Berry Flux Research Articles

Endless Dirac nodal lines and high mobility in kagome semimetal Ni3In2Se2 : a theoretical and experimental study

Kagome-lattice crystal is crucial in quantum materials research, exhibiting unique transport properties due to its rich band structure and the presence of nodal lines and rings. Here, we investigate the electronic transport properties and perform first-principles calculations for Ni3In2Se2kagome topological semimetal. First-principles calculations of the band structure without the inclusion of spin-orbit coupling (SOC) shows that three bands are crossing the Fermi level (EF), indicating the semi-metallic nature. With SOC, the band structure reveals a gap opening of the order of 10 meV.Z2index calculations suggest the topologically nontrivial natures (ν0;ν1ν2ν3) = (1;111) both without and with SOC. Our detailed calculations also indicate six endless Dirac nodal lines and two nodal rings with aπ-Berry phase in the absence of SOC. The temperature-dependent resistivity is dominated by two scattering mechanisms:s-dinterband scattering occurs below 50 K, while electron-phonon (e-p) scattering is observed above 50 K. The magnetoresistance (MR) curve aligns with the theory of extended Kohler's rule, suggesting multiple scattering origins and temperature-dependent carrier densities. A maximum MR of 120% at 2 K and 9 T, with a maximum estimated mobility of approximately 3000 cm2V-1s-1are observed. Ni3In2Se2is an electron-hole compensated topological semimetal, as we have carrier density of electron (ne) and hole (nh) arene≈nh, estimated from Hall effect data fitted to a two-band model. Consequently, there is an increase in the mobility of electrons and holes, leading to a higher carrier mobility and a comparatively higher MR. The quantum interference effect leading to the two dimensional (2D) weak antilocalization effect (-σxx∝ln(B)) manifests as the diffusion of nodal line fermions in the 2D poloidal plane and the associated encircling Berry flux of nodal-line fermions.

In-plane Wilson loop for measurement of quantized non-Abelian Berry flux

In-plane Wilson loop for measurement of quantized non-Abelian Berry flux

Berry curvature inside a PT -symmetry protected exceptional surface

A three-dimensional non-Hermitian Hamiltonian with parity-time symmetry can exhibit a closed exceptional surface (EP surface) in momentum space, which is a non-Hermitian deformation of the degeneracy line. Since the degeneracy line lacks an internal space, the distributions of Berry curvature inside the EP surface become particularly intriguing. This paper studies the distributions taking a toruslike EP surface as an example. In a meridian cross section, the Berry connection exhibits a vortexlike field with only angular components, while the Berry curvature is perpendicular to this cross section; in a equatorial cross section, the Berry curvature forms a closed curve surrounding the central genus. Both Berry connection and curvature converge along the coplanar axis and diverge at the surface. We find the Berry flux depends on the radius of the integration region and is not quantized inside the EP torus. Approaching the surface, the Berry flux tends to infinity and the dynamical phase oscillates violently. We point out that the streamlines of Berry curvature can be used to estimate the zero or nonzero Berry flux. We generalize the above patterns to the case of EP surfaces with complex shapes and present a proposal of realizing the EP surface in an electrical circuit. Our research outcomes enhance the comprehension of EP surfaces and the topological characteristics of non-Hermitian systems with parity-time (PT) symmetry. Published by the American Physical Society 2024

CoFeSn, a possible contender for spintronics: A first-principles study

Anomalous carrier transport in magnetic Heusler compounds has evolved as a lively field of research owing to their unusual band structure and broken time-reversal symmetry. They have attractive properties for spintronics due to their high Curie temperature (Tc), high spin polarization, and extravagant transport properties. Here, we scrutinize CoFeSn. Based on the inferences from structural stability, lattice dynamics, and magnetic analysis, we propose a cubic polymorph of hexagonal CoFeSn and explain why we must consider cubic CoFeSn. Through density-functional-theory calculations, we predict a robust 3D half-metallic ferromagnetic compound, CoFeSn (P4¯3m) with a Tc ∼ 693 K, calculated via the Heisenberg magnetic exchange interactions under mean-field approximation, and a magnetic moment of 3 μB. In addition, Wannier interpolation suggests anomalous Hall conductivity (AHC) and spin Hall conductivity (SHC) in cubic CoFeSn, the largest SHC at the Fermi level being ≈ 47 (h/2πe) S/cm. Our theoretical results show that spin–orbit interaction at the Fermi level brings on finite Berry flux that gives an intrinsic AHC ∼ 122 S/cm at room temperature. We note that adjusting the Fermi level can be a sensible way to achieve high values of AHC or SHC. Our findings pave the way for the realization of the quantum anomalous and spin Hall effect in half-Heusler compounds.

Extrinsic and intrinsic nonlinear Hall effects across Berry-dipole transitions

Three-dimensional Hopf insulators are a class of topological phases beyond the tenfold-way classification. At the critical point of the transition between two distinct Hopf insulators with rotational symmetry, the band-touching points are point Berry dipoles with two opposite Berry charges overlapping in a mirror-symmetric way, and carry unique Berry curvature structures leading to a special quantization of Berry flux. Close to such Berry-dipole transitions, we find that the extrinsic and intrinsic nonlinear Hall conductivity tensors in the weakly doped regime are characterized by two universal functions of the ratio between doping level and bulk energy gap, and are directly proportional to the change in Hopf invariant across the transition. Our work suggests that the nonlinear Hall effects display a generalized-sense quantized behavior across Berry-dipole transitions, establishing a correspondence between nonlinear Hall effects and Hopf invariants.

Observation of Spin-Tensor Induced Topological Phase Transitions of Triply Degenerate Points with a Trapped Ion.

Triply degenerate points (TDPs), which correspond to new types of topological semimetals, can support novel quasiparticles possessing effective integer spins while preserving Fermi statistics. Here by mapping the momentum space to the parameter space of a three-level system in a trapped ion, we experimentally explore the transitions between different types of TDPs driven by spin-tensor-momentum couplings. We observe the phase transitions between TDPs with different topological charges by measuring the Berry flux on a loop surrounding the gap-closing lines, and the jump of the Berry flux gives the jump of the topological charge (up to a 2π factor) across the transitions. For the Berry flux measurement, we employ a new method by examining the geometric rotations of both spin vectors and tensors, which lead to a generalized solid angle equal to the Berry flux. The controllability of a multilevel ion offers a versatile platform to study high-spin physics, and our Letter paves the way to explore novel topological phenomena therein.

Assessing Nontrivial Topology in Weyl Semimetals by Dichroic Photoemission

The electronic structure of Weyl semimetals features Berry flux monopoles in the bulk and Fermi arcs at the surface. While angle-resolved photoelectron spectroscopy (ARPES) is successfully used to map the bulk and surface bands, it remains a challenge to explicitly resolve and pinpoint these topological features. Here we combine state-of-the-art photoemission theory and experiments over a wide range of excitation energies for the Weyl semimetals TaAs and TaP. Our results show that simple surface-band-counting schemes, proposed previously to identify nonzero Chern numbers, are ambiguous due to pronounced momentum-dependent spectral weight variations and the pronounced surface-bulk hybridization. Instead, our findings indicate that dichroic ARPES provides an improved approach to identify Fermi arcs but requires an accurate description of the photoelectron final state.

Quantum transport evidence of isolated topological nodal-line fermions

Anomalous transport responses, dictated by the nontrivial band topology, are the key for application of topological materials to advanced electronics and spintronics. One promising platform is topological nodal-line semimetals due to their rich topology and exotic physical properties. However, their transport signatures have often been masked by the complexity in band crossings or the coexisting topologically trivial states. Here we show that, in slightly hole-doped SrAs3, the single-loop nodal-line states are well-isolated from the trivial states and entirely determine the transport responses. The characteristic torus-shaped Fermi surface and the associated encircling Berry flux of nodal-line fermions are clearly manifested by quantum oscillations of the magnetotransport properties and the quantum interference effect resulting in the two-dimensional behaviors of weak antilocalization. These unique quantum transport signatures make the isolated nodal-line fermions in SrAs3 desirable for novel devices based on their topological charge and spin transport.

Chiral Berry plasmon dispersion of the two-dimensional electron gas based on a quantum hydrodynamic model

We employ the quantum hydrodynamic model to investigate the properties of chiral Berry plasmons (CBPs) generated by a high-density two-dimensional electron gas (2DEG) film covering a semi-infinite dielectric substrate with a finite Berry flux. By coupling Maxwell's equations, Poisson's equation, and the boundary conditions, we derive the dispersion relations of plasmon with a nonzero Berry flux in detail. We present the difference in the dispersion of CBPs with quantum effects and the classical model. We show how the quantum effect, Berry curvature, the dielectric constant of the substrate, and electron density in 2DEG affect the behavior of the CBPs. Parameter dependence of the effects is calculated and discussed.

Band splitting induced Berry flux and intrinsic anomalous Hall conductivity in the NiCoMnGa quaternary Heusler compound

The anomalous transport properties of Heusler compounds become a hotspot of research in recent years due to their unique band structure and possible application in spintronics. In this paper, we report the anomalous Hall effect in polycrystalline NiCoMnGa quaternary Heusler compound by experimental means and theoretical calculations. The experimental anomalous Hall conductivity (AHC) was found at about 256 S/cm at 10K with an intrinsic contribution of ~ 121 S/cm. The analysis of Hall data reveals the presence of both extrinsic and intrinsic contributions in AHE. Our theoretical calculations show that a pair of spin-orbit coupled band formed by the band splitting due to spin-orbit interaction (SOI) at the Fermi level produces a finite Berry flux in the system that provides the intrinsic AHC about 100 S/cm, which is in good agreement with the experiment.

Ideal nodal rings of one-dimensional photonic crystals in the visible region

Three-dimensional (3D) artificial metacrystals host rich topological phases, such as Weyl points, nodal rings, and 3D photonic topological insulators. These topological states enable a wide range of applications, including 3D robust waveguides, one-way fiber, and negative refraction of the surface wave. However, these carefully designed metacrystals are usually very complex, hindering their extension to nanoscale photonic systems. Here, we theoretically proposed and experimentally realized an ideal nodal ring in the visible region using a simple 1D photonic crystal. The π-Berry phase around the ring is manifested by a 2π reflection phase’s winding and the resultant drumhead surface states. By breaking the inversion symmetry, the nodal ring can be gapped and the π-Berry phase would diffuse into a toroidal-shaped Berry flux, resulting in photonic ridge states (the 3D extension of quantum valley Hall states). Our results provide a simple and feasible platform for exploring 3D topological physics and its potential applications in nanophotonics.

Observation of chiral and slow plasmons in twisted bilayer graphene.

Moiré superlattices have led to observations of exotic emergent electronic properties such as superconductivity and strong correlated states in small-rotation-angle twisted bilayer graphene (tBLG)1,2. Recently, these findings have inspired the search for new properties in moiré plasmons. Although plasmon propagation in the tBLG basal plane has been studied by near-field nano-imaging techniques3-7, the general electromagnetic character and properties of these plasmons remain elusive. Here we report the direct observation of two new plasmon modes in macroscopic tBLG with a highly ordered moiré superlattice. Using spiral structured nanoribbons of tBLG, we identify signatures of chiral plasmons that arise owing to the uncompensated Berry flux of the electron gas under optical pumping. The salient features of these chiral plasmons are shown through their dependence on optical pumping intensity and electron fillings, in conjunction with distinct resonance splitting and Faraday rotation coinciding with the spectral window of maximal Berry flux. Moreover, we also identify a slow plasmonic mode around 0.4 electronvolts, which stems from the interband transitions between the nested subbands in lattice-relaxed AB-stacked domains. This mode may open up opportunities for strong light-matter interactions within the highly sought after mid-wave infrared spectral window8. Our results unveil the new electromagnetic dynamics of small-angle tBLG and exemplify it as a unique quantum optical platform.

Magnetic Weyl Semimetallic Phase in Thin Films of Eu_{2}Ir_{2}O_{7}.

The interplay between electronic interactions and strong spin-orbit coupling is expected to create a plethora of fascinating correlated topological states of quantum matter. Of particular interest are magnetic Weyl semimetals originally proposed in the pyrochlore iridates, which are only expected to reveal their topological nature in thin film form. To date, however, direct experimental demonstrations of these exotic phases remain elusive, due to the lack of usable single crystals and the insufficient quality of available films. Here, we report on the discovery of signatures for the long-sought magnetic Weyl semimetallic phase in (111)-oriented Eu_{2}Ir_{2}O_{7} high-quality epitaxial thin films. We observed an intrinsic anomalous Hall effect with colossal coercivity but vanishing net magnetization, which emerges right below the onset of a peculiar magnetic phase with all-in-all-out (AIAO) antiferromagnetic ordering. The anomalous Hall conductivity obtained experimentally is consistent with the theoretical prediction, likely arising from the nonzero Berry curvature emanated by Weyl node pairs near the Fermi level that act as sources and sinks of Berry flux, activated by broken cubic crystal symmetry at the top and bottom terminations of the thin film.

Holographic quantum singularity

In this study, we addressed the influence of quantum singularity on the topological state. The quantum singularity creates the defect in the momentum space ubiquitously and leads to the phase transition for the topological material. The kinetic equation reveals that the defect generates an anomaly without the characteristic energy scale. In the holographic model, the three-dimensional dislocations map into the gravitational bulk as domain walls extending along the AdS radial direction from the boundary. The creation/annihilation of the domain wall causes the quantum phase transition by ’t Hooft anomaly generation and is controlled by the gauge field. In other words, the phase transition is realized by the anomaly inflow. This ’t Hooft anomaly is caused by a phase ambiguity of the ground state resulting from the singularity in parameter space. This singularity gives the basis for the boundary’s topological state with the Berry connection. ’t Hooft anomaly’s renormalization group invariance shows that the total Berry flux is conserved in the UV layer to the IR layer. Phase transition entails domain wall constitution, which generates the entropy from the non-universal form or quantum entropy correction.

Momentum-space signatures of Berry flux monopoles in the Weyl semimetal TaAs

Since the early days of Dirac flux quantization, magnetic monopoles have been sought after as a potential corollary of quantized electric charge. As opposed to magnetic monopoles embedded into the theory of electromagnetism, Weyl semimetals (WSM) exhibit Berry flux monopoles in reciprocal parameter space. As a function of crystal momentum, such monopoles locate at the crossing point of spin-polarized bands forming the Weyl cone. Here, we report momentum-resolved spectroscopic signatures of Berry flux monopoles in TaAs as a paradigmatic WSM. We carried out angle-resolved photoelectron spectroscopy at bulk-sensitive soft X-ray energies (SX-ARPES) combined with photoelectron spin detection and circular dichroism. The experiments reveal large spin- and orbital-angular-momentum (SAM and OAM) polarizations of the Weyl-fermion states, resulting from the broken crystalline inversion symmetry in TaAs. Supported by first-principles calculations, our measurements image signatures of a topologically non-trivial winding of the OAM at the Weyl nodes and unveil a chirality-dependent SAM of the Weyl bands. Our results provide directly bulk-sensitive spectroscopic support for the non-trivial band topology in the WSM TaAs, promising to have profound implications for the study of quantum-geometric effects in solids.

Negative thermal Hall conductance in a two-dimer Shastry-Sutherland model with a π -flux Dirac triplon

We introduce an effective 2-dimer tight-binding model for the family of Shastry-Sutherland models with geometrically tunable triplon excitations. The Rashba pseudospin-orbit coupling induced by the tilted external magnetic field leads to elementary excitations having nontrivial topological properties with {\pi}-Berry flux. The interplay between the in-plane and out-of-plane magnetic field thus allows us to effectively engineer the band structure in this bosonic system. In particular, the in-plane magnetic field gives rise to Berry curvature hotspot near the bottom of the triplon band, and at the same time significantly increases the critical magnetic field for the topological triplon band. We calculate explicitly the experimental signature of the thermal Hall effect of triplons in SrCu2(BO3)2, and show a pronounced and tunabled transport signals within the accessible parameter range, particularly with a change of sign of the thermal Hall conductance. The tilted magnetic field is also useful in reducing the bandwidth of the lowest triplon band. We show it can thus be a flexible theoretical and experimental platform for the correlated bosonic topological system.

Floquet dynamics in light-driven solids

We demonstrate how the properties of light-induced electronic Floquet states in solids impact natural physical observables, such as transport properties, by capturing the environmental influence on the electrons. We include the environment as dissipative processes, such as inter-band decay and dephasing, often ignored in Floquet predictions. These dissipative processes determine the Floquet band occupations of the emergent steady state, by balancing out the optical driving force. In order to benchmark and illustrate our framework for Floquet physics in a realistic solid, we consider the light-induced Hall conductivity in graphene recently reported by J.~W.~McIver, et al., Nature Physics (2020). We show that the Hall conductivity is estimated by the Berry flux of the occupied states of the light-induced Floquet bands, in addition to the kinetic contribution given by the average band velocity. Hence, Floquet theory provides an interpretation of this Hall conductivity as a geometric-dissipative effect. We demonstrate this mechanism within a master equation formalism, and obtain good quantitative agreement with the experimentally measured Hall conductivity, underscoring the validity of this approach which establishes a broadly applicable framework for the understanding of ultrafast non-equilibrium dynamics in solids.

Visualizing Half-Metallic Bulk Band Structure with Multiple Weyl Cones of the Heusler Ferromagnet.

Using a well-focused soft x-ray synchrotron radiation beam, angle-resolved photoelectron spectroscopy was applied to a full-Heusler-type Co_{2}MnGe alloy to elucidate its bulk band structure. A large parabolic band at the Brillouin zone center and several bands that cross the Fermi level near the Brillouin zone boundary were identified in line with the results from first-principles calculations. These Fermi-level crossings are ascribed to majority spin bands that are responsible for electron transport with extremely high spin polarization especially along the direction perpendicular to the interface of magnetoresistive devices. The spectroscopy confirms there is no contribution of the minority spin bands to the Fermi surface, signifying half-metallicity for the alloy. Furthermore, two topological Weyl cones with band crossing points were identified around the X point, yielding the conclusion that Co_{2}MnGe could exhibit topologically meaningful behavior such as large anomalous Hall and Nernst effects driven by the Berry flux in its half-metallic band structure.

Topological electronic properties of silicon

The central role that materials play in human history is exemplified by the three-age division of prehistory into the stone, bronze, and iron ages. References to our present time as the information age or silicon age epitomizes the important role that this semiconducting material came to play in the development of computers and devices that permeate our daily lives. Here we show that the electronic states in silicon have nontrivial topological structures that are captured by a network of Berry flux lines that link at points of high symmetry in the Brillouin zone. This complex network has ice-nodal points where fluxes satisfy ice rules, making silicon a "nodal-chain insulator". Fixing the longitudinal momentum parallel to such flux lines yields a two-dimensional Dirac Hamiltonian for the transverse degrees of freedom. This complex Berry-flux network implies a topologically stable two-fold degeneracy along the X-W direction in all of silicon bands, a fact that is supported by crystal symmetry arguments as well as direct inspection of the vast literature on silicon band structures. Similarly to nodal-chain semimetals, we find drumhead-like states in the regions that are delimited by the projections of the bulk Berry flux network on the surface Brillouin zone.

Quantum field theory of topological spin dynamics

We develop a field theory of quantum magnets and magnetic (semi)metals, which is suitable for the analysis of their universal and topological properties. The systems of interest include collinear, coplanar and general non-coplanar magnets. At the basic level, we describe the dynamics of magnetic moments using smooth vector fields in the continuum limit. Dzyaloshinskii-Moriya interaction is captured by a non-Abelian vector gauge field, and chiral spin couplings related to topological defects appear as higher-rank antisymmetric tensor gauge fields. We distinguish type-I and type-II magnets by their equilibrium response to the non-Abelian gauge flux, and characterize the resulting lattices of skyrmions and hedgehogs, the spectra of spin waves, and the chiral response to external perturbations. The general spin-orbit coupling of electrons is similarly described by non-Abelian gauge fields, including higher-rank tensors related to the electronic Berry flux. Itinerant electrons and local moments exchange their gauge fluxes through Kondo and Hund interactions. Hence, by utilizing gauge fields, this theory provides a unifying physical picture of ``intrinsic'' and ``topological'' anomalous Hall effects, spin-Hall effects, and other correlations between the topological properties of electrons and moments. We predict ``topological'' magnetoelectric effect in materials prone to hosting hedgehogs. Links to experiments and model calculations are provided by deriving the couplings and gauge fields from generic microscopic models, including the Hubbard model with spin-orbit interactions. We establish the possible existence of novel quantum spin liquids that exhibit a fractional magnetoelectric effect, and discuss a few applications to topological magnetic conductors like Mn$_3$Sn and Pr$_2$Ir$_2$O$_7$.