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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]

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]

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]

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]

Abstract 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.

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]

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]

Abstract 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.

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 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 The quantum geometric Berry curvature results in an anomalous correction to the band velocity of crystal electrons with a corresponding transverse (thermo)electric conductivity. However, time‐reversal symmetry typically constrains the direct observation and exploitation of anomalous transport to magnetic compounds. Here, it is demonstrated the anomalous Hall and Nernst conductivities are essential for describing the optoelectronic transport in thin films of the non‐magnetic, weakly gapped semimetal HfTe5 subject to an external magnetic field. A focused photoexcitation adresses the symmetries of the local Nernst conductivity, which unveils a hitherto hidden, anomalous photo‐Nernst effect of three‐dimensional (3D) massive Dirac fermions. The experimental temperature and density dependencies are compared with a semiclassical Boltzmann transport model. For HfTe5 thin films with the Fermi level close to the gap, the model suggests that the anomalous photo‐Nernst currents originate from an intrinsic Berry curvature mechanism, where the Zeeman interaction effectively breaks time‐reversal symmetry of the massive Dirac fermions already at moderate external magnetic fields.

Abstract 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 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.

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]

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]

Abstract 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 $$\eta =3$$ η = 3 . These results provide some novel insights to the relationship between the non-Hermitian graphene, geometry, and topological invariants.

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]

We construct a two-dimensional mechanical wave machine based on a hexagonal lattice to investigate low-frequency flexural plate waves whose propagation mimicks a topological quantum valley Hall system. We thereby demonstrate “mechanical graphene” by extension of the one-dimensional Shive wave machine to two dimensions. Imaging experiments, backed up by simulations, reveal the presence of boundary modes along a topological interface. This work provides an alternative route for the investigation of topological phononic crystals, and should lead to new insights into the design and observation of artificial phononic structures.

Computational modules were developed to numerically determine electronic band structures, berry curvatures, Chern numbers, localization lengths, and critical exponents for tight- binding and related models. These modules were applied to a variety tight-binding and related models including the Hofstadter Model, Anderson Model, and the Chalker- Coddington model. When analytic solutions were available, numeric energy bands agreed with analytic solutions to within machine precision. In addition Chern numbers for well known models were reproduced, and localization lengths and critical exponents agreed with values in the literature.

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]

The ferromagnetic materials with large anomalous Hall effect have attracted numerous interests due to their excellent physical properties and wide application in spintronic devices. Here, we report the magnetic and electrical transport properties of MnGaGe single crystal grown by Ga flux method. Easy-axis ferromagnetic ordering and large magnetocrystalline anisotropy are observed below Curie temperature T C = 459 K in MnGaGe single crystal. The positive magnetoresistance is observed at low temperature and becomes negative above 60 K. The magnetoresistance presents nearly linear behavior without any sign of saturation with the applied magnetic field up to 5 T. The anomalous Hall effect of MnGaGe is mainly contributed from the extrinsic mechanism. Moreover, we find that the phonon-induced skew scattering plays an important role in this system and increases with increasing temperature. The high transition temperature, large anisotropic out-of-plane magnetism, and remarkable anomalous Hall effect render MnGaGe potential material for spintronic devices. • The easy-axis ferromagnetic order is observed in MnGaGe single crystal. • The unsaturated magnetoresistance with nearly linear behavior is observed. • The large anomalous Hall effect dominated by the extrinsic mechanism is obtained. [ABSTRACT FROM AUTHOR]

Abstract 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.

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]

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]

Covalent 2D magnets such as Cr 2 Te 3 , which feature self-intercalated magnetic cations located between monolayers of transition-metal dichalcogenide material, offer a unique platform for controlling magnetic order and spin texture, enabling new potential applications for spintronic devices. Here, it is demonstrated that the unconventional anomalous Hall effect (AHE) in Cr 2 Te 3 , characterized by additional humps and dips near the coercive field in AHE hysteresis, originates from an intrinsic mechanism dictated by the self-intercalation. This mechanism is distinctly different from previously proposed mechanisms such as topological Hall effect, or two-channel AHE arising from spatial inhomogeneities. Crucially, multiple Weyl-like nodes emerge in the electronic band structure due to strong spin-orbit coupling, whose positions relative to the Fermi level is sensitively modulated by the canting angles of the self-intercalated Cr cations. These nodes contribute strongly to the Berry curvature and AHE conductivity. This component competes with the contribution from bands that are less affected by the self-intercalation, resulting in a sign change in AHE with temperature and the emergence of additional humps and dips. The findings provide compelling evidence for the intrinsic origin of the unconventional AHE in Cr 2 Te 3  and further establish self-intercalation as a control knob for engineering AHE in complex magnets., (© 2024 The Author(s). Advanced Science published by Wiley‐VCH GmbH.)

Abstract Materials hosting noncollinear magnetic ordering and sizeable spin‐orbit coupling can manifest perpendicular magnetic anisotropy and a Berry curvature‐driven 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.

From the recent empirical discovery of the quantum anomalous Hall effect (QAHE), the interaction of the particle with spin–orbit coupling (SOC) plays an essential role in the cause of the QAHE, which includes three terms: external, internal, and chiral symmetric terms. Then, the non-Abelian quantum field theory was adopted to analyze and prove the conjecture on the causes that can lead to the fractional quantum Hall effect (FQHE). The spontaneously topological chiral symmetry breaking is the main contribution to the FQHE, which also includes two terms: the hopping of sublattice and Coulomb energy by the interaction of many-body particles. More generally, this exciton possesses an intermediate characteristic between the Wannier regimes and displays a peculiar two-dimensional wavefunction in the three-dimensional FQHE states. Finally, a bilayer three-dimensional model is proposed to implement the FQHE on the lattice by incorporating ferromagnetic dopants into three-dimensional topological insulative thin films. This study theoretically predicts the FQHE on the basis of other reports that have experimentally verified the rationality of the proposed model in magnetic topological insulators.

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.

Understanding the transport behavior of an electronic system under the influence of a magnetic field remains a key subject in condensed matter physics. Particularly in topological materials, their nonvanishing Berry curvature can lead to many interesting phenomena in magnetotransport owing to the coupling between the magnetic field and Berry curvature. By fully incorporating both the field-driven anisotropy and inherent anisotropy in the band dispersion, we study the semiclassical Boltzmann magnetotransport theory in topological materials with a nonvanishing Berry curvature. We show that as a solution to the Boltzmann transport equation the effective mean-free-path vector is given by the integral equation, including the effective velocity arising from the coupling between the magnetic field, Berry curvature and mobility. We also calculate the conductivity of Weyl semimetals with an isotropic energy dispersion, and find that the coupling between the magnetic field and Berry curvature induces anisotropy in the relaxation time, showing a substantial deviation from the result obtained assuming a constant relaxation time.

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]

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 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]

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]

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]

In transition metal dichalcogenides (TMDCs), charge carriers have spin, pseudospin, and valley degrees of freedom associated with magnetic moments. The monolayers and bilayers of the TMDCs, in particular, MoS2, lead to strong couplings between the spin and pseudospin effects. This feature has drawn attention to TMDCs for their potential use in advanced tech devices. Meanwhile, high-order harmonic generation (HHG) has recently been applied to the characterization of the electronic structure of solids, such as energy dispersion, Berry-curvature, and topological properties. Here, we show theoretical results obtained with the ‘philosophy’ of using HHG to investigate the structural effects of the monolayer and bilayers of MoS2 on nonlinear optical emission. We use a simple model for MoS2 in the 3R AB staking. We find that the pseudospin and valley indexes (the Berry curvature and the dipole transition matrix element) in TMDC driven by a circularly polarized laser (CPL) can encode in the high-energy photon emissions. This theoretical investigation is expected to pave the way for the ultrafast manipulation of valleytronics and lead to new questions concerning the spin-obit-coupling (SOC) effects on TMDC materials, Weyl Semimetals, and topological phases and transitions in topological insulators.

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]

Janus transition metal dichalcogenides, with intrinsic mirror asymmetry, exhibit a wide array of interesting properties. In this work, we study Janus monolayers derived from WTe _2 using first-principles and tight-binding calculations. We discover that WSeTe and WSTe are topologically trivial, in contrast to the parent quantum spin Hall insulator WTe _2 . Motivated by the growing interest in non-linear Hall effect, which also requires asymmetric structures, we investigate the Berry curvature and its dipole in these Janus systems and find that they exhibit strikingly large values of Berry curvature dipole, despite being in the topologically trivial phase. We track down the origin of this behaviour and put forth a low-energy massive Dirac model to understand the central features of our ab inito computations. Our predictions introduce Janus monolayers as promising new platforms for exploring as well as engineering non-linear Hall effect.

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.

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 rare-earth based magnetic kagome materials RMn 6 Sn 6 have attracted tremendous interest for their potential to host exotic topological quantum states. Here, we report the observation of the anomalous Hall effect in the kagome ferromagnet YbMn 6 Sn 6 single crystal. YbMn 6 Sn 6 has an easy-plane ferromagnetic structure till 2 K without magnetic ordering of the R ions. The low-temperature magnetoresistance is positive and does not exhibit a tendency to saturate up to 5 T. The magnetoresistance becomes negative with the increasing temperature. An intrinsic anomalous Hall conductivity with the value of 40.2 Ω−1·cm−1 is obtained in YbMn 6 Sn 6 , which is associated with the Berry curvature of electronic band structure in momentum space. Our results indicate that YbMn 6 Sn 6 may be an excellent platform to study the relationship between the magnetic and electronic structure and to explore novel quantum phenomenon. • The magnetic and transport properties of YbMn 6 Sn 6 single crystal have been investigated systematically. • Both positive and negative MR is observed in YbMn 6 Sn 6. • The intrinsic AHC deriving from Mn-based kagome lattice is comparable with that for DyMn 6 Sn 6. [ABSTRACT FROM AUTHOR]

Based on the numerical solution of the Quantum Lattice Boltzmann Method in curved space, we predicted the onset of a quantized alternating current on curved graphene sheets. This numerical prediction was verified analytically via a set of semi-classical equations that related the Berry curvature to real space curvature. The proposed quantized oscillating current on curved graphene could form the basis for the implementation of quantum information-processing algorithms.

Non-trivial Bloch band overlaps endow rich phenomena to a wide variety of quantum materials. The most prominent example is a transverse current in the absence of a magnetic field (i.e. the anomalous Hall effect). Here we show that, in addition to a dc Hall effect, anomalous Hall materials possess circulating currents and cyclotron motion without magnetic field. These are generated from the intricate wavefunction dynamics within the unit cell. Curiously, anomalous cyclotron motion exhibits an intrinsic decay in time (even in pristine materials) displaying a characteristic power law decay. This reveals an intrinsic dephasing similar to that of inhomogeneous broadening of spins. Circulating currents can manifest as the emission of circularly polarized light pulses in response to an incident linearly polarized (pulsed) electric field, and provide a direct means of interrogating a type of Zitterbewegung of quantum materials with broken time reversal symmetry.