enables direct experimental measurement and numerical calculation of the many-body quantum metric. On the other hand, for three-dimensional Coulomb systems, we show that the quantum weight is distinct from the many-body quantum metric due to dielectric screening in three dimensions. We further use dielectric sum rules to derive upper and lower bounds on the quantum weight of real materials in terms of their electron density, static dielectric constant, and plasmon energy. Our work highlights quantum weight as a fundamental material parameter, which can be experimentally determined by x-ray scattering or electron-loss spectroscopy.

Nodal planes, two-dimensional symmetry-enforced band crossings, can carry a topological charge, similar to Weyl points. While the transport properties of Weyl points are well understood, those of nodal planes remain largely unexplored. These properties are influenced not only by the Berry curvature, but also by other quantum geometric quantities. In this work we study the quantum geometry, specifically the Berry curvature and quantum metric, and the linear optical conductivity of topological nodal planes. We introduce a low-energy model and investigate its low-frequency optical responses to determine the unique signatures of nodal planes. By comparing these findings to the optical response in a tight-binding model with a topological nodal plane, we observe consistent low-frequency behavior with a cubic power law. This paves the way for the experimental detection of nodal planes through optical conductivity measurements for which we suggest suitable materials, most promisingly the material group XMo3S3 (X= Rb, K, Cs).

The Berry phase picture provides important insights into the electronic properties of condensed matter systems. The intrinsic anomalous Hall (AH) effect can be understood as the consequence of non-zero Berry curvature in momentum space. Here, we fabricate TI/magnetic TI heterostructures and find that the sign of the AH effect in the magnetic TI layer can be changed from being positive to negative with increasing the thickness of the top TI layer. Our first-principles calculations show that the built-in electric fields at the TI/magnetic TI interface influence the band structure of the magnetic TI layer, and thus lead to a reconstruction of the Berry curvature in the heterostructure samples. Based on the interface-induced AH effect with a negative sign in TI/V-doped TI bilayer structures, we create an artificial “topological Hall effect”-like feature in the Hall trace of the V-doped TI/TI/Cr-doped TI sandwich heterostructures. Our study provides a new route to create the Berry curvature change in magnetic topological materials that may lead to potential technological applications.

Generally, the dissipationless Hall effect in solids requires time-reversal symmetry breaking (TRSB), where TRSB induced by external magnetic field results in the ordinary Hall effect, while TRSB caused by spontaneous magnetization gives rise to the anomalous Hall effect (AHE) which scales with the net magnetization. The AHE is therefore not expected in antiferromagnets with vanishing small magnetization. However, large AHE was recently observed in certain antiferromagnets with noncollinear spin structure and nonvanishing Berry curvature. Here, we report another origin of AHE in a layered antiferromagnet EuAl_{2}Si_{2}, namely, the domain wall (DW) skew scattering with Weyl points near the Fermi level, in experiments for the first time. Interestingly, the DWs form a unique periodic stripe structure with controllable periodicity by external magnetic field, which decreases nearly monotonically from 975nm at 0T to 232nm at 4T. Electrons incident on DW with topological bound states experience strong asymmetric scattering, leading to a giant AHE, with the DW Hall conductivity (DWHC) at 2K and 1.2T reaching a record value of ∼1.51×10^{4} Scm^{-1} among bulk systems and being 2 orders of magnitude larger than the intrinsic anomalous Hall conductivity. The observation not only sets a new paradigm for exploration of large anomalous Hall effect, but also provides potential applications in spintronic devices.

Topological physics relies on the structure of the eigenstates of the Hamiltonians. The geometry of the eigenstates is encoded in the quantum geometric tensor1-comprising the Berry curvature2 (crucial for topological matter)3 and the quantum metric4, which defines the distance between the eigenstates. Knowledge of the quantum metric is essential for understanding many phenomena, such as superfluidity in flat bands5, orbital magnetic susceptibility6,7, the exciton Lamb shift8 and the non-adiabatic anomalous Hall effect6,9. However, the quantum geometry of energy bands has not been measured. Here we report the direct measurement of both the Berry curvature and the quantum metric in a two-dimensional continuous medium-a high-finesse planar microcavity10-together with the related anomalous Hall drift. The microcavity hosts strongly coupled exciton-photon modes (exciton polaritons) that are subject to photonic spin-orbit coupling11 from which Dirac cones emerge12, and to exciton Zeeman splitting, breaking time-reversal symmetry. The monopolar and half-skyrmion pseudospin textures are measured using polarization-resolved photoluminescence. The associated quantum geometry of the bands is extracted, enabling prediction of the anomalous Hall drift, which we measure independently using high-resolution spatially resolved epifluorescence. Our results unveil the intrinsic chirality of photonic modes, the cornerstone of topological photonics13-15. These results also experimentally validate the semiclassical description of wavepacket motion in geometrically non-trivial bands9,16. The use of exciton polaritons (interacting photons) opens up possibilities for future studies of quantum fluid physics in topological systems.