Search

This report reviews recent progress in computing Kubo formulas for general interacting Hamiltonians. The aim is to calculate electric and thermal magneto-conductivities in strong scattering regimes where Boltzmann equation and Hall conductivity proxies exceed their validity. Three primary approaches are explained. 1. Degeneracy-projected polarization formulas for Hall-type conductivities, which substantially reduce the number of calculated current matrix elements. These expressions generalize the Berry curvature integral formulas to imperfect lattices. 2. Continued fraction representation of dynamical longitudinal conductivities. The calculations produce a set of thermodynamic averages, which can be controllably extrapolated using their mathematical relations to low and high frequency conductivity asymptotics. 3. Hall-type coefficients summation formulas, which are constructed from thermodynamic averages. The thermodynamic formulas are derived in the operator Hilbert space formalism, which avoids the opacity and high computational cost of the Hamiltonian eigenspectrum. The coefficients can be obtained by well established imaginary-time Monte Carlo sampling, high temperature expansion, traces of operator products, and variational wavefunctions at low temperatures. We demonstrate the power of approaches 1–3 by their application to well known models of lattice electrons and bosons. The calculations clarify the far-reaching influence of strong local interactions on the metallic transport near Mott insulators. Future directions for these approaches are discussed. [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]

In the recent years, the thermal Hall transport has risen as an important diagnosis of the physical properties of the elementary excitations in various quantum materials, especially among the Mott insulating systems where the electronic transports are often featureless. Here we review the recent development of thermal Hall effects in quantum magnets where all the relevant excitations are charge-neutral. In addition to summarizing the existing experiments, we pay a special attention to the underlying mechanisms of the thermal Hall effects in various magnetic systems, and clarify the connection between the microscopic physical variables and the emergent degrees of freedom in different quantum phases. The external magnetic field is shown to modify the intrinsic Berry curvature properties of various emergent and/or exotic quasiparticle excitations in distinct fashions for different quantum systems and quantum phases, contributing to the thermal Hall transports. These include, for example, the conventional ones like the magnons in ordered magnets, the triplons in dimerized magnets, the exotic and fractionalized quasiparticles such as the spinons and the magnetic monopoles in quantum spin liquids. We review their contribution and discuss their presence in the thermal Hall conductivity in different physical contexts. We expect this review to provide a useful guidance for the physical mechanism of the thermal Hall transports in quantum magnets. [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]

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.

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]

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]

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]

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]

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]

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]

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]

Pseudospin, a degree of freedom in a two-level quantum system of two sublattices, is a basic quantum number that poses a fundamental symmetry prone to the electronic nature of graphene. We propose an extended Hamiltonian that involves the SU(2) rotation of the pseudospin for electron-phonon scattering, which has a significant advantage over the conventional second-quantized polar coupling. A phonon satellite accompanied by an electron linearly pumped to the upper Dirac cone corresponds to a rotated pseudospin within a scheme of the time-resolved photoemission spectroscopy (TRPES), which is found to carry nonzero angular momenta and induce nonvanishing Berry curvatures through the dichroic mode of TRPES. A phonon bringing the pseudospin rotation is identified to be an elliptically polarized one, which compensates for the angular momenta delivered to the pseudospin. This is an indication of the chiral phonon excitation without the circularly polarized pulse pumping. Our findings suggest that the controlled generation of phonon builds up a new roadmap for engineering the Berry curvature and topology in Dirac semiconductors. [Display omitted] [ABSTRACT FROM AUTHOR]

This study aimed to explore the electronic and topological properties of nanoribbons as a highly applicable nano-scale material. By using the first principle calculations of density functional theory (DFT), we examined the electronic properties with and without spin-polarization for Sulfur (-S) and Bismuth (Bi) terminated of short stanene nanoribbons (SStNRs) which have armchair edges along the zigzag configuration of nanoribbons. Spin-orbit coupling (SOC), vertical electrical fields and percentages of strain were used to study different electronic parameters on the short nanoribbon systems. In addition, topological properties (Berry curvature, chern number and Z2 invariant) were obtained to investigate the edge and bulk states of the nanoribbons. Edge states were studied by band theory by the conduction band minimum (CBM), valence band maximum (VBM) and frontier molecular orbital theory using the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). Investigation of spin-dependence for S-SStNR showed that there was no spin-dependence for S-SStNR while by presence of SOC, spin-dependence was observed in distribution of HOMO-LUMO orbitals. • Exploring the electronic and topological properties of –S/-Bi stanene nanoribbons by DFT aprroach. • Direct band gap in S-stanene nanoribbons and direct and indirect band gaps in -Bi stanene nanoribbons. • Observing even edge states in –S/-Bi stanene nanoribbons. • Obtaining Berry curvatures (trivial) and Chern number (Cn = 0) and Z2 = 0 for –S/-Bi stanene nanoribbons. • Spin-dependence in the presence of SOC for S- stanene nanoribbons. [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.

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]

The irradiation of topological insulator surface with elliptically polarized light modifies the topological properties in a phase-dependent manner impacting the Floquet Chern number which is a crucial topological invariant associated with such driven systems. Employing Floquet theory in presence of hexagonal warping term in the Dirac fermion Hamiltonian under off-resonant conditions, we derive an effective Hamiltonian that highlights distinct features in the Floquet-Dirac surface states. Specifically, we identify a helicity and ellipticity-dependent mass term in the quasi-static Hamiltonian, breaking time reversal symmetry. This mass term changes sign with variations in the helicity and ellipticity of incident radiation, potentially driving the system into trivial or Floquet-Chern topological insulating phases. We calculate the Berry curvature associated with the bandstructure and the resulting anomalous Hall conductivity, finding a strong dependence on the ellipticity and amplitude of the radiation., (© 2024 IOP Publishing Ltd. All rights, including for text and data mining, AI training, and similar technologies, are reserved.)

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.

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]

Kagome lattice, made of corner-sharing triangles, provides an excellent platform for hosting exotic topological quantum phases. Here, we report the observation of large anomalous Hall effect and topological Hall effect in the Kagome lattice material Yb 0.90 Mn 6 Ge 3.25 Ga 0.39 single crystal. Compared to the antiferromagnetic pristine compound YbMn 6 Ge 6 , Yb 0.90 Mn 6 Ge 3.25 Ga 0.39 has an easy plane ferromagnetic structure below 361 K and presents a spin-reorientation transition at 218 K. An intrinsic anomalous Hall conductivity with the value of 604.2 Ω-1·cm-1 is obtained in Yb 0.90 Mn 6 Ge 3.25 Ga 0.39 , which is the largest in RMn 6 X 6 (X = Ge and Sn) family. Besides, a remarkable topological Hall signal is also observed near room temperature. The topological Hall resistivity of Yb 0.90 Mn 6 Ge 3.25 Ga 0.39 is determined to be -1.86 μΩ·cm at 280 K under μ 0 H = 0.3 T. Our results indicate that Yb 0.90 Mn 6 Ge 3.25 Ga 0.39 may be an excellent platform to study the relationship between the magnetic and electronic structure and to explore novel quantum phenomenon. [Display omitted] [ABSTRACT FROM AUTHOR]

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.

In this paper, we study the intrinsic contribution of nonlinear magnon thermal Hall Effect. We derive the intrinsic second-order thermal Hall conductivity of magnon by the thermal scalar potential method and the thermal vector potential method. We find that the intrinsic second-order magnon thermal Hall conductivity is related to the thermal Berry-connection polarizability. We apply our theory to the monolayer ferromagnetic Hexagonal lattice, and we find that the second-order magnon thermal Hall conductivity can be controlled by changing Dzyaloshinskii-Moriya strength and applying strain., (© 2024 IOP Publishing Ltd.)