Berry Curvature Research Articles

Tunable valley polarization in two-dimensional H-HfI2/T-VBrCl van der Waals heterostructure

The electronic band structure and valley splitting of monolayer H-HfI2 and H-HfI2/T-VBrCl heterostructure have been investigated by first principles calculations. The monolayer H-HfI2 exhibits valleytronic feature at K and K’ points of the valence bands. The valley polarization in monolayer H-HfI2 arises from the magnetic proximity effect induced by T-VBrCl monolayer. The stacking configurations have a significant influence on the valley polarization of the H-HfI2/T-VBrCl heterostructure. The maximum valley polarization can be as high as −20 meV. It is possible to manipulate the magnitude of valley polarization by adjusting the layer spacing and applying biaxial strain. The Berry curvature between two valleys indicates that the H-HfI2/T-VBrCl heterostructure should be a potential candidate for valleytronic devices.

Topological properties and anomalous transport in van der Waals ferromagnets Fe n GeTe2: a comparative study

Recently synthesized topological van der Waals (vdW) Fe n GeTe2 (n=3,4, and 5) series of compounds have drawn a lot of research interest due to their interesting magnetic properties and anomalous transport behavior. However, understanding the topological aspect of these materials’ electronic band structure is either scant or absent in the literature. In this work, we perform a comparative study of the electronic structure of all three materials to understand their topological properties and their effect on transport properties using the first-principles calculations and to derive the effective tight-binding model for these systems. All three systems exhibit ferromagnetic behavior, and the contribution of various Fe d-orbitals are also studied. Spin-orbit coupling (SOC) causes the degeneracy to be lifted and results in a finite Berry curvature (BC). Finite BC contributes to the intrinsic anomalous Hall conductivity (AHC) and Nernst conductivity (ANC) of these systems. We show that Fe3GeTe2 and Fe5GeTe2 have similar nodal line formations, while Fe4GeTe2 exhibits nodal points close to Fermi energy E F . We calculate AHC (σ xy ) at zero temperature and ANC (α xy ) at room temperature for n = 3, 4 and 5 and find that our values are consistent with transport and magnetic measurement.

Anomalous Nernst effect in honeycomb and kagome magnet LaCo5 at room temperature

Magnetic order-induced time reversal symmetry breaking in the kagome lattice is predicted to generate Weyl semimetal and Chern insulating phases. The two-dimensional (2D) honeycomb lattices with spin orbit coupling (SOC) and ferromagnetism are also known to host the Chern insulating phase. Here, we study the transport properties of the ferromagnetic topological material LaCo5 crystals with TC = 840 K, which is the highest among the reported magnetic topological materials up to now. It is composed of 2D Co2 kagome layers that are separated by La–Co1 layers, in which the Co1 atoms exhibit a honeycomb structure. Both the 2D kagome and honeycomb layers exhibit out-of-plane magnetization. The large intrinsic anomalous Hall effect and anomalous Nernst effect of about 4.6 μVK−1 are observed in the ab plane with the B//c configuration at room temperature, which can be attributed to non-zero Berry curvature according to the first-principles calculations. Our results enrich the magnetic topological materials with honeycomb and kagome lattices, providing a good platform for the further study of the QAHE. The excellent thermoelectric performance, high TC, nontoxicity, and low cost also make LaCo5 a promising candidate for the applications of thermoelectric generators and heat flow sensors at high temperatures.

Analog of Foucault precession in two-dimensional quantum harmonic oscillators with Berry curvature

Analog of Foucault precession in two-dimensional quantum harmonic oscillators with Berry curvature

Berry: A code for the differentiation of Bloch wavefunctions from DFT calculations

Density functional calculation of electronic structures of materials is one of the most used techniques in theoretical solid state physics. These calculations retrieve single electron wavefunctions and their eigenenergies.The berry suite of programs amplifies the usefulness of DFT by ordering the eigenstates in analytic bands, allowing the differentiation of the wavefunctions in reciprocal space. It can then calculate Berry connections and curvatures and the second harmonic generation conductivity.The berry software is implemented for two dimensional materials and was tested in hBN and InSe. In the near future, more properties and functionalities are expected to be added. Program summaryProgram Title: berryCPC Library link to program files:https://doi.org/10.17632/mpbbksz2t7.1Developer's repository link:https://github.com/ricardoribeiro-2020/berryLicensing provisions: MITProgramming language: Python3Nature of problem: Differentiation of Bloch wavefunctions in reciprocal space, numerically obtained from a DFT software, applied to two dimensional materials. This enables the numeric calculation of material's properties such as Berry geometries and Second Harmonic conductivity.Solution method: Extracts Kohn-Sham functions from a DFT calculation, orders them by analytic bands using graph and AI methods and calculates the gradient of the wavefunctions along an electronic band.Additional comments including restrictions and unusual features: Applies only to two dimensional materials, and only imports Kohn-Sham functions from Quantum Espresso package.

Design of Sn-doped cadmium chalcogenide based monolayers for valleytronics properties

Valleytronics has emerged as an interesting field of research in two-dimensional (2D) systems and uses the valley index or valley pseudospin to encode information. Spin–orbit coupling (SOC) and inversion symmetry breaking lead to spin-splitting of bands near the valleys. This property has promising device applications. In order to find a new 2D material useful for valleytronics, we have designed hexagonal planar monolayers of cadmium chalcogenides (CdX, X = S, Se, Te) from the (111) surface of bulk CdX zinc blende structure. The structural, dynamic, mechanical and thermal stability of these structures is confirmed. A band structure study reveals valence band local maxima (valleys) at the K and K′ symmetry points. The application of SOC initiates spin-splitting in the valleys that lifts the energy degeneracy and shows strong valley–spin coupling. To initiate stronger SOC, we substituted two Cd atoms in the almost-planar monolayers with Sn atoms, which increases the spin-splitting significantly. Zeeman-type spin-splitting is observed in the valley region and Rashba spin-splitting is observed at the Γ point for Sn-doped CdSe and CdTe monolayers. Berry curvature values are higher in all the Sn-doped monolayers than in the pristine monolayers. These newly designed monolayers are thus found to be suitable for valleytronics applications. Sn-doped monolayers show band inversion deep in the valence and conduction bands between Sn s and p and X p states but lack topological properties.

Possible way to achieve valley-polarized quantum anomalous Hall insulator

The valley-polarized quantum anomalous Hall insulator (VQAHI), which combines valleytronics and topology in one material, provides a path toward integrating valleytronics, topological quantum effects, and spintronics. Here, we propose a way of realizing VQAHIs in tetragonal quantum anomalous Hall insulators (QAHIs) by introducing valley polarization, which can be achieved by breaking C4 rotational symmetry. We use a concrete example of a QAHI Fe2I2 monolayer, where there are equivalent valleys along the Γ-X and Γ-Y lines in momentum space, to illustrate our proposal through first-principle calculations. By applying uniaxial strain along the x direction, the rotational symmetry C4 is reduced into C2, which induces valley polarization. With uniaxial strain from a compressive one to a tensile one, valley polarization transition can be induced. Moreover, the nonzero Berry curvature around valleys can produce the anomalous valley Hall effect. With the considered strain range, the quantum anomalous Hall properties can be maintained. Therefore, a VQAHI can be realized in strained Fe2I2. Our works propose an experimentally feasible way to realize valley polarization and VQAHIs.

Roses in the nonperturbative current response of artificial crystals.

In two-dimensional artificial crystals with large real-space periodicity, the nonlinear current response to a large applied electric field can feature a strong angular dependence, which encodes information about the band dispersion and Berry curvature of isolated electronic Bloch minibands. Within the relaxation-time approximation, we obtain analytic expressions up to infinite order in the driving field for the current in a band-projected theory with time-reversal and trigonal symmetry. For a fixed field strength, the dependence of the current on the direction of the applied field is given by rose curves whose petal structure is symmetry constrained and is obtained from an expansion in real-space translation vectors. We illustrate our theory with calculations on periodically buckled graphene and twisted double bilayer graphene, wherein the discussed physics can be accessed at experimentally relevant field strengths.

Coexistence of Chiral and Antichiral Edge States in Photonic Crystals

AbstractThis study reports a modified Haldane model that supports transitions between valley and Chern topological phases in photonic crystals. Berry curvatures of this system can be flexibly diffused, converged, or flipped by endowing different model parameters, thus exhibiting exotic topological interface/edge behaviors, such as topological bound states with ideally zero dispersion. Importantly, the coexistence of chiral and antichiral edge states preserved simultaneously by valley and Chern topological phases is achieved by splicing together two kinds of topological structures as an entirety. It further employs a honeycomb lattice comprising gyromagnetic and ceramic cylinders at microwave frequencies, where inversion and time‐reversal symmetries can be flexibly manipulated. Topological interface transport is demonstrated, including two opposite signs of group velocities jointly protected by topologically distinct regimes. These results bridge the gap between valley and Chern topological physics and shed light on developing reconfigurable integrated device applications for classical (quantum) information processing and photonic computing.

Berry Curvature Dipole Induced Giant Mid-Infrared Second-Harmonic Generation in 2D Weyl Semiconductor.

Due to its inversion-broken triple helix structure and the nature of Weyl semiconductor, 2D Tellurene (2D Te) is promising to possess a strong nonlinear optical response in the infrared region, which is rarely reported in 2D materials. Here, a giant nonlinear infrared response induced by large Berry curvature dipole (BCD) is demonstrated in the Weyl semiconductor 2D Te. Ultrahigh second-harmonic generation response is acquired from 2D Te with a large second-order nonlinear optical susceptibility (χ(2) ), which is up to 23.3 times higher than that of monolayer MoS2 in the range of 700-1500nm. Notably, distinct from other 2D nonlinear semiconductors, χ(2) of 2D Te increases extraordinarily with increasing wavelength and reaches up to 5.58nmV-1 at ≈2300nm, which is the best infrared performance among the reported 2D nonlinear materials. Large χ(2) of 2D Te also enables the high-intensity sum-frequency generation with an ultralow continuous-wave (CW) pump power. Theoretical calculations reveal that the exceptional performance is attributed to the presence of large BCD located at the Weyl points of 2D Te. These results unravel a new linkage between Weyl semiconductor and strong optical nonlinear responses, rendering 2D Te a competitive candidate for highly efficient nonlinear 2D semiconductors in the infrared region.

Adiabatic deformations of quantum Hall droplets

We consider area-preserving deformations of the plane, acting on electronic wave functions through “quantomorphisms” that change both the underlying metric and the confining potential. We show that adiabatic sequences of such transformations produce Berry phases that can be written in closed form in terms of the many-body current and density, even in the presence of interactions. For a large class of deformations that generalize squeezing and shearing, the leading piece of the phase is a super-extensive Aharonov-Bohm term (\propto N^2∝N2 for NN electrons) in the thermodynamic limit. Its gauge-invariant subleading partner only measures the current, whose dominant contribution to the phase stems from a jump at the edge in the limit of strong magnetic fields. This results in a finite Berry curvature per unit area, reminiscent of the Hall viscosity. We show that the latter is in fact included in our formalism, bypassing its standard derivation on a torus and suggesting realistic experimental setups for its observation in quantum simulators.

Ferroelectricity and Large Rashba Splitting in Two-Dimensional Tellurium

Two-dimensional (2D) ferroelectric (FE) systems are promising candidates for non-volatile nanodevices. Previous studies mainly focused on 2D compounds. Though counter-intuitive, here we propose several new phases of tellurium with (anti)ferroelectricity. Two-dimensional films can be viewed as a collection of one-dimensional chains, and lone-pair instability is responsible for the (anti)ferroelectricity. The total polarization is determined to be 0.34 × 10−10 C/m for the FE ground state. Due to the local polarization field in the FE film, we show a large Rashba splitting (α R ∼ 2 eV⋅Å) with nonzero spin Hall conductivity for experimental detection. Furthermore, a dipole-like distribution of Berry curvature is verified, which may facilitate a nonlinear Hall effect. Because Rashba-splitting/Berry-curvature distributions are fully coupled with a polarization field, they can be reversed through FE phase transition. Our results not only broaden the elemental FE materials, but also shed light on their intriguing transport phenomena.

Large anomalous Hall effect and unusual domain switching in an orthorhombic antiferromagnetic material NbMnP

Specific antiferromagnetic (AF) spin configurations generate large anomalous Hall effects (AHEs) even at zero magnetic field through nonvanishing Berry curvature in momentum space. In addition to restrictions on AF structures, suitable control of AF domains is essential to observe this effect without cancellations among its domains; therefore, compatible materials remain limited. Here we show that an orthorhombic noncollinear AF material, NbMnP, acquired AF structure-based AHE and controllability of the AF domains. Theoretical calculations indicated that a large Hall conductivity of ~230 Ω−1cm−1 originated from the AF structure of NbMnP. Symmetry considerations explained the production of a small net magnetization, whose anisotropy enabled the generation and cancellation of the Hall responses using magnetic fields in different directions. Finally, asymmetric hysteresis in NbMnP shows potential for the development of controllability of responses in AF materials.

Valley dependent tunable Berry curvature related properties in heterojunction of graphene on WSe 2

Heterojunction of graphene on WSe 2 has strong spin–orbit coupling (SOC) in terms of valley Zeeman λ vz and Rashba λ r contributions. The interplay of SOC terms and lattice potential term are shown to tune the behavior of the heterojunction in terms of energy dispersion. The valley and spin degree of freedom are useful for the tuning and use of the heterojunction as a potential candidate in valleytronics and spintronics. We have shown Berry curvature, magnetic moment, orbital magnetization and Nernst coefficient to be valley, spin and SOC dependent. All these factors are shown to influence the behavior of the graphene on WSe 2. We are able to tune and vary the behavior according to the needs by the interplay of these factors.

Valley-dependent topological phase transition in monolayer ferrovalley materials RuXY (X, Y = F, Cl, Br)

Due to the breaking of the time reversal symmetry and spatial inversion symmetry, hexagonal ferrovalley materials have intrinsic large valley polarization. Model analysis shows that tuning the two different band gaps of valleys can realize phase transitions between ferrovalley semiconductors, half valley metals, and valley-polarized quantum anomalous Hall semiconductors. Through first-principle calculations, monolayer ferrovalley materials RuXY (X, Y = F, Cl, Br), which exhibit valley splitting at the top valence band and the bottom conduction band, are predicted to achieve this valley-dependent topological phase transition. Due to the different orbital proportions of d orbitals, the valley splitting at the top valence band is much greater than that at the bottom conduction band. Strain can regulate the interaction between orbitals, thus producing valley-dependent band inversion, leading to the quantum spin or valley Hall effect. The chiral edge states are demonstrated under appropriate biaxial strain. The topological phase transition is related to the inversion of the band structure and Berry curvatures at K and K′ valleys. These results have certain significance for the design of two-dimensional valley-dependent quantum materials and the application of valleytronic devices.

Berry curvature induced spontaneous and topological-like Hall effect in magnetic Weyl semimetallic Nd2Ir2O7 (111) thin films

We report a study of longitudinal resistivity, anisotropic magnetoresistance (MR), and Hall effect on epitaxial Nd2Ir2O7 (111) thin films grown by the solid phase epitaxy technique, in which spin–orbit coupling, electronic correlation, magnetic frustration, and f-d exchange interaction are present. Temperature-dependent longitudinal resistivity (ρxx) data indicate semimetallic charge transport in the low-temperature region. Field-cooled longitudinal resistivity measurements detect negligible domain-wall conductance compared to the polycrystal or single-crystal samples. Angle-dependent MR measurement shows that the magnetic structure of Ir4+ 5d moments can be finely tuned by applying a magnetic field along different crystallographic directions. MR measurements show a field-induced modification of the Nd3+ 4f spin structure from all-in-all-out/all-out-all-in (AIAO/AOAI) (4-in-0-out) to 1-in-3-out for the applied field (H) along the [111] direction, resulting in field-induced plastic deformation of the Ir4+ domain distribution. In contrast, the application of field (H) along the [001] and [011] directions could not modify any domain distribution. A large spontaneous Hall effect (SHE) signal has been observed on Nd2Ir2O7 (111) thin film with AIAO/AOAI antiferromagnetic ordering for the application of field (H) along [001], [1̄1̄0], and [111] directions. The appearance of a large spontaneous Hall signal for the applied field along [001] and [1̄1̄0] directions rules out domain switching as the origin of the Hall effect and confirms the presence of the Weyl semimetallic phase in Nd2Ir2O7 (111) thin films. In addition to SHE, a large topological-like Hall signal is also observed, possibly due to the presence of multiple Weyl nodes in the electronic band structure.

Berry Curvature and Bulk-Boundary Correspondence from Transport Measurement for Photonic Chern Bands.

Berry curvature is a fundamental element to characterize topological quantum physics, while a full measurement of Berry curvature in momentum space was not reported for topological states. Here we achieve two-dimensional Berry curvature reconstruction in a photonic quantum anomalous Hall system via Hall transport measurement of a momentum-resolved wave packet. Integrating measured Berry curvature over the two-dimensional Brillouin zone, we obtain Chern numbers corresponding to -1 and 0. Further, we identify bulk-boundary correspondence by measuring topology-linked chiral edge states at the boundary. The full topological characterization of photonic Chern bands from Berry curvature, Chern number, and edge transport measurements enables our photonic system to serve as a versatile platform for further in-depth study of novel topological physics.

Optoelectronic Manifestation of Orbital Angular Momentum Driven by Chiral Hopping in Helical Se Chains.

Chiral materials have garnered significant attention in the field of condensed matter physics. Nevertheless, the magnetic moment induced by the chiral spatial motion of electrons in helical materials, such as elemental Te and Se, remains inadequately understood. In this work, we investigate the development of quantum angular momentum enforced by chirality by using static and time-dependent density functional theory calculations for an elemental Se chain. Our findings reveal the emergence of an unconventional orbital texture driven by the chiral geometry, giving rise to a nonvanishing current-induced orbital moment. By incorporating spin-orbit coupling, we demonstrate that current-induced spin accumulation arises in the chiral chain, which fundamentally differs from the conventional Edelstein effect. Furthermore, we demonstrate optoelectronic detection of the orbital angular momentum in the chiral Se chain, providing an alternative to the interband Berry curvature, which is ill-defined in low dimensions.

Giant Nonvolatile Electric Field Control of Proximity‐Induced Magnetism in the Spin–Orbit Semimetal SrIrO3

AbstractWith its potential for drastically reduced operation power of information processing devices, electric field control of magnetism has generated huge research interest. Recently, novel perspectives offered by the inherently large spin–orbit coupling of 5d transition metals have emerged. Here, nonvolatile electrical control of the proximity‐induced magnetism in SrIrO3 based back‐gated heterostructures is demonstrated. Up to a 700% variation of the anomalous Hall conductivity (σAHE) and Hall angle (ΘAHE) as function of the applied gate voltage Vg is reported. In contrast, the Curie temperature TC ≈ 100 K and magnetic anisotropy of the system remain essentially unaffected by Vg indicating a robust ferromagnetic state in SrIrO3 which strongly hints to gating‐induced changes of the anomalous Berry curvature. The electric‐field induced ferroelectric‐like state of SrTiO3 enables nonvolatile switching behavior of σAHE and ΘAHE below 60 K. The large tunability of this system, opens new avenues toward efficient electric‐field manipulation of magnetism.

Flow of higher Berry curvature and bulk-boundary correspondence in parametrized quantum systems

Flow of higher Berry curvature and bulk-boundary correspondence in parametrized quantum systems