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In a three-dimensional Dirac semimetal the time reversal symmetry (TRS) or the inversion symmetry (IS) is not broken. With either of these symmetries broken, the Dirac points in the threedimensional band structure split up into pairs of so-called Weyl points. The ferromagnetic Weyl semimetals (FMWSM), such as Co3Sn2S2, feature pairs of Weyl points characterized by the opposite chiralities. In this communication we study FMWSM based on TRS broken continuum and lattice Hamiltonians. The latter one is more realistic and represents Co3Sn2S2. These models include all essential ingredients leading to the formation of a pair of Weyl nodes and tilted Weyl cones. Our analysis shows a large anomalous Nernst conductivity which is unlocked due to the divergent Berry curvature-a local manifestation of the geometric properties of electronic wavefunctions-at Weyl points. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this review, the thermoelectric properties in nodal‐point semimetals with two bands are discussed. For the two‐dimensional (2D) cases, it is shown that the expressions of the thermoelectric coefficients take different values depending on the nature of the scattering mechanism responsible for transport, by considering examples of short‐ranged disorder potential and screened charged impurities. An anisotropy in the energy dispersion spectrum invariably affects the thermopower quite significantly, as illustrated by the results for a node of semi‐Dirac semimetal and a single valley of graphene. The scenario when a magnetic field of magnitude B$B$ is applied perpendicular to the plane of the 2D semimetal is also considered. The computations for the three‐dimensional (3D) cases necessarily involve the inclusion of nontrivial Berry phase effects. In addition to demonstrating the expressions for the response tensors, the exotic behavior observed in planar Hall and planar thermal Hall set‐ups is discussed. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Topological phononics, a fascinating frontier in condensed matter physics, holds great promise for advancing energy‐related applications. Topologically nontrivial phonons typically possess gapless edge or surface states. These exotic states of lattice vibrations, characterized by their nontrivial topology, offer unique opportunities for manipulating and harnessing energy transport. The exploration of topological phonons opens new avenues in understanding and controlling thermal transport properties, with potential applications in fields such as thermoelectric materials, phononic devices, and waste heat recovery. Here, an overview of concepts such as Berry curvature and topological invariants, along with the applications of phonon tight‐binding method and nonequilibrium Green's function method in the field of topological phononics is provided. This review encompasses the latest research progress of various topological phonon states within crystalline materials, including topological optical phonons, topological acoustical phonons, and higher‐order topological phonons. Furthermore, the study delves into the prospective applications of topological phonons in the realm of thermoelectric conversion, focusing on aspects like size effects and symmetry engineering. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We theoretically studied the exciton geometric structure in layered semiconducting transition metal dichalcogenides. Based on a three-orbital tight-binding model for Bloch electrons which incorporates their geometric structures, an effective exciton Hamiltonian is constructed and solved perturbatively to reveal the relation between the exciton and its electron/hole constituent. We show that the electron—hole Coulomb interaction gives rise to a non-trivial inheritance of the exciton geometric structure from Bloch electrons, which manifests as a valley-dependent center-of-mass anomalous Hall velocity of the exciton when two external fields are applied on the electron and hole constituents, respectively. The obtained center-of-mass anomalous velocity is found to exhibit a non-trivial dependence on the fields, as well as the wave function and valley index of the exciton. These findings can serve as a general guide for the field-control of the valley-dependent exciton transport, enabling the design of novel quantum optoelectronic and valleytronic devices. [ABSTRACT FROM AUTHOR]

Topological magnets (TMs) with the coupled topology of electronic band structures and spin configuration have exhibited exotic transport properties that are overwhelmingly appealing for transverse thermoelectric applications. Despite the continuous discovery of TMs in recent years, the development of Nernst generators has much lagged. Here, high‐performance Nernst generators are developed utilizing polycrystalline topological Heusler bulk magnets. Benefiting from the robustness of topological effect to grain boundary scattering, polycrystalline Co2MnGa is found to exhibit a large Nernst thermopower of ≈6.5 µV K−1 at 300 K, which is comparable to the previously reported record value in its single crystal. The developed Nernst generators thereby exhibit excellent performance with an output voltage of 5.4 mV and power of 14.3 µW, significantly higher than that of Nernst thermopiles assembled using conventional ferromagnets. These results pave the way to advancing TMs with intrinsically large Berry curvature for transverse thermoelectric applications. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The thermal Hall effect (THE) is an important experimental probe of band topology and elementary excitations. Here, a large thermal Hall angle (THA) κxy/κxx ≈ 7 × 10−3 discovered so far in ferrimagnetic spinel FeCr2S4 and a large thermal Hall conductivity (κxy) discovered first in spinel structure and reaching a magnitude of κxy≈1.8×10−2WK−1m−1$\kappa _{xy} \approx 1.8 \times 10^{-2} \rm {W K^{-1} m^{-1}}$ at 50 K with a small magnetic field of 0.1 T are reported. These results suggest the emergence of nontrivial topological excitations in FeCr2S4. A large THA in spin caloritronics devices means that a small number of excitations can produce a large transverse signal. FeCr2S4 is therefore a potential platform for spintronics‐magnonics applications, and may enhance the knowledge of the thermal Hall effect. [ABSTRACT FROM AUTHOR]

The anomalous Hall effect (AHE) that associated with the Berry curvature of occupied electronic states in momentum‐space is one of the intriguing aspects in condensed matter physics, and provides an alternative for potential applications in topological electronics. Previous experiments reported the tunable Berry curvature and the resulting magnetization switching process in the AHE based on strain engineering or chemical doping. However, the AHE modulation by these strategies are usually irreversible, making it difficult to realize switchable control of the AHE and the resultant spintronic applications. Here, we demonstrated the switchable control of the Berry‐curvature‐related AHE by electrical gating in itinerant ferromagnetic Cr7Te8 with excellent ambient stability. The gate‐tunable sign reversal of the AHE can be attributed to the redistribution of the Berry curvature in the band structure of Cr7Te8 due to the intercalation‐induced change in the Fermi level. Our work facilitates the applications of magnetic switchable devices based on gate‐tunable Berry curvature. [ABSTRACT FROM AUTHOR]

Ab initio molecular dynamics in a magnetic field requires solving equations of motion with velocity-dependent forces – namely, the Lorentz force arising from the nuclear charges moving in a magnetic field and the Berry force arising from the shielding of these charges from the magnetic field by the surrounding electrons. In this work, we revisit two existing propagators for these equations of motion, the auxiliary-coordinates-and-momenta (ACM) propagator and the Tajima propagator (TAJ), and compare them with a new exponential (EXP) propagator based on the Magnus expansion. Additionally, we explore limits (for example, the zero-shielding limit), the implementation of higher-order integration schemes, and series truncation to reduce computational cost by carrying out simulations of a HeH $ ^+ $ + model system for a wide range of field strengths. While being as efficient as the TAJ propagator, the EXP propagator is the only propagator that converges to both the schemes of Spreiter and Walter (derived for systems without shielding of the Lorentz force) and to the exact cyclotronic motion of a charged particle. Since it also performs best in our model simulations, we conclude that the EXP propagator is the recommended propagator for molecules in magnetic fields. [ABSTRACT FROM AUTHOR]

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 μΩcm$\mu \Omega \, \textnormal {cm}$ 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We fabricate SrRuO3/PbZr0.52Ti0.48O3 heterostructures each with an in-plane tensile-strained SrRuO3 layer and investigate the effect of an applied electric field on anomalous Hall effect. The four-fold symmetry of anisotropic magnetoresistance and the nonmonotonic variation of anomalous Hall resistivity are observed. By applying positive electric field or negative electric field, the intersecting hump-like feature is suppressed or enhanced, respectively. The sign and magnitude of the anomalous Hall conductivity can be effectively controlled with an electric field under a high magnetic field. The electric-field-modulated anomalous Hall effect is associated with the magnetization rotation in SrRuO3. The experimental results are helpful in modulating the magnetization rotation in spintronic devices based on SrRuO3 heterostructures. [ABSTRACT FROM AUTHOR]

The paper focuses on transport properties of double perovskite Sr2FeMoO6−δ, which were studied experimentally and using First principles calculations. The strontium ferromolybdate specimens were prepared using citrate-gel method followed by compacting and thermal treatment at different regimes. The Hall effect was calculated using Quantum Espresso and Wannier90 software packages. The study conformed high sensitivity of Sr2FeMoO6 to the processing parameters such as pressure and temperature of powder compacting as well as the temperature and duration of the subsequent annealing in Ar/O2 atmosphere. The optimal regime of compacting to avoid cracking involved pressing under 4 GPa at T = 800 K. Further heat treatment of the compacted specimens in Ar/O2 atmosphere has shown that three types of electric conductivity, namely metallic, semiconducting and mixed one can be realized in the Sr2FeMoO6 specimens. The highest magnitude of magnetoresistance was found in the semiconducting specimen (about 44%), while the specimen of metallic type demonstrated magnetoresistance of about 21%. The elevated values of magnetoresistance in the semiconducting specimen were achieved due to conduction mechanism related to tunneling through intergrain dielectric layers formed by secondary SrMoO4 phase. The Hall effect was computed by constructing the Hamiltonian in the maximally-localized Wannier functions basis. Calculations of the Berry curvature, which is the origin of the high intrinsic Hall effect showed that its highest magnitudes concentrate near avoided band crossings gapped out due to spin-orbit coupling. The Hall conductivity calculated by integrating the Berry curvature over all occupied bands was found to be ~22 S/cm. [ABSTRACT FROM AUTHOR]

Combining the nontrivial band topology with the intrinsic ferrovalley (FV), the valley-nonequilibrium quantum anomalous Hall effect (VQAHE) attracts growing attention both for its potential applications and basic physics. The electronic properties of some systems with localized orbital distribution and special structures could be influenced by the electronic correlation effect. In our work, the electronic correlation effect on the electronic structures for a Janus RuClF monolayer (ML) is investigated based on the first-principles calculations + U method. For the magnetization orientation along the out-of-plane (OOP) direction, RuClF ML undergoes FV to half-valley-metal (HVM) to VQAHE to HVM to FV transitions with increasing electron correlation effects. There is a chiral edge state connecting the valence and conduction bands and an integer Chern number (C = 1) when 2.52 < U < 2.55 eV. No obvious valley polarization and special VQAHE phases occur for the magnetization orientation along the in-plane (IP) direction. Regardless of IP or OOP magnetic anisotropy, the sign-reversible Berry curvature can be found with increasing U values. Notably, with increasing U values, the magnetization of RuClF ML varies from OOP to IP, and the key U value is approximately 2.41 eV. When taking into account the intrinsic magnetic anisotropy, no HVM and VQAHE states exist. This work finds the significance of magnetic anisotropy and electronic correlation effects in RuClF ML and highlights that electronic correlation effects can induce unusual topological phase transitions. Our consequences manifest that RuClF ML is an admirable material for topological electronic, spintronic, and valleytronic applications. [ABSTRACT FROM AUTHOR]

Solid-state high-order harmonic generation (HHG) now is a strong tool for detecting target properties, like band structure, Berry curvature and transition dipole moments (TDMs). However, the physical mechanism of high-order harmonic generation (HHG) in solids has not been fully elucidated. According to previously published works, in addition to the inter-band polarization, intra-band currents, and anomalous currents due to Berry curvature, there is another term which will be called the mixture term (MT). Taking monolayer ZnO as a sample, it is found that the intensity of the mixture term, which has been ignored for a long time in previous works, actually is comparable with other terms. Additionally, we compare the orientation-dependent HHG spectra that originated from different mechanisms. It is found that the inter-band and mixture HHG show similar orientation features. Meanwhile, Berry curvature only produces perpendicularly polarized even harmonics, and intra-band perpendicularly polarized even harmonics show special orientation features which can be explained by the orientation-dependent group velocity. This work will help people understand the mechanisms of solid-HHG better. [ABSTRACT FROM AUTHOR]

We proposed a reconfigurable valley topological acoustic waveguide constructed using a 2D phononic crystal (PnC) with C 3v symmetric arrangement of three rods in the unit cell. An interface between two types of PnCs with differently oriented unit cells exhibits high robustness of the valley transport of acoustic waves via the topologically protected state. Structural reconfiguration was introduced by the continuous translation of rod arrays in the PnCs. The topological phase transition in this translational change was quantitatively identified by the change in the Berry curvature. The translation of the rods leaves a dimer array at the interface, creating a localized/defective mode along the waveguide. Despite the presence of the localized mode, the acoustic wave can propagate along the reconfigurable waveguide the same as the original waveguide. The continuous translation of a rod array can be used to turn on and off the bandgap. This can be a new approach to design a robust acoustic device with a high reconfigurability. [ABSTRACT FROM AUTHOR]

Quantum materials have exhibited attractive electro-mechanical responses, but their piezoelectric coefficients are far from satisfactory due to the lack of feasible strategies to benefit from the quantum effects. We discovered the valley piezoelectric mechanism that is absent in the traditional piezoelectric theories yet promising to overcome this challenge. A theoretical model was developed to elucidate the valley piezoelectricity in 2D materials as originating from the strong spin-orbit coupling. Consistent analytical and density-functional-theory calculations validate the model and unveil the crucial dependence of valley piezoelectricity on valley/spin splitting and hybridization energy. Up to 50% of electro-mechanical responses in our tested two-dimensional systems are attributed to the valley piezoelectric mechanisms. Rational strategies including doping, passivation, and external strain are proposed to optimize piezoelectricity, with a more than 127% increase in piezoelectricity demonstrated by density-functional-theory simulations. The general valley piezoelectric model not only opens an opportunity to achieve outstanding piezoelectricity via optimizing intrinsic variables but also makes the large family of valley materials promising for piezoelectric sensing and energy harvesting. [ABSTRACT FROM AUTHOR]

The electronic band structure in crystalline semiconductors represents a relationship between crystal momentum and energy of the electrons and is often depicted by a series of extremum known as valleys. While the use of charge or spin degree of freedom for carrying information is prevalent in today's technology, the use of electron's valley degrees of freedom for encoding and processing information (valleytronics) has remained inaccessible for many decades because of inadequate coupling between external excitation and the valley. The advent of two-dimensional materials such as graphene and transition metal dichalcogenides has opened a new avenue for valleytronics which seeks to use valley degrees of freedom to carry and process information, analogues to spin-based spintronics and charge-based electronics. These materials have unique spin-valley locking, imparting a great ability to control and harness electronic valley degrees of freedom with light, electric, and magnetic fields. Here, we present a viewpoint on the fundamental aspects of valleytronics, emphasising valley contrasting characters of two-dimensional semiconductors. [ABSTRACT FROM AUTHOR]

Topologically protected flat surface bands make thin films of rhombohedral graphite an appealing platform for searching for strongly correlated states of 2D electrons. In this work, rhombohedral graphite is studied with a twin boundary stacking fault and the semimetallic and topological properties of low‐energy bands, localized at the surfaces and at the twinned interface, are analyzed. An effective 4‐band low energy model is derived, where the full set of Slonczewski–Weiss–McClure (SWMcC) parameters is implemented, and the conditions for the bands are found to be localized at the twin boundary, protected from the environment‐induced disorder. This protection together with a high density of states at the charge neutrality point, in some cases—due to a Lifshitz transition, makes this system a promising candidate for hosting strongly‐correlated effects. [ABSTRACT FROM AUTHOR]

Materials hosting noncollinear magnetic ordering and sizeable spin-orbit coupling can manifest perpendicular magnetic anisotropy and a Berry curvaturedriven intrinsic anomalous Hall effect. In this work, the structural, magnetic, and magnetotransport properties of crystalline hexagonal Heusler MnPtGa epitaxial thin films are reported. The centrosymmetric MnPtGa films (P63/mmc space group) crystallize with a preferred c-axis (0001) crystal orientation. Along this crystallographic direction, the MnPtGa films exhibit preferential perpendicular magnetic anisotropy, below the Curie temperature TC = 263 K, with a large effective uniaxial magnetic anisotropy Keff = 0.735 MJ m-3, at 150 K. In addition, the MnPtGa system undergoes a thermally induced spin reorientation transition below Tsr = 160 K, which marks the onset of a noncollinear spin-canted state. The anomalous Hall conductivity (AHC) of MnPtGa films exhibits a nonmonotonic behavior as a function of temperature, which changes sign at T* = 110 K. Concurrently with the reported unusual dependence of the AHC on the longitudinal conductivity in MnPtGa crystalline thin films, these findings strongly suggest an anomalous Hall effect of intrinsic origin, driven by a momentum-space Berry curvature mechanism, as supported by first-principle calculations. [ABSTRACT FROM AUTHOR]

Non-Hermitian quantum systems exhibit many novel physical properties of quantum states. We consider a non-Hermtian graphene model based on the tight-binding approximation with the coupling of the graphene and the substrate. We analyze the complex energy structure of this model and its exceptional points as well as relevant topological invariants. We give the analytic complex Berry connection and Berry curvature in the Brillouin zone and investigate numerically the relationships between the complex Berry curvature and the complex energy band structures. We find that the behaviors of the complex Berry curvature depend on the complex energy band structures. The occurrence of the peaks of both real and imaginary parts of the complex Berry curvature corresponds to the exceptional (gapless) points in the Brillouin zone. In particular, the Dirac cone of the imaginary part of the Berry curvature occurs and corresponding to the occurrence of the flat real energy band for the non-Hermitian parameter η = 3 . These results provide some novel insights to the relationship between the non-Hermitian graphene, geometry, and topological invariants. [ABSTRACT FROM AUTHOR]

Topology is now securely established as a means to explore and classify electronic states in crystalline solids. This review provides a gentle but firm introduction to topological electronic band structure suitable for new researchers in the field. I begin by outlining the relevant concepts from topology, then give a summary of the theory of non-interacting electrons in periodic potentials. Next, I explain the concepts of the Berry phase and Berry curvature, and derive key formulae. The remainder of the article deals with how these ideas are applied to classify crystalline solids according to the topology of the electronic states, and the implications for observable properties. Among the topics covered are the role of symmetry in determining band degeneracies in momentum space, the Chern number and Z 2 topological invariants, surface electronic states, two- and three-dimensional topological insulators, and Weyl and Dirac semimetals [ABSTRACT FROM AUTHOR]

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 MR = e/h BΩF, with B being the applied magnetic field and ΩF 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. [ABSTRACT FROM AUTHOR]

2D compounds with nonzero Berry curvature are ideal systems to study exotic and technologically favorable thermoelectric and magnetoelectric properties. Within this class of materials, the topological trivial and nontrivial regimes have to present very different behaviors, which are encoded for the orbital susceptibility and magnetization. To try to reveal them, it is found that it was necessary to introduce a k‐dependent mass term in the relativistic formalism of these materials. Thus, while a topologically trivial insulator is predicted to have a very limited response, in the nontrivial regime, a singular contribution to the orbital magnetic susceptibility, which is inversely proportional to the square of the quantum magnetic flux is unveiled. In this scenario, besides determining the measurement conditions a new route for enhancing the intrinsic orbital magnetism of topological materials widening the range of temperatures and magnetic fields without involving tiny bandgaps is found. [ABSTRACT FROM AUTHOR]

Recently, the magnetic topological insulator (TI) MnBi2Te4 emerged as a competitive platform to realize quantum anomalous Hall (QAH) states. We report a Berry curvature splitting mechanism to realize the QAH effect in the disordered magnetic TI multilayers when switching from an antiferromagnetic order to a ferromagnetic order. We reveal that the splitting of spin-resolved Berry curvature, originating from the separation of the critical points during the magnetic switching, can give rise to a QAH insulator. We present a global phase diagram, and also provide a phenomenological picture to elucidate the Berry curvature splitting mechanism by the evolution of topological charges. At last, we predict that the Berry curvature splitting mechanism will lead to a reentrant QAH effect, which can be detected by tuning the gate voltage. Our theory will be instructive for the studies of the QAH effect in MnBi2Te4 in future experiments. [ABSTRACT FROM AUTHOR]

Within a relativistic quantum formalism we examine the role of second-order corrections caused by the application of magnetic fields in two-dimensional topological and Chern insulators. This allows to reach analytical expressions for the change of the Berry curvature, orbital magnetic moment, density of states and energy determining their canonical grand potential and transport properties. The present corrections, which become relevant at relatively low fields due to the small gap characterizing these systems, determine the zero-field diamagnetic susceptibility of non-zero Berry curvature systems and unveil additional contributions from the magnetic field. Video Abstract: Orbital dynamics in 2D topological and Chern insulators [ABSTRACT FROM AUTHOR]

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−xSnxTe 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The toolbox quantities used for manipulating the flow of light include typically amplitude, phase, and polarization. Pseudospins, such as those arising from valley degrees of freedom in photonic structures, have recently emerged as an excellent candidate for this toolbox, in parallel with rapid development of spintronics and valleytronics in condensed‐matter physics. Here, by employing symmetry‐broken honeycomb photonic lattices, valley‐dependent wavepacket self‐rotation manifested in spiraling intensity patterns is demonstrated, which occurs without any initial orbital angular momentum. Theoretically, it is shown that such wavepacket self‐rotation is induced by the Berry phase and results in Zitterbewegung oscillations. The frequency of Zitterbewegung is proportional to the gap size, while the helicity of self‐rotation is valley‐dependent, i.e., correlated with the Berry curvature. These results lead to new understanding of the venerable Zitterbewegung phenomenon from the perspective of topology and are readily applicable on other platforms such as 2D Dirac materials and ultracold atoms. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Geometrical phases, such as the Berry phase, have proven to be powerful concepts to understand numerous physical phenomena, from the precession of the Foucault pendulum to the quantum Hall effect and the existence of topological insulators. The Berry phase is generated by a quantity named the Berry curvature, which describes the local geometry of wave polarization relations and is known to appear in the equations of motion of multi-component wave packets. Such a geometrical contribution in ray propagation of vectorial fields has been observed in condensed matter, optics and cold atom physics. Here, we use a variational method with a vectorial Wentzel–Kramers–Brillouin ansatz to derive ray- tracing equations for geophysical waves and to reveal the contribution of the Berry curvature. We detail the case of shallow-water wave packets and propose a new interpretation of their oscillating motion around the equator. Our result shows a mismatch with the textbook scalar approach for ray tracing, by predicting a larger eastward velocity for Poincaré wave packets. This work enlightens the role of the geometry of wave polarization in various geophysical and astrophysical fluid waves, beyond the shallow-water model. [ABSTRACT FROM AUTHOR]

Geometrical phases, such as the Berry phase, have proven to be powerful concepts to understand numerous physical phenomena, from the precession of the Foucault pendulum to the quantum Hall effect and the existence of topological insulators. The Berry phase is generated by a quantity named the Berry curvature, which describes the local geometry of wave polarization relations and is known to appear in the equations of motion of multi-component wave packets. Such a geometrical contribution in ray propagation of vectorial fields has been observed in condensed matter, optics and cold atom physics. Here, we use a variational method with a vectorial Wentzel–Kramers–Brillouin ansatz to derive ray- tracing equations for geophysical waves and to reveal the contribution of the Berry curvature. We detail the case of shallow-water wave packets and propose a new interpretation of their oscillating motion around the equator. Our result shows a mismatch with the textbook scalar approach for ray tracing, by predicting a larger eastward velocity for Poincaré wave packets. This work enlightens the role of the geometry of wave polarization in various geophysical and astrophysical fluid waves, beyond the shallow-water model. [ABSTRACT FROM AUTHOR]

Based on the semiclassical description of the dynamics of electrons in topological media, the gyrotropic properties of which are determined by a nonzero Berry curvature, a phenomenological model is proposed that allows one to consider some nonlinear optical processes—the generation of the third harmonic and the intensity dependent rotation of the wave polarization vector. The third-order nonlinear susceptibilities are determined, which determine the interaction of waves with allowance for the rotation of their polarization vector. Gyrotropy manifests itself in the dependence of the efficiency of conversion to the harmonic on the circular polarization of radiation, which can be used to measure the parameters of these media. [ABSTRACT FROM AUTHOR]

Berry phase and Berry curvature play a key role in the development of topology in physics and do contribute to the transport properties in solid state systems. In this paper, we report the finding of novel nonzero Hall effect in topological material ZrTe5 flakes when the in-plane magnetic field is parallel and perpendicular to the current. Surprisingly, both symmetric and antisymmetric components with respect to magnetic field are detected in the in-plane Hall resistivity. Further theoretical analysis suggests that the magnetotransport properties originate from the anomalous velocity induced by Berry curvature in a tilted Weyl semimetal. Our work not only enriches the Hall family but also provides new insights into the Berry phase effect in topological materials. [ABSTRACT FROM AUTHOR]

The Drude–Lorentz model, which makes it possible to describe a nonlinear response of a dielectric or conducting medium, can be suited for the description of nonlinear nonresonant responses of some exotic media: topological insulators, a Weil semimetal, or a Dirac metal. A generalized Drude–Lorentz model and its simplified version, in which topological effects are taken into account to a minimum extent, are presented. As an example of application of the simplified model, the second-order nonlinear conductivity is derived, which is responsible for the second harmonic generation and the effect of optical rectification. It is shown that the ratio of the topological conductivity to the ordinary linear conductivity contains constants that are proportional to the fine structure constant and the axion field gradient. [ABSTRACT FROM AUTHOR]

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 cellaveraged 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. [ABSTRACT FROM AUTHOR]

The connection between topology and nonreciprocity in photonic systems is reviewed. Topological properties such as Chern number, and momentum-space properties such as Berry phase and Berry connection, are used to explain backscattering immune edge states and their topological protection. We consider several examples to illustrate the role of momentum-space topology on wave propagation, and discuss recent magnet-less approaches. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The neutrino asymmetry in the early universe plasma, , is calculated both before and after the electroweak phase transition (EWPT). In the Standard Model, before EWPT, the leptogenesis is well known to be driven by the abelian anomaly in a massless hypercharge field. The generation of the neutrino asymmetry in the Higgs phase after EWPT, in its turn, has not been considered previously because of the absence of any quantum anomaly in an external electromagnetic field for such electroneutral particles as neutrino, unlike the Adler-Bell-Jackiw anomaly for charged left and right polarized massless electrons in the same electromagnetic field. Using the neutrino Boltzmann equation, modified by the Berry curvature term in the momentum space, we establish the violation of the macroscopic neutrino current in plasma after EWPT and exactly reproduce the nonconservation of the lepton current in the symmetric phase before EWPT arising in quantum field theory due to the nonzero lepton hypercharge and corresponding triangle anomaly in an external hypercharge field. In the last case, the nonconservation of the lepton current is derived through the kinetic approach without a computation of corresponding Feynman diagrams. Then, the new kinetic equation is applied for the calculation of the neutrino asymmetry accounting for the Berry curvature and the electroweak interaction with background fermions in the Higgs phase. Such an interaction generates a neutrino asymmetry through the electroweak coupling of neutrino currents with electromagnetic fields in plasma, which is . It turns out that this effect is especially efficient for maximally helical magnetic fields. [ABSTRACT FROM AUTHOR]

Emergence of high pseudo‐magnetic field as a result of mechanical deformations is one of the intriguing characteristics of the graphene honeycomb structure. For a time‐dependent nonuniform strain and in the context of Berry curvature approach, the topological charge pumping is studied theoretically. Calculations have been performed in time–momentum parametric space. Within the Berry curvature approach, it has been revealed that time‐dependent deformations result in nonzero valley‐dependent charge pumping in the gapped graphene when there is a population imbalance between the valleys. This indicates that the valley polarization can be measured by the amount of topological charge pumping in the system. Results also show that the strain can remove the valley degeneracy at nonzero Fermi energies. Therefore, population imbalance or valley polarization can be realized as a result of the external strain. Strain has been considered as gauge field that couples oppositely with two valleys of the Brillouin zone. [ABSTRACT FROM AUTHOR]

As novel topological phases in correlated electron systems, we have found two examples of non-ferromagnetic states that exhibit a large anomalous Hall effect. One is the chiral spin liquid compound, which exhibits a spontaneous Hall effect in a spin liquid state due to spin ice correlation. The other is the chiral antiferromagnetsandthat exhibit a large anomalous Hall effect at room temperature. The latter shows a sign change of the anomalous Hall effect by a small change in the magnetic field by a few 100 G, which should be useful for various applications. We will discuss that the magnetic Weyl metal states are the origin for such a large anomalous Hall effect observed in both the spin liquid and antiferromagnet that possess almost no magnetisation. [ABSTRACT FROM PUBLISHER]

We describe a method for measuring the Berry curvature from the wave-packet dynamics in perturbed arrays of evanescently coupled optical waveguides with honeycomb lattice structure. To disentangle the effects of the Berry curvature and the energy dispersion we utilize a difference measurement by propagating the wave packet under the influence of a constant external force back and forth. In this way a non-vanishing Berry curvature is obtained for photonic graphene with small sublattice bias or strain, where the relative error between the exact Berry curvature and the one derived from the semiclassical dynamics is negligible. For the strained lattice we demonstrate the robustness of the Berry curvature texture over the Brillouin zone compared to the energy dispersion. We also comment on the experimental realization of the proposed Berry curvature mapping in photonics. [ABSTRACT FROM AUTHOR]

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We propose an experimental scheme to simulate the many-body dynamical quantum Hall effect with ultra-cold bosonic atoms in a one-dimensional optical lattice. We first show that the required model Hamiltonian of a spin-1/2 Heisenberg chain with an effective magnetic field and tunable parameters can be realized in this system. For dynamical response to ramping the external fields, the quantized plateaus emerge in the Berry curvature of the interacting atomic spin chain as a function of the effective spin-exchange interaction. The quantization of this response in the parameter space with the interaction-induced topological transition characterizes the many-body dynamical quantum Hall effect. Furthermore, we demonstrate that this phenomenon can be observed in practical cold atom experiments with numerical simulations. [ABSTRACT FROM AUTHOR]

Plasmons, the collective oscillations of interacting electrons, possess emergent properties that dramatically alter the optical response of metals. We predict the existence of a new class of plasmons--chiral Berry plasmons (CBPs)--for a wide range of 2D metallic systems including gapped Dirac materials. As we show, in these materials the interplay between Berry curvature and electron- electron interactions yields chiral plasmonic modes at zero magnetic field. The CBP modes are confined to system boundaries, even in the absence of topological edge states, with chirality manifested in split energy dispersions for oppositely directed plasmon waves. We unveil a rich CBP phenomenology and propose setups for realizing them, including in anomalous Hall metals and optically pumped 2D Dirac materials. Realization of CBPs will offer a powerful paradigm for magnetic field-free, subwavelength optical nonreciprocity, in the mid-IR to terahertz range, with tunable splittings as large as tens of THz, as well as sensitive all-optical diagnostics of topological bands. [ABSTRACT FROM AUTHOR]