Large Berry Curvature Research Articles

Non-classical high harmonic generation in graphene driven by linearly-polarized laser pulses.

Recent studies in high-order harmonic generation (HHG) in solid targets reveal new scenarios of extraordinary rich electronic dynamics, in comparison to the atomic and molecular cases. For the later, the main aspects of the process can be described semiclassically in terms of electrons that recombine when the trajectories revisit the parent ion. HHG in solids has been described by an analogous mechanism, in this case involving electron-hole pair recombinations. However, it has been recently reported that a substantial part of the HHG emission corresponds to situations where the electron and hole trajectories do not overlap in space. According to the present knowledge, HHG from this imperfect recollisions reflects the quantum nature of the process, arising in systems with large Berry curvatures or for elliptically polarized driving fields. In this work, we demonstrate that imperfect recollisions are also relevant in the more general case. We show the signature of such recollisions in the HHG spectrum from monolayer graphene -a system with null Berry curvature- irradiated by linearly polarized driving fields. Our calculations also reveal that imperfect multiple-order recollisions contribute to the harmonic emission when electron-hole excursion times exceed one cycle of the driving field. We believe that our work adds a substantial contribution to the full understanding of the sub-femtosecond dynamics of HHG in solid systems.

Janus VXY monolayers with tunable large Berry curvature

Abstract The Rashba effect and valley polarization provide a novel paradigm in quantum information technology. However, practical materials are scarce. Here, we found a new class of Janus monolayers VXY (X = Cl, Br, I; Y = Se, Te) with excellent valley polarization effect. In particular, Janus VBrSe shows Zeeman type spin splitting of 14 meV, large Berry curvature of 182.73 bohr2, and, at the same time, a large Rashba parameter of 176.89 meV·Å. We use the k·p theory to analyze the relationship between the lattice constant and the curvature of the Berry. The Berry curvature can be adjusted by changing the lattice parameter, which will greatly improve the transverse velocities of carriers and promote the efficiency of the valley Hall device. By applying biaxial strain onto VBrSe, we can see that there is a correlation between Berry curvature and lattice constant, which further validates the above theory. All these results provide tantalizing opportunities for efficient spintronics and valleytronics.

Anomalous transport properties of the antiferromagnetic Weyl semimetals Mn3 X (X = Sn, Ge)

Noncollinear antiferromagnets Mn3 X (X = Sn, Ge) are characterized by a large anomalous Hall effect originating from a large Berry curvature despite a vanishingly small magnetization. From recent first-principle theories, the large Berry curvature is predicted to be induced by a existence of Weyl nodes broken time-reversal symmetry. The large anomalous Nernst effect is also contributed by the magnetic Weyl state around the Fermi level EF, and likely shares its origin with the anomalous Hall effect. The thermoelectric transport S(T) and thermomagnetic transport Sji(T) are thus investigated in single crystals of Mn3 X. Here, Mn3 X exhibits a large anomalous Nernst effect; in particular, the signal magnitude of Mn3Ge exceeds 1μV/K, which is 1.5 times that of Mn3Sn. The Weyl properties are discussed by analyzing the thermal conductivity, specific heat, and Seebeck and Nernst effects. We also evaluate the zero-field Nernst-driven thermoelectric figure of merit for device applications in the antiferromagnets Mn3 X.

Ab initio study on the possible magnetic topological semimetallic state in MnMg2O4

We study the electronic state of an inverse spinel compound MnMg2O4 based on first-principles calculations. The high-spin state is realized in Mn ions on the diamond lattice, resulting in that this material is found to be a half-metallic semimetal with the minority spin-gap about 3eV, and also with line nodes in the Brillouin zone. The intrinsic anomalous Hall conductivity (AHC) is also computed as a function of the chemical potential of the system assuming the rigid band structure, and is found to exhibit a peak structure with a maximum value of 200 S/cm at only 15 meV above the Fermi level. The relation between the large AHC and Berry curvature in the Brillouin zone is also discussed.

Lattice dynamics with molecular Berry curvature: Chiral optical phonons

Under the Born-Oppenheimer approximation, the electronic ground state evolves adiabatically and can accumulate geometrical phases characterized by the molecular Berry curvature. In this work, we study the effect of the molecular Berry curvature on the lattice dynamics in a system with broken time-reversal symmetry. The molecular Berry curvature is formulated based on the single-particle electronic Bloch states. It manifests as a nonlocal effective magnetic field in the equations of motion of the ions that are beyond the widely adopted Raman spin-lattice coupling model. We employ the Bogoliubov transformation to solve the quantized equations of motion and to obtain phonon polarization vectors. We apply our formula to the Haldane model on a honeycomb lattice and find a large molecular Berry curvature around the Brillouin zone center. As a result, the degeneracy of the optical branches at this point is lifted intrinsically. The lifted optical phonons show circular polarizations, possess large phonon Berry curvature, and have a nearly quantized angular momentum that modifies the Einstein-de Haas effect.

The flow of the Berry curvature vector field

The concept of Berry phase and Berry curvature has become ubiquitous in solid state physics as it relates to variety of phenomena, such as topological insulators, polarization, and various Hall effects. It is well known that large Berry curvatures arise from close proximity of hybridizing bands, however, the vectorial nature of the Berry curvature is not utilized in current research. On bulk bcc Fe, we demonstrate the flow of the Berry curvature vector field which features not only monopoles but also higher dimensional structures with its own topological features. They can provide a novel unique view on the electronic structure in all three dimensions. This knowledge is also used to quantify particular contributions to the intrinsic anomalous Hall effect in a simple analytical form.

Low-symmetry topological materials for large charge-to-spin interconversion: The case of transition metal dichalcogenide monolayers

The spin polarization induced by the spin Hall effect (SHE) in thin films typically points out of the plane. This is rooted on the specific symmetries of traditionally studied systems, not in a fundamental constraint. Recently, experiments on few-layer ${\rm MoTe}_2$ and ${\rm WTe}_2$ showed that the reduced symmetry of these strong spin-orbit coupling materials enables a new form of {\it canted} spin Hall effect, characterized by concurrent in-plane and out-of-plane spin polarizations. Here, through quantum transport calculations on realistic device geometries, including disorder, we predict a very large gate-tunable SHE figure of merit $\lambda_s\theta_{xy}\sim 1\text{--}50$ nm in ${\rm MoTe}_2$ and ${\rm WTe}_2$ monolayers that significantly exceeds values of conventional SHE materials. This stems from a concurrent long spin diffusion length ($\lambda_s$) and charge-to-spin interconversion efficiency as large as $\theta_{xy} \approx 80$\%, originating from momentum-invariant (persistent) spin textures together with large spin Berry curvature along the Fermi contour, respectively. Generalization to other materials and specific guidelines for unambiguous experimental confirmation are proposed, paving the way towards exploiting such phenomena in spintronic devices. These findings vividly emphasize how crystal symmetry and electronic topology can govern the intrinsic SHE and spin relaxation, and how they may be exploited to broaden the range and efficiency of spintronic materials and functionalities.

Anomalous Hall signatures of nonsymmorphic nodal lines in the doped chromium chalcospinel CuCr2Se4

An emerging phase of matter among the class of topological materials is nodal line semimetal, possessing symmetry-protected one-dimensional gapless lines at the (or close to) the Fermi level in $k$-space. When the $k$-dispersion of the nodal line is weak, van Hove singularities generated by the almost flat nodal lines may be prone to instabilities introduced by additional perturbations such as spin-orbit coupling or magnetism. Here, we study Cr-based ferromagnetic chalcospinel compound CuCr$_2$Se$_4$ (CCS) via first-principles electronic structure methods and reveal the true origin of its dissipationless anomalous Hall conductivity, which was not well understood previously. We find that CCS hosts nodal lines protected by nonsymmorphic symmetries, located in the vicinity of Fermi level, and that such nodal lines are the origin of the previously observed distinct behavior of the anomalous Hall signature in the presence of electron doping. The splitting of nodal line via spin-orbit coupling produces a large Berry curvature, which leads to a significant response in anomalous Hall conductivity. Upon electron doping via chemical substitution or gating, or rotation of magnetization via external magnetic field, steep change of anomalous Hall behavior occurs, which makes CCS a promising compound for low energy spintronics applications.

Giant anomalous Nernst signal in the antiferromagnet YbMnBi2

A large anomalous Nernst effect (ANE) is crucial for thermoelectric energy conversion applications because the associated unique transverse geometry facilitates module fabrication. Topological ferromagnets with large Berry curvatures show large ANEs; however, they face drawbacks such as strong magnetic disturbances and low mobility due to high magnetization. Herein, we demonstrate that YbMnBi2, a canted antiferromagnet, has a large ANE conductivity of ~10 A m−1 K−1 that surpasses large values observed in other ferromagnets (3–5 A m−1 K−1). The canted spin structure of Mn guarantees a non-zero Berry curvature, but generates only a weak magnetization three orders of magnitude lower than that of general ferromagnets. The heavy Bi with a large spin–orbit coupling enables a large ANE and low thermal conductivity, whereas its highly dispersive px/y orbitals ensure low resistivity. The high anomalous transverse thermoelectric performance and extremely small magnetization make YbMnBi2 an excellent candidate for transverse thermoelectrics.

Topological Magnets: Functions Based on Berry Phase and Multipoles

Macroscopic responses of magnets are often governed by magnetization and, thus, have been restricted to ferromagnets. However, such responses are strikingly large in the newly developed topological magnets, breaking the conventional scaling with magnetization. Taking the recently discovered antiferromagnetic (AF) Weyl semimetals as a prime example, we highlight the two central ingredients driving the significant macroscopic responses: the Berry curvature enhanced because of nontrivial band topology in momentum space, and the cluster magnetic multipoles in real space. The combination of large Berry curvature and multipoles enables large macroscopic responses such as the anomalous Hall and Nernst effects, the magneto-optical effect, and the novel magnetic spin Hall effect in antiferromagnets with negligible net magnetization, but also allows us to manipulate these effects by electrical means. Furthermore, nodal-point and nodal-line semimetallic states in ferromagnets may provide the strongly enhanced Berry curvature near the Fermi energy, leading to large responses beyond the conventional magnetization scaling. These significant properties and functions of the topological magnets lay the foundation for future technological development such as spintronics and thermoelectric technology.

Strain-gated nonlinear Hall effect in two-dimensional MoSe2/WSe2 van der Waals heterostructure

It is recently found that the Hall effect can survive in the presence of time-reversal symmetry but with inversion-symmetry breaking, which is known as the nonlinear Hall effect. So far, the studies concerning the nonlinear Hall effect are mainly focused on the homogeneous systems, while less attention has been paid to the van der Waals (vdW) heterostructure, which in fact naturally breaks the spatial inversion symmetry. In this study, we systematically study the nonlinear electric response in $1{\text{T}}^{\ensuremath{'}}$-phase ${\mathrm{MoSe}}_{2}/{\mathrm{WSe}}_{2}$ vdW heterostructure. Our results demonstrate that ${\mathrm{MoSe}}_{2}/{\mathrm{WSe}}_{2}$ vdW heterostructure owns a large Berry curvature dipole, which is comparable with those of homogeneous multilayers and much larger than that predicted for monolayers under the in-plane uniaxial strain. In addition, the nonlinear Hall response in vdW heterostructure is sensitive to the relative position between the Fermi energy and tilted Dirac cones, and can be effectively manipulated from positive to negative values by applying an out-of-plane strain. Further study indicates that this can be ascribed to the charge transfer within the vdW interlayer. Based on these findings, our work provides a fundamental understanding of the nature of strain-gated nonlinear Hall effect in vdW heterostructures, which may facilitate the design of novel high-frequency nanodevices.

Vertical transverse transport induced by hidden in-plane Berry curvature in two dimensions

The discovery of Berry curvature (BC) has spurred a tremendous surge of research into various quantum phenomena such as the anomalous transport of electrons and the topological phases of matter. In two-dimensional crystalline systems, the conventional definition of the BC lacks the in-plane components and thus it cannot explain the transverse transport along the plane-normal direction. Here, we modify the BC to newly provide in-plane components in two dimensions, giving rise to the vertical Hall effects that describe out-of-plane transports in response to in-plane perturbations and their Onsager reciprocity. Our first-principles calculations show that a large in-plane BC can appear even in an atomic-thick GdAg2 monolayer, and a hexagonal BiAg2 monolayer can host a large BC dipole known to vanish in the conventional BC. The quantum transports driven by the hitherto-hidden BC will become more significant in recently emerging two-dimensional platforms, including van der Waals heterostructures.

Large Anomalous Hall and Nernst Effects in High Curie-Temperature Iron-Based Heusler Compounds.

The interplay between topology and magnetism has recently sparked the frontier studies of magnetic topological materials that exhibit intriguing anomalous Hall and Nernst effects owning to the large intrinsic Berry curvature (BC). To better understand the anomalous quantum transport properties of these materials and their implications for future applications such as electronic and thermoelectric devices, it is crucial to discover more novel material platforms for performing anomalous transverse transport studies. Here, it is experimentally demonstrated that low‐cost Fe‐based Heusler compounds exhibit large anomalous Hall and Nernst effects. An anomalous Hall conductivity of 250–750 S cm−1 and Nernst thermopower of above 2 µV K−1 are observed near room temperature. The positive effect of anti‐site disorder on the anomalous Hall transport is revealed. Considering the very high Curie temperature (nearly 1000 K), larger Nernst thermopowers at high temperatures are expected owing to the existing magnetic order and the intrinsic BC. This work provides a background for developing low‐cost Fe‐based Heusler compounds as a new material platform for anomalous transport studies and applications, in particular, near and above room temperature.

Concurrence of anomalous Hall effect and charge density wave in a superconducting topological kagome metal

As one of the most fundamental physical phenomena, the anomalous Hall effect (AHE) typically occurs in ferromagnetic materials but is not expected in the conventional superconductors. Here, we have observed a giant AHE in kagome superconductor CsV3Sb5 with transition temperature (Tc) of 2.7 K. The anomalous Hall conductivity reaches up to 2.1*10^4 {\Omega}-1 cm-1 which is larger than those observed in most of the ferromagnetic metals. Strikingly, the emergence of AHE exactly follows the higher-temperature charge-density-wave (CDW) transition with TCDW ~ 94 K, indicating a strong correlation between the CDW state and AHE. Furthermore, AHE disappears when the CDW transition is completely suppressed at high pressure. The origin for AHE is attributed to enhanced skew scattering in CDW state and large Berry curvature arose from the kagome lattice. These discoveries make CsV3Sb5 as an ideal platform to study the interplay among nontrivial band topology, CDW and unconventional superconductivity.

Nonlinear transport in Weyl semimetals induced by Berry curvature dipole

Topological Weyl semimetals (WSMs) have been predicted to be excellent candidates for detecting Berry curvature dipole (BCD) and the related non-linear effects in electronics and optics due to the large Berry curvature concentrated around the Weyl nodes. And yet, linearized models of isolated tilted Weyl cones only realize a diagonal non-zero BCD tensor which sum to zero in the model of WSM with multiple Weyl nodes in the presence of mirror symmetry. On the other hand, recent \textit{ab initio} work has found that realistic WSMs like TaAs-type or MoTe$_2$-type compounds, which have mirror symmetry, indeed show an off-diagonal BCD tensor with an enhanced magnitude for its non-zero components. So far, there is a lack of theoretical work addressing this contradiction for 3D WSMs. In this paper, we systematically study the BCD in 3D WSMs using lattice Weyl Hamiltonians, which go beyond the linearized models. We find that the non-zero BCD and its related important features for these WSMs do not rely on the contribution from the Weyl nodes. Instead, they are dependent on the part of the Fermi surface that lies \textit{between} the Weyl nodes, in the region of the reciprocal space where neighboring Weyl cones overlap. For large enough chemical potential such Fermi surfaces are present in the lattice Weyl Hamiltonians as well as in the realistic WSMs. We also show that, a lattice Weyl Hamitonian with a non-zero chiral chemical potential for the Weyl cones can also support dips or peaks in the off-diagonal components of the BCD tensor near the Weyl nodes themselves, consistent with recent \textit{ab initio} work.

Low Gilbert damping in epitaxial thin films of the nodal-line semimetal D03−Fe3Ga

$D{0}_{3}$-ordered ${\mathrm{Fe}}_{3}\mathrm{Ga}$ has been recently reported to show a giant anomalous Nernst effect due to a large Berry curvature along the interconnected nodal lines concentrated near the Fermi level. This peculiar band structure may be advantageous for spintronics device applications because one can expect a strong response to a gate-voltage application. This study evaluates the Gilbert damping constants, a key parameter governing the magnetization dynamics of epitaxial thin films of $D{0}_{3}\text{\ensuremath{-}}{\mathrm{Fe}}_{3}\mathrm{Ga}$ and bcc-Fe by ferromagnetic resonance measurements. We find that the Gilbert damping constant of $D{0}_{3}\text{\ensuremath{-}}{\mathrm{Fe}}_{3}\mathrm{Ga} [(6.0\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}]$ is relatively low and comparable to that of Fe $[(2.3\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}]$. The low Gilbert damping suggests that the interconnected nodal lines near the Fermi level do not hinder magnetization dynamics, making $D{0}_{3}\text{\ensuremath{-}}{\mathrm{Fe}}_{3}\mathrm{Ga}$ even more attractive as a building block of spintronics devices.

Omnidirectional Control of Large Electrical Output in a Topological Antiferromagnet

AbstractControl of magnetization direction is essential for the wide application of ferromagnets; it defines the signal size of memory and sensor. However, the magnetization itself causes a dilemma. While its size matters to obtain strong responses upon its reversal, the large magnetization concomitantly suppresses the range of its directional control because of the demagnetizing field. On the other hand, realization of the desired magnetic anisotropy requires careful engineering of crystalline and interfacial effects to overcome the demagnetization barrier. Thus, it would be ideal if one could find alternative magnets that carry no magnetization but strong responses. The discovery of a topological metallic state in the antiferromagnet Mn3Sn is significant; they host a large Berry curvature in momentum space, enabling the observation of disproportionately large transverse responses such as anomalous Hall and Nernst effects, the key functionalities for replacing ferromagnets in the magnetic devices. Here, the experimental realization of omnidirectional control of the large responses in an antiferromagnet is reported. In particular, it is demonstrated that the absence of shape anisotropy enables the omnidirectional control, and lifts the shape constraint in designing the magnetic devices. This work lays the technological foundation for developing simple‐structured high‐performance devices including multi‐level memory and heat flux sensor.

Berry curvature origin of the thickness-dependent anomalous Hall effect in a ferromagnetic Weyl semimetal

Magnetic Weyl semimetals with spontaneously broken time-reversal symmetry exhibit a large intrinsic anomalous Hall effect originating from the Berry curvature. To employ this large Hall current for room temperature topo-spintronics applications, it is necessary to fabricate these materials as thin or ultrathin films. Here, we experimentally demonstrate that Weyl semimetal Co2MnGa thin films (20–50 nm) show a large anomalous Hall angle ~11.4% at low temperature and ~9.7% at room temperature, which can be ascribed to the non-trivial topology of the band structure with large intrinsic Berry curvature. However, the anomalous Hall angle decreases significantly with thicknesses below 20 nm, which band structure calculations confirm is due to the reduction of the majority spin contribution to the Berry curvature. Our results suggest that Co2MnGa is an excellent material to realize room temperature topo-spintronics applications; however, the significant thickness dependence of the Berry curvature has important implications for thin-film device design.

Tunable spin Hall and spin Nernst effects in Dirac line-node semimetals XCuYAs ( X=Zr,Hf ; Y=Si,Ge )

The quaternary arsenide compounds XCuYAs (X=Zr, Hf; Y= Si, Ge) belong to the vast family of the 1111-type quaternary compounds, which possess outstanding physical properties ranging from $p$-type transparent semiconductors to high-temperature Fe-based superconductors. In this paper, we study the electronic structure topology, spin Hall effect (SHE) and spin Nernst effect (SNE) in these compounds based on density functional theory calculations. First we find that the four considered compounds are Dirac semimetals with the nonsymmorphic symmetry-protected Dirac line nodes along the Brillouin zone boundary $A$-$M$ and $X$-$R$ and low density of states (DOS) near the Fermi level ($E_F$). Second, the intrinsic SHE and SNE in some of these considered compounds are found to be large. In particular, the calculated spin Hall conductivity (SHC) of HfCuGeAs is as large as -514 ($\hbar$/e)(S/cm). The spin Nernst conductivity (SNC) of HfCuGeAs at room temperature is also large, being -0.73 ($\hbar$/e)(A/m-K). Moreover, both the magnitude and sign of the SHC and SNC in these compounds can be manipulated by varying either the applied electric field direction or spin current direction. The SHE and SNE in these compounds can also be enhanced by tuning the Fermi level via chemical doping or electric gating. Finally, a detailed analysis of the band-decomposed and $k$-resolved spin Berry curvatures reveals that these large SHC and SNC as well as their notable tunabilities originate largely from the presence of a large number of spin-orbit coupling-gapped Dirac points near the Fermi level as well as the gapless Dirac line-nodes, which give rise to large spin Berry curvatures. Our findings thus suggest that the four XCuYAs compounds not only provide a valuable platform for exploring the interplay between SHE, SNE and band topology but also have promising applications in spintronics and spin caloritronics.

Inverse spin Hall effect and spin pumping in the polycrystalline noncollinear antiferromagnetic Mn3Ga

Noncollinear antiferromagnetic (AFM) materials have drawn research interest because they exhibit large anomalous Hall effect at room temperature (RT) due to large Berry curvature. ${\mathrm{Mn}}_{3}\mathrm{Ga}$ is a noncollinear AFM in which the order of Mn magnetic moments is arranged in inverse triangular configuration on a kagome lattice. It makes ${\mathrm{Mn}}_{3}\mathrm{Ga}$ a promising candidate for inverse spin Hall effect (ISHE) study which has not been studied before. In this work, investigation of ISHE and spin pumping in polycrystalline ${\mathrm{Mn}}_{3}\mathrm{Ga}$/CoFeB heterostructures at RT has been performed. Angle-dependent measurements of ISHE have been performed in order to disentangle various spin-rectification effects. Spin-mixing conductance (${g}_{\mathrm{eff}}^{\ensuremath{\uparrow}\ensuremath{\downarrow}})$, spin Hall angle $({\ensuremath{\theta}}_{SH})$, and spin Hall conductivity (${\ensuremath{\sigma}}_{SH}$) are evaluated to be $(5.0\ifmmode\pm\else\textpm\fi{}1.8)\ifmmode\times\else\texttimes\fi{}{10}^{18}\phantom{\rule{0.16em}{0ex}}{\mathrm{m}}^{\ensuremath{-}2}, 0.31\ifmmode\pm\else\textpm\fi{}0.01$, and $7.5\ifmmode\times\else\texttimes\fi{}{10}^{5}\phantom{\rule{0.28em}{0ex}}(\ensuremath{\hbar}/2e)\phantom{\rule{0.16em}{0ex}}{\mathrm{\ensuremath{\Omega}}}^{\ensuremath{-}1\phantom{\rule{4pt}{0ex}}}\phantom{\rule{0.16em}{0ex}}{\mathrm{m}}^{\ensuremath{-}1}$, respectively. The observed value of ${\ensuremath{\theta}}_{SH}$ is higher than ${\mathrm{Mn}}_{3}\mathrm{Sn}$ and comparable to the ${\mathrm{IrMn}}_{3}$, which is also a noncollinear AFM. Large spin Hall angle makes ${\mathrm{Mn}}_{3}\mathrm{Ga}$ a promising candidate for future spintronics devices.