Inversion Symmetry Research Articles

Giant Rashba splitting in PtTe/PtTe2 heterostructure

Achieving a large spin splitting is highly desirable for spintronic devices, which often requires breaking of the inversion symmetry. However, many atomically thin films are centrosymmetric, making them unsuitable for spintronic applications. Here, we report a strategy to achieve inversion symmetry breaking from a centrosymmetric transition metal dichalcogenide (TMDC) bilayer PtTe2, leading to a giant Rashba spin splitting. Specifically, the thermal annealing turns one layer of PtTe2 sample into a transition metal monochalcogenide (TMMC) PtTe through Te extraction, thus forming PtTe/PtTe2 heterostructure with inversion symmetry breaking. In this naturally-formed PtTe/PtTe2 heterostructure, we observe a giant Rashba spin splitting with Rashba coefficient of αR = 1.8 eV ⋅ Å, as revealed by spin- and angle-resolved photoemission spectroscopy measurements. Our work demonstrates a convenient and effective pathway for achieving pronounced Rashba splitting in centrosymmetric TMDC thin films by creating TMMC/TMDC heterostructure, thereby extending their potential applications to spintronics.

Investigation of Turbulence Characteristics Influenced by Flow Velocity, Roughness, and Eccentricity in Horizontal Annuli Based on Numerical Simulation

Annular flow channels, which are distinct from circular pipes, represent a complex flow structure widely applied in fields such as food engineering and petroleum engineering. Discovering the internal flow patterns is conducive to the study of heat and mass transfer laws, thereby playing a crucial role in optimizing flow processes and selecting equipment. However, the mechanism underlying the influence of annular turbulent flow on macro-pressure drop remains to be further investigated. This paper focuses on the roughness of both inner and outer pipes, as well as positive and negative eccentricities. Numerical simulation is employed to study the microscopic characteristics of the flow field, and the numerical model is validated through indoor experimental measurements of pressure drop laws. Further numerical simulations are conducted to explore the microscopic variations in the flow field, analyzed from the perspectives of wall shear force and turbulence characteristics. The results indicate that an increase in inner pipe roughness significantly enhances the wall shear force on both the inner and outer pipes, and vice versa. In the concentric case, wall shear force and turbulence characteristics exhibit central symmetry. Eccentricity leads to uneven distributions of velocity, turbulence intensity, and shear force, with such unevenness presenting axial symmetry under both positive and negative eccentricities. Additionally, eccentricity demonstrates turbulence drag reduction characteristics. This study enhances our understanding of the mechanism by which annular turbulent flow influences pressure drop. Furthermore, it offers theoretical backing for the design and optimization of annular space piping, thereby aiding in the enhancement of the performance and stability of associated industrial systems.

Evidence of ferroelectricity in an antiferromagnetic vanadium trichloride monolayer.

A reduced dimensionality of multiferroic materials is highly desired for device miniaturization, but the coexistence of ferroelectricity and magnetism at the two-dimensional limit is yet to be conclusively demonstrated. Here, we used a NbSe2 substrate to break both the C3 rotational and inversion symmetries in monolayer VCl3 and, thus, introduced exceptional in-plane ferroelectricity into a two-dimensional magnet. Scanning tunneling spectroscopy directly visualized ferroelectric domains and manipulated their domain boundaries in monolayer VCl3, where coexisting antiferromagnetic order with canted magnetic moments was verified by vibrating sample magnetometer measurements. Our density functional theory calculations highlight the crucial role that highly directional interfacial Cl-Se interactions play in breaking the symmetries and, thus, in introducing in-plane ferroelectricity, which was further verified by examining an ML-VCl3/graphene sample. Our work demonstrates an approach to manipulate the ferroelectric states in monolayered magnets through van der Waals interfacial interactions.

Rigidity of Symmetric Frameworks on the Cylinder

A bar-joint framework (G, p) is the combination of a finite simple graph G=(V,E) and a placement p:V→Rd. The framework is rigid if the only edge-length preserving continuous motions of the vertices arise from isometries of the space. This article combines two recent extensions of the generic theory of rigid and flexible graphs by considering symmetric frameworks in R3 restricted to move on a surface. In particular necessary combinatorial conditions are given for a symmetric framework on the cylinder to be isostatic (i.e. minimally infinitesimally rigid) under any finite point group symmetry. In every case when the symmetry group is cyclic, which we prove restricts the group to being inversion, half-turn or reflection symmetry, these conditions are then shown to be sufficient under suitable genericity assumptions, giving precise combinatorial descriptions of symmetric isostatic graphs in these contexts.

Engineering Symmetry Breaking Interfaces by Nanoscale Structural-Energetics in Orthorhombic Perovskite Thin Films.

The atomic configuration of phases and their interfaces is fundamental to materials design and engineering. Here, we unveil a transition metal oxide interface, whose formation is driven by energetic influences─epitaxial tensile strain versus oxygen octahedra connectivity─that compete in determining the orientation of an orthorhombic perovskite film. We study this phenomenon in layers of LaVO3 grown on (101) DyScO3, using atomic-resolution scanning transmission electron microscopy to measure intrinsic markers of orthorhombic symmetry. We identify that the film resolves this energetic conflict by switching its orientation by 90° at an atomically flat plane within its volume, not at the film-substrate interface. At either side of this "switching plane", characteristic orthorhombic distortions tend to zero to couple mismatched oxygen octahedra rotations. The resulting boundary is highly energetic, which makes it a priori unlikely; by using second-principles atomistic modeling, we show how its formation requires structural relaxation of an entire film grown beyond a critical thickness measuring tens of unit cells. The switching plane breaks the inversion symmetry of the Pnma orthorhombic structure, and sharply joins two regions, a thin intermediate layer and the film bulk, that are held under different mechanical strain states. By contacting two distinct phases of one compound that would never otherwise coexist, this alternative type of interface will enable nanoscale engineering of functional systems, such as creating a chemically uniform but magnetically inhomogeneous heterostructure.

Post‐synthetic Breaking of Inversion Symmetry in Metal Complex‐based Host–guest Systems

Post‐synthetic Breaking of Inversion Symmetry in Metal Complex‐based Host–guest Systems

Intrinsic and Extrinsic Unity for Chiral-Spin Alignment and Charge-to-Spin Conversion Induced by the Rashba-Edelstein Effect.

Reducing the dimensionality in layered materials typically yields properties distinct from bulk properties. In systems with broken inversion symmetry, strong spin-orbit coupling induces relativistic electron interactions such as the Rashba-Edelstein effect (REE). Initially proposed in two-dimensional magnets, applying the REE theory to real three-dimensional systems poses challenges, necessitating experimental validation. In this study, we empirically ascertained an REE-induced intrinsic and extrinsic fundamental unity between two distinct and dissimilar phenomena, namely, charge-to-spin conversion and chiral-spin alignment. Atomically thin quasi-two-dimensional ferromagnetic materials were used to observe such universal unity by examining the thickness dependences of the Heisenberg exchange interaction, the Dzyaloshinskii-Moriya interaction, and spin-orbit torques. The results revealed a correlation that is highly consistent with the underlying theoretical REE model. These findings not only highlight the role of REE in fundamental physics but also illuminate the intricate impact of interfacial effects on magnetic materials.

Dzyaloshinskii–Moriya interaction and current-induced magnetization switching in ferrimagnetic [Co/Gd]N multilayers

The Dzyaloshinskii–Moriya interactions (DMI) naturally breaking spatial inversion symmetry are considered a key factor in realizing current-induced magnetization switching by spin–orbit torque (SOT) without an in-plane assistance field. Ferrimagnets (FIM) composed of rare earth and transition metals show peculiar properties near the magnetic compensation point, including an exceptionally high SOT efficiency and a significantly enhanced DMI effective field. Here, we investigate FIM [Co/Gd]N multilayers with a magnetic compensation by varying the number of stacking layers (N). The net magnetization is dominated by Co and Gd at small and large N, respectively, with the magnetic compensation point located at N = 9. The DMI effective field, obtained by using a magnetic droplet model, increases substantially when the multilayer approaches its magnetic compensation. Correspondingly, we found the emergence of current-induced magnetization switching in the Gd-dominated region, among which the case of N = 10 was realized without an assistance field. We attribute such magnetization switching behavior to the symmetry breaking provided by DMI, together with its large value and the huge SOT associated with it near the magnetic compensation. Our work establishes the direct connection between the DMI and the field-free SOT switching in rare-earth/transition-metal FIM systems.

Terahertz broadband one-way transparency with spontaneous magnon decay.

Nonreciprocity is a phenomenon in which broken spatial inversion symmetry appears on a macroscopic scale and is an essential issue in condensed matter physics. Directional dichroism is the nonreciprocal phenomenon of light; the light transmittance varies depending on the direction of light propagation. It arises from interference between electromagnetic fields of light, resulting in the nonreciprocal transmittance determined by the resonance light absorption. For the maximum interference, it shows one-way transparency, and achieving this is an outstanding experimental challenge. Concerning energy dispersion, the resonance generally occurs only at a specific energy with a narrow bandwidth. When the excited state of the magnon spontaneously decays into lower energy states, the absorption linewidth gets broader. Here, using electron spin resonance, we identify the specific absorption mode in a multiferroic material Sr2CoSi2O7 with the spontaneous magnon decay accompanied by the maximum interference, achieving the broadband one-way transparency.

Quantum Geometric Moment Encodes Stacking Order of Moiré Matter.

Exploring the topological characteristics of electronic bands is essential in condensed matter physics. Moiré materials featuring flat bands provide a versatile platform for engineering band topology and correlation effects. In moiré materials that break either time-reversal symmetry or inversion symmetry or both, electronic bands exhibit Berry curvature hotspots. Different stacking orders in these materials result in varied Berry curvature distributions within the flat bands, even when the band dispersion remains similar. However, experimental studies probing the impact of stacking order on the quantum geometric quantities are lacking. 1.4° twisted double bilayer graphene (TDBG) facilitates two distinct stacking orders (AB-AB, AB-BA) and forms an inversion broken moiré superlattice with electrically tunable flat bands. The valley Chern numbers of the flat bands depend on the stacking order, and the nonlinear Hall (NLH) effect distinguishes the differences in Berry curvature dipole (BCD), the first moment of Berry curvature. The BCD exhibits antisymmetric behavior, flipping its sign with the polarity of the perpendicular electric field in AB-AB TDBG, while it displays a symmetric behavior, maintaining the same sign regardless of the electric field's polarity in AB-BA TDBG. This approach electronically detects stacking-induced quantum geometry, while opening a pathway to quantum geometry engineering anddetection.

Two Quantum Triatomic Hamiltonians: Applications to Non-Adiabatic Effects in NO2 Spectroscopy and in Kr + OH(A2Σ+) Electronic Quenching

This review discusses two triatomic Hamiltonians and their applications to some non-adiabatic spectroscopic and collision problems. Carter and Handy in 1984 presented the first Hamiltonian in bond lengths–bond angle coordinates, that is here applied for studying the NO2 spectroscopy: vibronic states, internal dynamics, and interaction with the radiation due to the X˜2A′(A1)−A˜2A′(B2) conical intersection. The second Hamiltonian was reported by Tennyson and Sutcliffe in 1983 in Jacobi coordinates and is here employed in the study of the Kr + OH(A2Σ+) electronic quenching due to conical intersection and Renner–Teller interactions among the 12A′, 22A′, and 12A″ electronic species. Within the non-relativistic approximation and the expansion method in diabatic electronic representations, the formalism is exact and allows a unified study of various non-adiabatic interactions between electronic states. The rotation, inversion, and nuclear permutation symmetries are considered for defining rovibronic representations, which are symmetry adapted for ABC and AB2 molecules, and the matrix elements of the Hamiltonians are then computed.

Magnetic-resonance-induced non-linear current response in magnetic Weyl semimetals

In this work, we propose a geometric non-linear current response induced by magnetic resonance in magnetic Weyl semimetals. This phenomenon is in analog to the quantized circular photogalvanic effect (de Juan et al., Nat. Commun. 8:15995, 2017) previously proposed for Weyl semimetal phases of chiral crystals. However, the non-linear current response in our case can occur in magnetic Weyl semimetals where time-reversal symmetry, instead of inversion symmetry, is broken. The occurrence of this phenomenon relies on the special coupling between Weyl electrons and magnetic fluctuations induced by magnetic resonance. To further support our analytical solution, we perform numerical studies on a model Hamiltonian describing the Weyl semimetal phase in a topological insulator system with ferromagnetism.

Theoretical Investigation of Stacked Two-Dimensional Transition-Metal Dichalcogenide Materials: The Role of Chemical Species and Number of Monolayers.

We report a theoretical investigation, based on density functional theory calculations, of the role of chalcogen species and the number of monolayers in the physical-chemical properties of multilayer two-dimensional transition-metal dichalcogenides (TMDs, MQ2), where M belongs to groups 8 and 10 of the periodic table, Q = S, Se, or Te, and the multilayer is composed of 1 to 6 layers. From the analysis of structural energetic, and electronic properties, we found significant changes in lattice parameters and exfoliation energies as a function of the number of layers, particularly affected by the chalcogen Q species. The TMDs in group 8 exhibit similar lattice parameters for the same choice of chalcogens, making them suitable for constructing commensurate heterostructures, while the crystal phase and the lattice parameter of the TMDs in group 10 strongly depend on the choice of the transition-metal species. Furthermore, the decreasing trend of electronegativity from S to Te results in stronger exfoliation energies due to lower surface charges, thus governing the structural and electronic characteristics of few-layer TMDs. We find unexpected electronic characteristics, such as band gap increases driven by spin-orbit coupling for certain compositions, the emergence of polarization electric fields due to point inversion symmetry breaking, and semiconductor-to-metal transitions with minimal layer additions to the monolayer. The presence of sulfur improves the sensitivity of the surface properties, enabling precise tuning of band edge positions with the layer number.

Surface magnetism in Fe3GeTe2 van der Waals ferromagnet

Abstract The surface magnetization of Fe3GeTe2 was examined by low-energy electron microscopy (LEEM) using an off-normal incidence electron beam. We found that the 180° domain walls are of Bloch type. Temperature-dependent LEEM measurements yield a surface magnetization with a surface critical exponent β1 = 0.79 ± 0.02. This result is consistent with surface magnetism in the 3D semi-infinite Heisenberg (β1 = 0.84 ± 0.01) or Ising (β1 = 0.78 ± 0.02) models, which is distinctly different from the bulk exponent (β = 0.34 ± 0.07). The measurements reveal the power of LEEM with a tilted beam to determine magnetic domain structure in quantum materials without the need for the use of spin-polarized electrons. Single crystal diffraction measurements reveal inversion symmetry-breaking weak peaks and yield space group P-6m2. This Fe site defect-derived loss of inversion symmetry enables the formation of skyrmions in this Fe3GeTe2 crystal.

Valley polarization in two-dimensional zero-net-magnetization magnets

Valleytronics in two-dimensional (2D) zero-net-magnetization magnets exhibits ultradense and ultrafast potential due to their intrinsic advantages of zero stray field and terahertz dynamics. The zero-net-magnetization magnets mainly include PT-antiferromagnet [the joint symmetry (PT) of space inversion symmetry (P) and time-reversal symmetry (T)], altermagnet, and fully compensated ferrimagnet. In these magnets, achieving controllable valley polarization is extremely important to the application of valleytronics. In this perspective article, we provide some possible design strategies to achieve valley polarization and spin-splitting in 2D zero-net-magnetization magnets. Furthermore, the anomalous valley Hall effect can be achieved in these zero-net-magnetization magnets. These proposed design strategies can encourage more theoretical and experimental works to explore valley polarization in these eminent magnets.

Hidden asymmetry in one-dimensional alignment of chiral molecules.

We studied the inversion symmetry of an ensemble of chiral molecules. We clarified that for rigid molecules aligned by dipole transitions, the positions of any two atoms depend on the molecular chirality, owing to the parity-odd second-rank tensors. This type of asymmetry, hidden in the so-called one-dimensional alignment, such as cos2θ, can be understood on the basis of the equivalence of inversion and rotation for any two points in space. Perfect chiral sensitivity is achieved when the transition dipole moment is 45° to an axis perpendicular to both position vectors of the two atoms. The positions of two specific atoms are calculated for a chiral isotopomer and methyloxirane using the spherical harmonic addition theorem. We discuss the absolute configuration and the orientation of chiral molecules.

Tunable sliding ferroelectricity in two-dimensional van der Waals RuX2 (X = Cl, Br, and I) multiferroic layers

Two-dimensional (2D) van der Waals (vdW) materials offer vast potential for designing ferroelectrics with desired properties through simple layer stacking. Here, based on first principles, we demonstrate that the vdW layered crystals RuX2 (X = Cl, Br, and I) are a class of 2D multiferroic sliding ferroelectrics. The stacking of two magnetic RuX2 monolayers with the same orientation breaks the spatial inversion symmetry, resulting in a stable vertical polarization. In addition, the direction of polarization can be reversed through slight interlayer sliding, in which it only needs to overcome the small energy barrier of 7.16 meV. Among these layered crystals, the bilayer RuI2 not only possesses a remarkable sliding ferroelectricity of 0.49 pC/m but also exhibits stable long-range magnetic order due to its large magnetic anisotropy energy. When the RuI2 stack is increased to trilayers, the polarization significantly increases to 1.03 pC/m, which is much larger than that of its bilayer structure. Furthermore, the application of compressive strain results in a substantial increase in vertical polarization. This work provides an efficient method for designing 2D multiferroic sliding ferroelectric materials by stack engineering.

Reconstructing Cranial Modification Practices: Methods, Motivations, and Evolution of Occipital Modification in Prehistoric China

ABSTRACTOccipital modification, the predominant form of cranial artificial modification in Prehistoric China, is characterized by its extensive and dense distribution, a rarity globally. This study aims to reconstruct the methods, processes, and motivations underlying occipital modification, investigating its inception, evolution, and eventual cessation in Prehistoric China. Morphological observations were conducted on over 800 individuals from representative sites like Baligang and Chuwan of the Yangshao culture, with 265 well‐preserved skulls subjected to three‐dimensional scanning, modeling, and measurement, segmented into BLG‐E, BLG‐M, and CW groups for detailed analysis. Observations and measurements revealed significant differences in occipital modification among the groups: the BLG‐E group displayed a high modification rate, featuring severe modification with a near‐perpendicular tilt angle and random lateral asymmetry; the BLG‐M group exhibited reduced modification rate and severity, with lateral asymmetry akin to BLG‐E but more variable tilt angles; and the CW group showed moderate occipital modification with variable tilt angles, though with greater central symmetry. Two distinct practices were identified: “primary utilitarian modification,” likely an expedient measure for infant care during early agricultural development, and “standardized symmetrical modification,” reflecting aesthetic preferences during a more mature agricultural stage. Following the transition from utilitarian to aesthetic purposes, the occipital modification disappeared in the Final Neolithic period, during the Longshan culture stage, possibly because of the emergence of new, complex hairstyle trends.

A tunable entangled photon-pair source based on a Van der Waals insulator

Scalable quantum photonic devices drive the development of compact sources of entangled photons, which are pivotal for quantum communication, computing, and cryptography. In this work, we present entangled photon pair generation in rhombohedral boron nitride (r-BN), leveraging its unique optical and structural properties. Unlike conventional hexagonal boron nitride, which suffers from reduced nonlinear response due to centrosymmetric structure in even-layered stacks, r-BN features interlayer ABC stacking and maintains robust in-plane inversion symmetry. These characteristics lead to highly efficient entangled photon generation. Our system demonstrates an entangled photon pair generation rate up to 8667 Hz/(mW·mm) and offers a tunable platform for Bell state generation by simply adjusting the pump polarization, without compromising the entanglement quality or generation efficiency. The polarization entangled state is measured with a fidelity up to 94%. This advancement not only marks a significant step towards ultrathin, scalable quantum devices but also establishes r-BN as a promising candidate for on-chip integrated quantum optical applications.

Thermal biasing for lattice symmetry breaking and topological edge state imaging

Marginally twisted bilayer graphene with large Bernal stacked domains involves symmetry-breaking features with domain boundaries that exhibit topological edge states normally obscured by trivial bands. A vertical electric field can activate these edge states through inversion symmetry breaking and opening a bandgap around the edge state energy. However, harnessing pristine topological states at the Fermi level without violent electric or magnetic bias remains challenging, particularly above room temperature. Here, we demonstrate that thermal biasing can break the vertically stacked lattice symmetry of twisted bilayer graphene via the interatomic Seebeck effect, enabling thermoelectric imaging of topological edge states at tunable Fermi levels above room temperature. The high spatial resolution in the imaging is achieved through atomic-scale thermopower generation between a metallic tip and the sample, reflecting the local electronic band structure and its derivative features of twisted bilayer graphene at the Fermi level. Our findings suggest that thermal biasing provides a sensitive, non-destructive method for symmetry breaking and topological state imaging above room temperature, making it a practical and accessible approach.