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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]

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]

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

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

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

The 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]

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

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

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]

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 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]

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

We propose a valley-dependent electromotive force in a graphene device based on a deformed graphene in the presence of magnetic field. The coexistence of the strain and magnetic field in the presented mechanism leads to a valley dependent electromotive force in zero Fermi energy. In the non-zero Fermi energies strain alone could induce a valley dependent electromotive force while the magnetic field alone could not induce any electromotive force in zero and any level of Fermi energy. The calculations are based on the Berry curvature approaches. [ABSTRACT FROM AUTHOR]

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

Carrier dynamics acquire a new character in the presence of Bloch-band Berry curvature, which naturally arises in gapped Dirac materials (GDMs). Here, we argue that photoresponse in GDMs with small band gaps is dramatically enhanced by Berry curvature. This manifests in a giant and saturable Hall photoconductivity when illuminated by circularly polarized light. Unlike Hall motion arising from a Lorentz force in a magnetic field, which impedes longitudinal carrier motion, Hall photoconductivity arising from Berry curvature can boost longitudinal carrier transport. In GDMs, this results in a helicity-dependent photoresponse in the Hall regime, where photoconductivity is dominated by its Hall component. We find that the induced Hall conductivity per incident irradiance is enhanced by up to 6 orders of magnitude when moving from the visible regime (with corresponding band gaps) to the far infrared. These results suggest that narrow-gap GDMs are an ideal test-bed for the unique physics that arise in the presence of Berry curvature and open a new avenue for infrared and terahertz optoelectronics. [ABSTRACT FROM AUTHOR]

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

Geometric phases in quantum mechanics play an extraordinary role in broadening our understanding of fundamental significance of geometry in nature. One of the best known examples is the Berry phase [M.V. Berry (1984), Proc. Royal. Soc. London A, 392:45], which naturally emerges in quantum adiabatic evolution. So far the applicability and measurements of the Berry phase were mostly limited to systems of weakly interacting quasi-particles, where interference experiments are feasible. Here we show how one can go beyond this limitation and observe the Berry curvature, and hence the Berry phase, in generic systems as a nonadiabatic response of physical observables to the rate of change of an external parameter. These results can be interpreted as a dynamical quantum Hall effect in a parameter space. The conventional quantum Hall effect is a particular example of the general relation if one views the electric field as a rate of change of the vector potential. We illustrate our findings by analyzing the response of interacting spin chains to a rotating magnetic field. We observe the quantization of this response, which we term the rotational quantum Hall effect. [ABSTRACT FROM AUTHOR]

Abstract: We present a theoretical description of local spin dynamics in magnetic systems with a chiral spin texture and finite spin–orbit coupling (SOC). Spin precession about the relativistic effective magnetic field in a SOC system gives rise to a non-Abelian SU(2) gauge field reminiscent of the Yang–Mills field. In addition, the adiabatic relaxation of electron spin along the local spin yields an U(1)⊗U(1) topological gauge (Berry) field. We derive the corresponding equation of motion i.e. modified Landau–Lifshitz–Gilbert (LLG) equation, for the local spin under the influence of these effects. Focusing on the SU(2) gauge, we obtain the spin torque magnitude, and the amplitude and frequency of spin oscillations in this system. Our theoretical estimates indicate significant spin torque and oscillations in systems with large spin–orbit coupling, which may be utilized in technological applications such as current-induced magnetization-switching and tunable microwave oscillators. [Copyright &y& Elsevier]

Abstract: A unified theoretical treatment is presented to describe the physics of electron dynamics in semiconductor and graphene systems. Electron spin''s fast alignment with the Zeeman magnetic field (physical or effective) is treated as a form of adiabatic spin evolution which necessarily generates a monopole in magnetic space. One could transform this monopole into the physical and intuitive topological magnetic fields in the useful momentum (K) or real spaces (R). The physics of electron dynamics related to spin Hall, torque, oscillations and other technologically useful spinor effects can be inferred from the topological magnetic fields in spintronic, graphene and other SU(2) systems. [Copyright &y& Elsevier]