Experimental demonstration of topological bounds in quantum metrology.

Quantum metrology is deeply connected to quantum geometry, through the fundamental notion of quantum Fisher information. Inspired by advances in topological matter, it was recently suggested that the Berry curvature and Chern numbers of band structures can dictate strict lower bounds on metrological properties, hence establishing a strong connection between topology and quantum metrology. In this work, we provide a first experimental verification of such topological bounds, by performing optimal quantum multi-parameter estimation and achieving the best possible measurement precision. By emulating the band structure of a Chern insulator, we experimentally determine the metrological potential across a topological phase transition, and demonstrate strong enhancement in the topologically non-trivial regime. Our work opens the door to metrological applications empowered by topology, with potential implications for quantum many-body systems.

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.

Valley-Dependent Electronic Properties of Metal Monochalcogenides GaX and Janus Ga2XY (X, Y = S, Se, and Te).

Two-dimensional (2D) materials have shown outstanding potential for new devices based on their interesting electrical properties beyond conventional 3D materials. In recent years, new concepts such as the valley degree of freedom have been studied to develop valleytronics in hexagonal lattice 2D materials. We investigated the valley degree of freedom of GaX and Janus GaXY (X, Y = S, Se, Te). By considering the spin-orbit coupling (SOC) effect in the band structure calculations, we identified the Rashba-type spin splitting in band structures of Janus Ga2SSe and Ga2STe. Further, we confirmed that the Zeeman-type spin splitting at the K and K' valleys of GaX and Janus Ga2XY show opposite spin contributions. We also calculated the Berry curvatures of GaX and Janus GaXY. In this study, we find that GaX and Janus Ga2XY have a similar magnitude of Berry curvatures, while having opposite signs at the K and K' points. In particular, GaTe and Ga2SeTe have relatively larger Berry curvatures of about 3.98 Å2 and 3.41 Å2, respectively, than other GaX and Janus Ga2XY.

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.

Topology-Driven Coulomb Drag in van der Waals Heterostructure with Broken Inversion Symmetry.

As Coulomb drag near charge neutrality (CN) is driven by fluctuations or inhomogeneity in charge density, the topology should play an extremely important role. Interlinking Coulomb drag and topology could reveal how the system's nontrivial topology influences the electron-electron interactions at the quantum level. However, such an aspect is overlooked as most studies focus on symmetric drag systems without topology. To understand this topological aspect, we need to study Coulomb drag in an asymmetric system with a broken inversion symmetry and strong spin-orbit coupling (SOC). Here we experimentally demonstrate the energy-driven Coulomb drag in an asymmetric van der Waals heterostructure composed of black phosphorus and rhenium disulfide characterized by broken inversion symmetry. Temperature-dependent transport measurements near CN provide compelling evidence for the energy-driven Coulomb drag due to electron-hole coupling that is energetically favored in a broken-gap heterojunction, as confirmed by Hall coefficient sign reversal with temperature. Moreover, contrary to the symmetric devices, our results exhibit magnetic-field-free, i.e., topology-driven, Hall drag, revealing an intrinsic coupling between energy and charge modes. This is the manifestation of nonzero Berry curvature, akin to a magnetic field in momentum space, in a Rashba system, which arises from the SOC and broken inversion symmetry of the heterostructure.

Extended Berry Curvature Tail in Ferromagnetic Weyl Semimetals NiMnSb and PtMnSb.

Heusler compounds belong to a large family of materials and exhibit numerous physical phenomena with promising applications, particularly ferromagnetic Weyl semimetals for their use in spintronics and memory devices. Here, anomalous Hall transport is reported in the room-temperature ferromagnets NiMnSb (half-metal with a Curie temperature (TC) of 660 K) and PtMnSb (pseudo half-metal with a TC of 560 K). They exhibit 4 µB/f.u. magnetic moments and non-trivial topological states. Moreover, NiMnSb and PtMnSb are the first half-Heusler ferromagnets to be reported as Weyl semimetals, and they exhibit anomalous Hall conductivity (AHC) due to the extended tail of the Berry curvature in these systems. The experimentally measured AHC values at 2 K are 1.8 × 102 Ω-1 cm-1 for NiMnSb and 2.2 × 103 Ω-1 cm-1 for PtMnSb. The comparatively large value between them can be explained in terms of the spin-orbit coupling strength. The combined approach of using ab initio calculations and a simple model shows that the Weyl nodes located far from the Fermi energy act as the driving mechanism for the intrinsic AHC. This contribution of topological features at higher energies can be generalized.

Intrinsic second-order magnon thermal Hall effect.

In this paper, we study the intrinsic contribution of nonlinear magnon thermal Hall Effect. We derive the intrinsic second-order thermal Hall conductivity of magnon by the thermal scalar potential method and the thermal vector potential method. We find that the intrinsic second-order magnon thermal Hall conductivity is related to the thermal Berry-connection polarizability. We apply our theory to the monolayer ferromagnetic Hexagonal lattice, and we find that the second-order magnon thermal Hall conductivity can be controlled by changing Dzyaloshinskii-Moriya strength and applying strain.

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.

Flat bands without twists: periodic holey graphene.

Holey Graphene(HG) is a widely used graphene material for the synthesis of high-purity and highly crystalline materials. The electronic properties of a periodic distribution of lattice holes are explored here, demonstrating the emergence of flat bands. It is established that such flat bands arise as a consequence of an induced sublattice site imbalance, i.e. by having more sites in one of the graphene's bipartite sublattice than in the other. This is equivalent to the breaking of a path-exchange symmetry. By further breaking the inversion symmetry, gaps and a nonzero Berry curvature are induced, leading to topological bands. In particular, the folding of the Dirac cones from the hexagonal Brillouin zone (BZ) to the holey superlattice rectangular BZ of HG, with sizes proportional to an integerntimes the graphene's lattice parameter, leads to a periodicity in the gap formation such thatn≡0(mod 3). A low-energy hamiltonian for the three central bands is also obtained revealing that the system behaves as an effectiveα-T3graphene material. Therefore, a simple protocol is presented here that allows for obtaining flat bands at will. Such bands are known to increase electron-electron correlation effects. Therefore, the present work provides an alternative system that is much easier to build than twisted systems, allowing for the production of flat bands and potentially highly correlated quantum phases.

Helicity-Sensitive Terahertz Detection in Monolayer 1T'-WTe2.

Valleytronics, identified as electronic properties of the energy band extrema in momentum space, has been intensively revived following the emergence of two-dimensional transition metal dichalcogenides (TMDCs) as their valley information can be controlled and probed through the spin angular momentum of light. Previous optical investigations of valleytronics have been limited to the visible/near-infrared spectral regime through which the carriers of most TMDCs can be excited. Monolayer 1T'-WTe2 with broken time-reversal symmetry provides a fertile platform to study the long-wavelength photonic properties in different valleys. Here, we employed a circularly polarized terahertz (THz) laser to selectively excite the valley of monolayer 1T'-WTe2 and demonstrate that the helicity-dependent photoresponse is generated via the photogalvanic effect (PGE). We also observed that the photocurrent is controlled by circular polarization and the external electric field. Because of the tunable Berry curvature dipole derived from the nontrivial wave functions near the inverted gap edge in monolayer WTe2, the bandgap can be tuned efficiently. Our results provide a versatile venue for controlling, detecting, and processing valleytronics and applications in on-chip THz imaging and quantum information processing.

Direction-dependent conductivity in planar Hall set-ups with tilted Weyl/multi-Weyl semimetals.

We compute the magnetoelectric conductivity tensors in planar Hall set-ups, which are built with tilted Weyl semimetals (WSMs) and multi-Weyl semimetals (mWSMs), considering all possible relative orientations of the electromagnetic fields (EandB) and the direction of the tilt. The non-Drude part of the response arises from a nonzero Berry curvature in the vicinity of the WSM/mWSM node under consideration. Only in the presence of a nonzero tilt do we find linear-in-|B|terms in set-ups where the tilt-axis is not perpendicular to the plane spanned byEandB. The advantage of the emergence of the linear-in-|B|terms is that, unlike the various|B|2-dependent terms that can contribute to experimental observations, they have purely a topological origin, and they dominate the overall response-characteristics in the realistic parameter regimes. The important signatures of these terms are that they (1) change the periodicity of the response fromπto 2π, when we consider their dependence on the angleθbetweenEandB; and (2) lead to an overall change in sign of the conductivity depending onθ, when measured with respect to theB=0case.

Tunable Colossal Anomalous Hall Conductivity in Half-Metallic Material Induced by d-Wave-Like Spin-Orbit Gap.

The anomalous Hall conductivity (AHC) in magnetic materials, resulting from inverted band topology, has emerged as a key adjustable function in spin-torque devices and advanced magnetic sensors. Among systems with near-half-metallicity and broken time-reversal symmetry, cobalt disulfide (CoS2) has proven to be a material capable of significantly enhancing its AHC. In this study, the AHC of CoS2 is empirically assessed by manipulating the chemical potential through Fe- (hole) and Ni- (electron) doping. The primary mechanism underlying the colossal AHC is identified through the application of density functional theory and tight-binding analyses. The main source of this substantial AHC is traced to four spin-polarized massive Dirac dispersions in the kz = 0 plane of the Brillouin zone, located slightly below the Fermi level. In Co0.95Fe0.05S2, the AHC, which is directly proportional to the momentum-space integral of the Berry curvature (BC), reached a record-breaking value of 2507 Ω-1cm-1. This is because the BCs of the four Dirac dispersions all exhibit the same sign, a consequence of the d-wave-like spin-orbit coupling among spin-polarized eg orbitals.

Berry curvature and quantum metric in copper-substituted lead phosphate apatite.

The recent discovery of copper-substituted lead phosphate apatite, also known as LK-99, has caught much attention owing to certain experimental evidence of room-temperature superconductivity, although this claim is currently under intensive debate. Be it superconducting or not, we show that the normal state of this material has peculiar quantum geometrical properties that may be related to the magnetism and the mechanism for flat band superconductivity. Based on a recently proposed spinless two-band tight-binding model for the Pb-Cu hexagonal lattice subset of the crystalline structure, which qualitatively captures the two flat bands in the band structure, we elaborate the highly anisotropic Berry curvature and quantum metric in the regions of Brillouin zone where one flat band is above and the other below the Fermi surface. In these regions, the Berry curvature has a pattern in the planar momentum that remains unchanged along the out-of-plane momentum. Moreover, the net orbital magnetization contributed from the Berry curvature is zero, signifying that the magnetism in this material should come from other sources. The quantum metric has a similar momentum dependence, and its two planar components are found to be roughly the same but the out-of-plane component vanishes, hinting that the superfluid stiffness of the flat band superconductivity, shall it occur, may be quite anisotropic.

Giant Third-Order Nonlinear Hall Effect in Misfit Layer Compound (SnS)1.17(NbS2)3.

The nonlinear Hall effect (NLHE) holds immense significance in recognizing the band geometry and its potential applications in current rectification. Recent discoveries have expanded the study from second-order to third-order nonlinear Hall effect (THE), which is governed by an intrinsic band geometric quantity called the Berry Connection Polarizability tensor. Here we demonstrate a giant THE in a misfit layer compound, (SnS)1.17(NbS2)3. While the THE is prohibited in individual NbS2 and SnS due to the constraints imposed by the crystal symmetry and their band structures, a remarkable THE emerges when a superlattice is formed by introducing a monolayer of SnS. The angular-dependent THE and its scaling relationship indicate that the phenomenon could be correlated to the band geometry modulation, concurrently with the symmetry breaking. The resulting strength of THE is orders of magnitude higher compared to recent studies. Our work illuminates the modulation of structural and electronic geometries for novel quantum phenomena through interface engineering.

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.

Layer Hall effect induced by hidden Berry curvature in antiferromagnetic insulators.

The layer Hall effect describes electrons spontaneously deflected to opposite sides at different layers, which has been experimentally reported in the MnBi2Te4 thin films under perpendicular electric fields. Here, we reveal a universal origin of the layer Hall effect in terms of the so-called hidden Berry curvature, as well as material design principles. Hence, it gives rise to zero Berry curvature in momentum space but non-zero layer-locked hidden Berry curvature in real space. We show that, compared to that of a trivial insulator, the layer Hall effect is significantly enhanced in antiferromagnetic topological insulators. Our universal picture provides a paradigm for revealing the hidden physics as a result of the interplay between the global and local symmetries, and can be generalized in various scenarios.

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.

Observation of the Anomalous Hall Effect in a Layered Polar Semiconductor.

Progress in magnetoelectric materials is hindered by apparently contradictory requirements for time-reversal symmetry broken and polar ferroelectric electronic structure in common ferromagnets and antiferromagnets. Alternative routes can be provided by recent discoveries of a time-reversal symmetry breaking anomalous Hall effect (AHE) in noncollinear magnets and altermagnets, but hitherto reported bulk materials are not polar. Here, the authors report the observation of a spontaneous AHE in doped AgCrSe2 , a layered polar semiconductor with an antiferromagnetic coupling between Cr spins in adjacent layers. The anomalous Hall resistivity 3 µ Ω c m $\mu \Omega \, \textnormal {cm}$ is comparable to the largest observed in compensated magnetic systems to date, and is rapidly switched off when the angle of an applied magnetic field is rotated to ≈80° from the crystalline c-axis. The ionic gating experiments show that the anomalous Hall conductivity magnitude can be enhanced by modulating the p-type carrier density. They also present theoretical results that suggest the AHE is driven by Berry curvature due to noncollinear antiferromagnetic correlations among Cr spins, which are consistent with the previously suggested magnetic ordering in AgCrSe2 . The results open the possibility to study the interplay of magnetic and ferroelectric-like responses in this fascinating class of materials.

A versatile model with three-dimensional triangular lattice for unconventional transport and various topological effects.

The finite Berry curvature in topological materials can induce many subtle phenomena, such as the anomalous Hall effect (AHE), spin Hall effect (SHE), anomalous Nernst effect (ANE), non-linear Hall effect (NLHE) and bulk photovoltaic effects. To explore these novel physics as well as their connection and coupling, a precise and effective model should be developed. Here, we propose such a versatile model-a 3D triangular lattice with alternating hopping parameters, which can yield various topological phases, including kagome bands, triply degenerate fermions, double Weyl semimetals and so on. We reveal that this special lattice can present unconventional transport due to its unique topological surface states and the aforementioned topological phenomena, such as AHE, ANE, NLHE and the topological photocurrent effect. In addition, we also provide a number of material candidates that have been synthesized experimentally with this lattice, and discuss two materials, including a non-magnetic triangular system for SHE, NLHE and the shift current, and a ferromagnetic triangular lattice for AHE and ANE. Our work provides an excellent platform, including both the model and materials, for the study of Berry-curvature-related physics.

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.