Magnetochiral tunneling in paramagnetic Co1/3NbS2.

Electric currents have the intriguing ability to induce magnetization in nonmagnetic crystals with sufficiently low crystallographic symmetry. Some associated phenomena include the non-linear anomalous Hall effect in polar crystals and the nonreciprocal directional dichroism in chiral crystals when magnetic fields are applied. In this work, we demonstrate that the same underlying physics is also manifested in the electronic tunneling process between the surface of a nonmagnetic chiral material and a magnetized scanning probe. In the paramagnetic but chiral metallic compound Co1/3NbS2, the magnetization induced by the tunneling current is shown to become detectable by its coupling to the magnetization of the tip itself. This results in a contrast across different chiral domains, achieving atomic-scale spatial resolution of structural chirality. To support the proposed mechanism, we used first-principles theory to compute the chirality-dependent current-induced magnetization and Berry curvature in the bulk of the material. Our demonstration of this magnetochiral tunneling effect opens up an avenue for investigating atomic-scale variations in the local crystallographic symmetry and electronic structure across the structural domain boundaries of low-symmetry nonmagnetic crystals.

Scaling of Berry-curvature monopole dominated large linear positive magnetoresistance.

The linear positive magnetoresistance (LPMR) is a widely observed phenomenon in topological materials, which is promising for potential applications on topological spintronics. However, its mechanism remains ambiguous yet, and the effect is thus uncontrollable. Here, we report a quantitative scaling model that correlates the LPMR with the Berry curvature, based on a ferromagnetic Weyl semimetal CoS2 that bears the largest LPMR of over 500% at 2 K and 9 T, among known magnetic topological semimetals. In this system, masses of Weyl nodes existing near the Fermi level, revealed by theoretical calculations, serve as Berry-curvature monopoles and low-effective-mass carriers. Based on the Weyl picture, we propose a relation [Formula: see text], with B being the applied magnetic field and [Formula: see text] the average Berry curvature near the Fermi surface, and further introduce temperature factor to both MR/B slope (MR per unit field) and anomalous Hall conductivity, which establishes the connection between the model and experimental measurements. A clear picture of the linearly slowing down of carriers, i.e., the LPMR effect, is demonstrated under the cooperation of the k-space Berry curvature and real-space magnetic field. Our study not only provides experimental evidence of Berry curvature-induced LPMR but also promotes the common understanding and functional designing of the large Berry-curvature MR in topological Dirac/Weyl systems for magnetic sensing or information storage.

Gate Modulation of Dissipationless Nonlinear Quantum Geometric Current in 2D Te.

Two-dimensional trigonal tellurium (2D Te), a narrow-bandgap semiconductor with a bandgap of approximately 0.3 eV, hosts Weyl points near the band edge and exhibits a narrow, strong Berry curvature dipole (BCD). By applying a back-gate bias to align the Fermi level with the BCD, a sharp increase in the dissipationless transverse nonlinear Hall response is observed in 2D Te. Gate modulation of the BCD demonstrates an on/off ratio of 104 and a responsivity of nearly 106 V/W, while the longitudinal current induced by band modulation reaches an on/off ratio of about 10. This current is sustained up to 200 K, exhibiting a change of 3 orders of magnitude. The inclusion of both transistor action and rectification enhances the temperature sensitivity of the dissipationless Hall current, offering potential applications in electrothermal detectors and sensors and highlighting the significance of topological properties in advancing electronic applications.

Effective Manipulation of a Colossal Second-Order Transverse Response in an Electric-Field-Tunable Graphene Moiré System.

The second-order nonlinear transport illuminates a frequency-doubling response emerging in quantum materials with a broken inversion symmetry. The two principal driving mechanisms, the Berry curvature dipole and the skew scattering, reflect various information including ground-state symmetries, band dispersions, and topology of electronic wave functions. However, effective manipulation of them in a single system has been lacking, hindering the pursuit of strong responses. Here, we report on the effective manipulation of the two mechanisms in a single graphene moiré superlattice, AB-BA stacked twisted double bilayer graphene. Most saliently, by virtue of the high tunability of moiré band structures and scattering rates, a record-high second-order transverse conductivity ∼ 510 µm S V-1 is observed, which is orders of magnitude higher than any reported values in the literature. Our findings establish the potential of electrically tunable graphene moiré systems for nonlinear transport manipulations and applications.

Hundred-Fold Enhancement in the Anomalous Hall Effect Induced by Hydrogenation.

The anomalous Hall effect (AHE) is one of the most fascinating transport properties in condensed matter physics. However, the AHE magnitude, which mainly depends on net spin polarization and band topology, is generally small in oxides and thus limits potential applications. Here, we demonstrate a giant enhancement of AHE in a LaCoO3-induced 5d itinerant ferromagnet SrIrO3 by hydrogenation. The anomalous Hall resistivity and anomalous Hall angle, which are two of the most critical parameters in AHE-based devices, are found to increase to 62.2 µΩ·cm and 3%, respectively, showing an unprecedentedly large enhancement ratio of ∼10000%. Theoretical analysis suggests the key roles of Berry curvature in enhancing AHE. Furthermore, the hydrogenation concomitantly induces the significant elevation of Curie temperature from 75 to 160 K and 40-fold reinforcement of coercivity. Such giant regulation and very large AHE magnitude observed in SrIrO3 could pave the path for 5d oxide devices.

Nonlinear Electrical Transport Unveils Fermi Surface Malleability in a Moiré Heterostructure.

Van Hove singularities enhance many-body interactions and induce collective states of matter ranging from superconductivity to magnetism. In magic-angle twisted bilayer graphene, van Hove singularities appear at low energies and are malleable with density, leading to a sequence of Lifshitz transitions and resets observable in Hall measurements. However, without a magnetic field, linear transport measurements have limited sensitivity to the band's topology. Here, we utilize nonlinear longitudinal and transverse transport measurements to probe these unique features in twisted bilayer graphene at zero magnetic field. We demonstrate that the nonlinear responses, induced by the Berry curvature dipole and extrinsic scattering processes, intricately map the Fermi surface reconstructions at various fillings. Importantly, our experiments highlight the intrinsic connection of these features with the moiré bands. Beyond corroborating the insights from linear Hall measurements, our findings establish nonlinear transport as a pivotal tool for probing band topology and correlated phenomena.

Terahertz detection based on nonlinear Hall effect without magnetic field.

We propose a method for broadband long-wavelength photodetection using the nonlinear Hall effect in noncentrosymmetric quantum materials. The inherently quadratic relation between transverse current and input voltage at zero magnetic field is used to rectify the incident terahertz or infrared electric field into a direct current, without invoking any diode. Our photodetector operates at zero external bias with fast response speed and has zero threshold voltage. Remarkably, the intrinsic current responsivity due to the Berry curvature mechanism is a material property independent of the incident frequency or the scattering rate, which can be evaluated from first-principles electronic structure calculations. We identify the Weyl semimetal NbP and ferroelectric semiconductor GeTe for terahertz/infrared photodetection with large current responsivity without external bias.

Berry curvature generation detected by Nernst responses in ferroelectric Weyl semimetal.

The quest for nonmagnetic Weyl semimetals with high tunability of phase has remained a demanding challenge. As the symmetry-breaking control parameter, the ferroelectric order can be steered to turn on/off the Weyl semimetals phase, adjust the band structures around the Fermi level, and enlarge/shrink the momentum separation of Weyl nodes which generate the Berry curvature as the emergent magnetic field. Here, we report the realization of a ferroelectric nonmagnetic Weyl semimetal based on indium-doped Pb1- x Sn x Te alloy in which the underlying inversion symmetry as well as mirror symmetry are broken with the strength of ferroelectricity adjustable via tuning the indium doping level and Sn/Pb ratio. The transverse thermoelectric effect (i.e., Nernst effect), both for out-of-plane and in-plane magnetic field geometry, is exploited as a Berry curvature-sensitive experimental probe to manifest the generation of Berry curvature via the redistribution of Weyl nodes under magnetic fields. The results demonstrate a clean, nonmagnetic Weyl semimetal coupled with highly tunable ferroelectric order, providing an ideal platform for manipulating the Weyl fermions in nonmagnetic systems.

Large Hall and Nernst responses from thermally induced spin chirality in a spin-trimer ferromagnet.

The long-range order of noncoplanar magnetic textures with scalar spin chirality (SSC) can couple to conduction electrons to produce an additional (termed geometrical or topological) Hall effect. One such example is the Hall effect in the skyrmion lattice state with quantized SSC. An alternative route to attain a finite SSC is via the spin canting caused by thermal fluctuations in the vicinity of the ferromagnetic ordering transition. Here, we report that for a highly conducting ferromagnet with a two-dimensional array of spin trimers, the thermally generated SSC can give rise to a gigantic geometrical Hall conductivity even larger than the intrinsic anomalous Hall conductivity of the ground state. We also demonstrate that the SSC induced by thermal fluctuations leads to a strong response in the Nernst effect. A comparison of the sign and magnitude of fluctuation-Nernst and Hall responses in fundamental units indicates the need for a momentum-space picture to model these thermally induced signals.

Manipulating Berry curvature of SrRuO3 thin films via epitaxial strain.

Berry curvature plays a crucial role in exotic electronic states of quantum materials, such as the intrinsic anomalous Hall effect. As Berry curvature is highly sensitive to subtle changes of electronic band structures, it can be finely tuned via external stimulus. Here, we demonstrate in SrRuO3 thin films that both the magnitude and sign of anomalous Hall resistivity can be effectively controlled with epitaxial strain. Our first-principles calculations reveal that epitaxial strain induces an additional crystal field splitting and changes the order of Ru d orbital energies, which alters the Berry curvature and leads to the sign and magnitude change of anomalous Hall conductivity. Furthermore, we show that the rotation of the Ru magnetic moment in real space of a tensile-strained sample can result in an exotic nonmonotonic change of anomalous Hall resistivity with the sweeping of magnetic field, resembling the topological Hall effect observed in noncoplanar spin systems. These findings not only deepen our understanding of anomalous Hall effect in SrRuO3 systems but also provide an effective tuning knob to manipulate Berry curvature and related physical properties in a wide range of quantum materials.

Ferroic Berry Curvature Dipole in a Topological Crystalline Insulator at Room Temperature.

The physics related to Berry curvature is now a central research topic in condensed matter physics. The Berry curvature dipole (BCD) is a significant and intriguing condensed matter phenomenon that involves inversion symmetry breaking. However, the creation and controllability of BCDs have so far been limited to far below room temperature (RT), and nonvolatile (i.e., ferroic) BCDs have not yet been discovered, hindering further progress in topological physics. In this work, we demonstrate a switchable and nonvolatile BCD effect at RT in a topological crystalline insulator, Pb1-xSnxTe (PST), which is attributed to ferroic distortion. Surprisingly, the magnitude of the ferroic BCD is several orders of magnitude greater than that of the nonferroic BCDs that appear, for example, in transition metal dichalcogenides. The discovery of this ferroic and extraordinarily large BCD in PST could pave the way for further progress in topological materials science and the engineering of novel topological devices.

Large Nonlinear Transverse Conductivity and Berry Curvature in KTaO3 Based Two-Dimensional Electron Gas.

Two-dimensional electron gas (2DEG) at oxide interfaces exhibits various exotic properties stemming from interfacial inversion and symmetry breaking. In this work, we report large nonlinear transverse conductivities in the LaAlO3/KTaO3 interface 2DEG under zero magnetic field. Skew scattering was identified as the dominant origin based on the cubic scaling of nonlinear transverse conductivity with linear longitudinal conductivity and 3-fold symmetry. Moreover, gate-tunable nonlinear transport with pronounced peak and dip was observed and reproduced by our theoretical calculation. These results indicate the presence of Berry curvature hotspots and thus a large Berry curvature triplet at the oxide interface. Our theoretical calculations confirm the existence of large Berry curvatures from the avoided crossing of multiple 5d-orbit bands, orders of magnitude larger than that in transition-metal dichalcogenides. Nonlinear transport offers a new pathway to probe the Berry curvature at oxide interfaces and facilitates new applications in oxide nonlinear electronics.

Giant and Controllable Valley Currents in Graphene by Double Pumped THz Light.

The field of valleytronics considers the creation and manipulation of "valley states", charge excitations characterized by a particular value of the crystal momentum in the Brillouin zone. Here we show, using the example of minimally gapped (≤40 meV) graphene, that there exist lightforms that create almost perfect valley contrasting current states (up to ∼80% valley purity) in the absence of a valley contrasting charge excitation. These "momentum streaked" THz waveforms act by deforming the excited state population in momentum space such that current flows at one valley yet is blocked at the conjugate valley. This approach both unlocks the potential of graphene as a materials platform for valleytronics, as gaps of 10-40 meV are robustly found in useful experimental contexts such as graphene/hBN systems, while simultaneously providing a tool toward ultrafast light control of valley currents in diverse minimally gapped matter, including many topological insulator systems.

Phonon Chirality Manipulation Mechanism in Transition-Metal Dichalcogenide Interlayer-Sliding Ferroelectrics.

As an ideal platform, both the theoretical prediction and first experimental verification of chiral phonons are based on transition-metal dichalcogenide materials. The manipulation of phonon chirality in these materials will have a profound effect on the study of chiral phonons. In this work, we utilize the sliding ferroelectric effect to realize the phonon chirality manipulation mechanism in transition-metal dichalcogenide materials. Based on first-principles calculations, we find the different manipulation effects of interlayer sliding on the phonon chirality and Berry curvature in bilayer and four-layer MoS2 sliding ferroelectrics. These further affect the phonon angular momentum and magnetization under a temperature gradient and the phonon Hall effect under a magnetic field. Our work connects two emerging fields and opens up a new route to manipulating phonon chirality in transition-metal dichalcogenide materials through the sliding ferroelectric mechanism.

Novel π/2-Periodic Planar Hall Effect Due to Orbital Magnetic Moments in MnBi2Te4.

The Berry curvature and orbital magnetic moment (OMM) come from either inversion symmetry or time-reversal symmetry breaking in quantum materials. Here, we demonstrate the significance of OMMs and Berry curvature in planar Hall effect (PHE) in antiferromagnetic topological insulator MnBi2Te4 flakes. We observe a PHE with period of π and positive magnitude at low fields, resembling the PHE of the surface states in nonmagnetic topological insulators. Remarkably, a novel predominant PHE with period of π/2 and negative magnitude emerges below the Néel temperature with B > 10 T. Our theoretical calculations reveal that this unusual π/2-periodic PHE originates from the topological OMMs of bulk Dirac electrons. Moreover, the competition between the contributions from the bulk and the surface states leads to nontrivial evolutions of PHE and anisotropic magnetoresistance. Our results reveal intriguing electromagnetic response due to the OMMs and also provide insight into the potential applications of magnetic topological insulators in spintronics.

Ferroelectricity-Driven Phonon Berry Curvature and Nonlinear Phonon Hall Transports.

Berry curvature (BC) governs topological phases of matter and generates anomalous transport. When a magnetic field is applied, phonons can acquire BC indirectly through spin-lattice coupling, leading to a linear phonon Hall effect. Here, we show that polar lattice distortion directly couples to a phonon BC dipole, which causes a switchable nonlinear phonon Hall effect. In a SnS monolayer, the in-plane ferroelectricity induces a phonon BC and leads to the phononic version of the nonvolatile BC memory effect. As a new type of ferroelectricity-phonon coupling, the phonon Rashba effect emerges and opens a mass gap in tilted Weyl phonon modes, resulting in a large phonon BC dipole. Furthermore, our ab initio non-equilibrium molecular dynamics simulations reveal that nonlinear phonon Hall transport occurs in a controllable manner via ferroelectric switching. The ferroelectricity-driven phonon BC and corresponding nonlinear phonon transports provide a novel scheme for constructing topological phononic transport/memory devices.

Unraveling materials Berry curvature and Chern numbers from real-time evolution of Bloch states.

Materials can be classified by the topological character of their electronic structure and, in this perspective, global attributes immune to local deformations have been discussed in terms of Berry curvature and Chern numbers. Except for instructional simple models, linear response theories have been ubiquitously used in calculations of topological properties of real materials. Here we propose a completely different and versatile approach to obtain the topological characteristics of materials by calculating physical observables from the real-time evolving Bloch states: The cell-averaged current density reveals the anomalous velocities that lead to the conductivity quantum. Results for prototypical cases are shown, including a spin-frozen valley Hall and a quantum anomalous Hall insulator. The advantage of this method is best illustrated by the example of a quantum spin Hall insulator: The quantized spin Hall conductivity is straightforwardly obtained irrespective of the non-Abelian nature in its Berry curvature. Moreover, the method can be extended to the description of real observables in nonequilibrium states of topological materials.

Enhanced Berry Curvature Dipole and Persistent Spin Texture in the Bi(110) Monolayer.

Nonvanishing Berry curvature dipole (BCD) and persistent spin texture (PST) are intriguing physical manifestations of electronic states in noncentrosymmetric 2D materials. The former induces a nonlinear Hall conductivity while the latter offers a coherent spin current. Based on density-functional-theory (DFT) calculations, we demonstrate the coexistence of both phenomena in a Bi(110) monolayer with a distorted phosphorene structure. Both effects are concurrently enhanced due to the strong spin-orbit coupling of Bi while the structural distortion creates internal in-plane ferroelectricity with inversion asymmetry. We further succeed in fabricating a Bi(110) monolayer in the desired phosphorene structure on the NbSe2 substrate. Detailed atomic and electronic structures of the Bi(110)/NbSe2 heterostructure are characterized by scanning tunneling microscopy/spectroscopy and angle-resolved-photoemission spectroscopy. These results are consistent with DFT calculations which indicate the large BCD and PST are retained. Our results suggest the Bi(110)/NbSe2 heterostructure as a promising platform to exploit nonlinear Hall and coherent spin transport properties together.

Anomalous Hall effect in Weyl semimetal half-Heusler compounds RPtBi (R = Gd and Nd).

Topological materials ranging from topological insulators to Weyl and Dirac semimetals form one of the most exciting current fields in condensed-matter research. Many half-Heusler compounds, RPtBi (R = rare earth), have been theoretically predicted to be topological semimetals. Among various topological attributes envisaged in RPtBi, topological surface states, chiral anomaly, and planar Hall effect have been observed experimentally. Here, we report an unusual intrinsic anomalous Hall effect (AHE) in the antiferromagnetic Heusler Weyl semimetal compounds GdPtBi and NdPtBi that is observed over a wide temperature range. In particular, GdPtBi exhibits an anomalous Hall conductivity of up to 60 Ω-1⋅cm-1 and an anomalous Hall angle as large as 23%. Muon spin-resonance (µSR) studies of GdPtBi indicate a sharp antiferromagnetic transition (TN) at 9 K without any noticeable magnetic correlations above TN Our studies indicate that Weyl points in these half-Heuslers are induced by a magnetic field via exchange splitting of the electronic bands at or near the Fermi energy, which is the source of the chiral anomaly and the AHE.

Visualization and Manipulation of Bilayer Graphene Quantum Dots with Broken Rotational Symmetry and Nontrivial Topology.

Electrostatically defined quantum dots (QDs) in Bernal stacked bilayer graphene (BLG) are a promising quantum information platform because of their long spin decoherence times, high sample quality, and tunability. Importantly, the shape of QD states determines the electron energy spectrum, the interactions between electrons, and the coupling of electrons to their environment, all of which are relevant for quantum information processing. Despite its importance, the shape of BLG QD states remains experimentally unexamined. Here we report direct visualization of BLG QD states by using a scanning tunneling microscope. Strikingly, we find these states exhibit a robust broken rotational symmetry. By using a numerical tight-binding model, we determine that the observed broken rotational symmetry can be attributed to low energy anisotropic bands. We then compare confined holes and electrons and demonstrate the influence of BLG's nontrivial band topology. Our study distinguishes BLG QDs from prior QD platforms with trivial band topology.