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Weyl semimetal (WSM) states can be achieved by breaking spatial-inversion symmetry or time reversal symmetry. However, the anisotropy of the energy reduction contributing to the emergence of WSM states has seldom been investigated by experiments. A van der Waals metal MoTe2 exhibits a type-II WSM phase below the monoclinic-to-orthorhombic-phase-transition temperature Tc ~ 250 K. Here, we report a combined linearly-polarized optical-spectroscopy and electrical-transport study of MoTe2 at different temperatures. The Drude components in the a-axis, b-axis and c-axis optical conductivity spectra, together with the metallic out-of-plane and in-plane electrical resistivities, indicate the coherent inter-layer and in-plane charge transports. Moreover, the Drude weight in {\sigma}1a({\omega}), rather than the Drude weights in {\sigma}1b({\omega}) and {\sigma}1c({\omega}), decreases dramatically below Tc, which exhibits a highly anisotropic decrease in its Drude weight and thus suggests a strongly anisotropic reduction of the electronic kinetic energy in the WSM phase. Furthermore, below Tc, due to the in-plane anisotropic spectral-weight transfer from Drude component to high-energy region, the in-plane inter-band-absorption anisotropy increases remarkably around 770 meV, and has the largest value (~ 0.68) of normalized linear dichroism among the reported type-II WSMs. Our work sheds light on seeking new WSMs and developing novel photonic devices based on WSMs., Comment: Accepted by Laser & Photonics Reviews

The balancing of chemical equations is a basic problem in chemistry. A commonly employed method is to convert the task to a linear algebra problem, and then solve the null space of the constructed formula matrix. However, in this method, the directly obtained solution may be invalid, and there is no canonical choice of independent basis reactions. Here, we show that these drawbacks originate from the fact that the fundamental structure of solutions here is not a linear space but a positive affine monoid. This new understanding enables a systematic approach and a complete description of all possible reactions by a unique set of independent elementary reactions, called Hilbert-basis reactions. By clarifying its underlying mathematical structure, our work offers a new perspective on this old problem of balancing chemical equations., Comment: 4 pages

Spin and valley are two fundamental properties of electrons in crystals. The similarity between them is well understood in valley-contrasting physics established decades ago in two-dimensional (2D) materials like graphene--with broken inversion symmetry, the two valleys in graphene exhibit opposite orbital magnetic moments, similar to the spin-1/2 behaviors of electrons, and opposite Berry curvature that leads to a half topological charge. However, valley-contrasting physics has never been explored in 3D crystals. Here, we develop a 3D acoustic crystal exhibiting 3D valley-contrasting physics. Unlike spin that is fundamentally binary, valley in 3D can take six different values, each carrying a vortex in a distinct direction. The topological valley transport is generalized from the edge states of 2D materials to the surface states of 3D materials, with interesting features including robust propagation, topological refraction, and valley-cavity localization. Our results open a new route for wave manipulation in 3D space., Comment: 8 pages, 5 figures

Electric control of spin in insulators is desired for low-consumption and ultrafast spintronics, but the underlying mechanism remains largely unexplored. Here, we propose an intrinsic effect of dynamic spin generation driven by time-varying electric field. In the intraband response regime, it can be nicely formulated as a Berry curvature effect and leads to two phenomena that are forbidden in the $dc$ limit: linear spin generation in nonmagnetic insulators and intrinsic N{\'e}el spin-orbit torque in $\mathcal{PT}$-symmetric antiferromagnetic insulators. These phenomena are driven by the time derivative of field rather than the field itself, and have a quantum origin in the first-order dynamic anomalous spin polarizability. Combined with first-principles calculations, we predict sizable effects driven by terahertz field in nonmagnetic monolayer Bi and in antiferromagnetic even-layer MnBi$_2$Te$_4$, which can be detected in experiment.

We propose an intrinsic nonlinear spin Hall effect, which enables the generation of collinearly-polarized spin current in a large class of nonmagnetic materials with the corresponding linear response being symmetry-forbidden. This opens a new avenue for field-free switching of perpendicular magnetization, which is required for the next-generation information storage technology. We develop the microscopic theory of this effect, and clarify its quantum origin in band geometric quantities which can be enhanced by topological nodal features. Combined with first-principles calculations, we predict pronounced effects at room temperature in topological metals $\mathrm{PbTaSe_{2}}$ and PdGa. Our work establishes a fundamental nonlinear response in spin transport, and opens the door to exploring spintronic applications based on nonlinear spin Hall effect.

The study of band connectivity is a fundamental problem in condensed matter physics. Here, we develop a new method for analyzing band connectivity, which completely solves the outstanding questions of the reducibility and decomposition of band complexes. By translating the symmetry conditions into a set of band balance equations, we show that all possible band structure solutions can be described by a positive affine monoid structure, which has a unique minimal set of generators, called Hilbert basis. We show that Hilbert basis completely determine whether a band complex is reducible and how it can be decomposed. The band complexes corresponding to Hilbert basis vectors, termed as Hilbert band complexes (HBCs), can be regarded as elementary building blocks of band structures. We develop algorithms to construct HBCs, analyze their graph features, and merge them into large complexes. We find some interesting examples, such as HBCs corresponding to complete bipartite graphs, and complexes which can grow without bound by successively merging a HBC., Comment: 9 pages, 7 figures

2D topological insulators promise novel approaches towards electronic, spintronic, and quantum device applications. This is owing to unique features of their electronic band structure, in which bulk-boundary correspondences enforces the existence of 1D spin-momentum locked metallic edge states - both helical and chiral - surrounding an electrically insulating bulk. Forty years since the first discoveries of topological phases in condensed matter, the abstract concept of band topology has sprung into realization with several materials now available in which sizable bulk energy gaps - up to a few hundred meV - promise to enable topology for applications even at room-temperature. Further, the possibility of combining 2D TIs in heterostructures with functional materials such as multiferroics, ferromagnets, and superconductors, vastly extends the range of applicability beyond their intrinsic properties. While 2D TIs remain a unique testbed for questions of fundamental condensed matter physics, proposals seek to control the topologically protected bulk or boundary states electrically, or even induce topological phase transitions to engender switching functionality. Induction of superconducting pairing in 2D TIs strives to realize non-Abelian quasiparticles, promising avenues towards fault-tolerant topological quantum computing. This roadmap aims to present a status update of the field, reviewing recent advances and remaining challenges in theoretical understanding, materials synthesis, physical characterization and, ultimately, device perspectives.

We show that the three commonly employed approaches that define the same intrinsic linear anomalous Hall response actually lead to different results for intrinsic nonlinear transport. The difference arises from an intrinsic anomalous distribution. It originates from scattering, but its value is completely independent of scattering, because it represents the local equilibration of electron wave packets with field corrected energy. As a manifestation, we find that under ac driving, the intrinsic contributions in rectified component and in double-frequency component exhibit distinct frequency dependence, which can be probed in experiment. Using first-principles calculations, we estimate the signals that can be probed in antiferromagnetic CuMnAs.

Molybdenum sulfide (MoS$_2$) has attracted significant attention due to its great potential as a low-cost and efficient catalyst for the hydrogen evolution reaction. Developing a facile, easily upscalable, and inexpensive approach to produce catalytically active nanostructured MoS$_2$ with a high yield would significantly advance its practical application. Colloidal synthesis offers several advantages over other preparation techniques to overcome the low reaction yield of exfoliation and drawbacks of expensive equipment and processes used in chemical vapor deposition. In this work, we report an efficient synthesis of alloyed Re$_x$Mo$_{1-x}$S$_2$ nanoflakes with an enlarged interlayer distance, among which the composition Re$_{0.55}$Mo$_{0.45}$S$_2$ exhibits excellent catalytic performance with overpotentials as low as 79 mV at 10 mA/cm2 and a small Tafel slope of 42 mV/dec. Density functional theory calculations prove that enlarging the distance between layers in the Re$_x$Mo$_{1-x}$S$_2$alloy can greatly improve its catalytic performance due to a significantly reduced free energy of hydrogen adsorption. The developed approach paves the way to design advanced transition metal dichalcogenide-based catalysts for hydrogen evolution and to promote their large-scale practical application.

Real topological phases protected by the spacetime inversion (P T) symmetry are a current research focus. The basis is that the P T symmetry endows a real structure in momentum space, which leads to Z2 topological classifications in 1D and 2D. Here, we provide solutions to two outstanding problems in the diagnosis of real topology. First, based on the stable equivalence in K-theory, we clarify that the 2D topological invariant remains well defined in the presence of nontrivial 1D invariant, and we develop a general numerical approach for its evaluation, which was hitherto unavailable. Second, under the unit-cell convention, noncentered P T symmetries assume momentum dependence, which violates the presumption in previous methods for computing the topological invariants. We clarify the classifications for this case and formulate the invariants by introducing a twisted Wilson-loop operator for both 1D and 2D. A simple model on a rectangular lattice is constructed to demonstrate our theory, which can be readily realized using artificial crystals.

The spin Hall effect (SHE) allows efficient generation of spin polarization or spin current through charge current and plays a crucial role in the development of spintronics. While SHE typically occurs in non-magnetic materials and is time-reversal even, exploring time-reversal-odd (T-odd) SHE, which couples SHE to magnetization in ferromagnetic materials, offers a new charge-spin conversion mechanism with new functionalities. Here, we report the observation of giant T-odd SHE in Fe3GeTe2/MoTe2 van der Waals heterostructure, representing a previously unidentified interfacial magnetic spin Hall effect (interfacial-MSHE). Through rigorous symmetry analysis and theoretical calculations, we attribute the interfacial-MSHE to a symmetry-breaking induced spin current dipole at the vdW interface. Furthermore, we show that this linear effect can be used for implementing multiply-accumulate operations and binary convolutional neural networks with cascaded multi-terminal devices. Our findings uncover an interfacial T-odd charge-spin conversion mechanism with promising potential for energy-efficient in-memory computing.

Andreev reflection at a normal-superconductor interface may be accompanied with an anomalous spatial shift. The studies so far are limited to the top incidence configuration. Here, we investigate this effect in the side incidence configuration, with the interface parallel to the principal axis of superconductor. We find that the shift exhibits rich behaviors reflecting the character of pair potential. It has two contributions: one from the $k$-dependent phase of pair potential, and the other from the evanescent mode. For chiral $p$-wave pairing, the pairing phase contribution is proportional to the chirality of pairing and is independent of excitation energy, whereas the evanescent mode contribution is independent of chirality and is nonzero only for excitation energy below the gap. The two contributions also have opposite parity with respect to the incident angle. For $d_{x^{2}-y^{2}}$-wave pairing, only the evanescent mode contribution exists, and the shift exhibits suppressed zones in incident angles, manifesting the superconducting nodes. The dependence of the shift on other factors, such as the angle of incident plane and Fermi surface anisotropy, are discussed.

Realizing ideal Weyl semimetal state with a single pair of Weyl points has been a long-sought goal in the field of topological semimetals. Here, we reveal such a state in the Cr-based half-Heusler compounds XCrTe (X=K, Rb). We show that these materials have a half metal ground state, with Fermi level crossing only one spin channel. Importantly, the Fermi surface is clean, consisting of the minimal number (i.e., a single pair) of spin-polarized Weyl points, so the state represents an ideal Weyl half semimetal. We show that the locations of the two Weyl points and the associated Chern vector can be flexibly tuned by rotating the magnetization vector. The minimal surface Fermi arc pattern and its contribution to anomalous Hall transport are discussed. Our finding offers an ideal material platform for exploring magnetic Weyl fermions, which will also facilitate the interplay between Weyl physics and spintronics.

It has been theoretically predicted that perturbation of the Berry curvature by electromagnetic fields gives rise to intrinsic nonlinear anomalous Hall effects that are independent of scattering. Two types of nonlinear anomalous Hall effects are expected. The electric nonlinear Hall effect has recently begun to receive attention, while very few studies are concerned with the magneto-nonlinear Hall effect. Here, we combine experiment and first-principles calculations to show that the kagome ferromagnet Fe$_3$Sn$_2$ displays such a magneto-nonlinear Hall effect. By systematic field angular and temperature-dependent transport measurements, we unambiguously identify a large anomalous Hall current that is linear in both applied in-plane electric and magnetic fields, utilizing a unique in-plane configuration. We clarify its dominant orbital origin and connect it to the magneto-nonlinear Hall effect. The effect is governed by the intrinsic quantum geometric properties of Bloch electrons. Our results demonstrate the significance of the quantum geometry of electron wave functions from the orbital degree of freedom and open up a new direction in Hall transport effects., Comment: 18 pages, 4 figures, featured in Physics: Viewpoint and Editors' suggestions

3D Dirac semimetals with square-net non-symmorphic symmetry, such as ternary ZrXY (X=Si, Ge; Y=S, Se, Te) compounds, have attracted significant attention owing to the presence of topological nodal lines, loops, or networks in their bulk. Orbital symmetry plays a profound role such materials as the different branches of the nodal dispersion can be distinguished by their distinct orbital symmetry eigenvalues. The presence of different eigenvalues suggests that scattering between states of different orbital symmetry may be strongly suppressed. Indeed, in ZrSiS, there has been no clear experimental evidence of quasiparticle scattering between states of different symmetry eigenvalue has been reported at small wave vector $q$. Here we show, using quasiparticle interference (QPI), that atomic step-edges in the ZrSiS surface facilitate quasiparticle scattering between states of different symmetry eigenvalues. This symmetry eigenvalue mixing quasiparticle scattering is the first to be reported for ZrSiS and contrasts quasiparticle scattering with no mixing of symmetry eigenvalues, where the latter occurs with scatterers preserving the glide mirror symmetry of the crystal lattice, e.g., native point defects in ZrSiS. Finally, we show that the electronic structure of the ZrSiS surface, including its unique floating band surface state (FBSS), can be tuned by a vertical electric field locally applied by the tip of a scanning tunneling microscope (STM), enabling control of a spin-orbit induced avoided crossing near the Fermi level by as much as 300%.

Effects manifesting quantum geometry have been a focus of physics research. Here, we reveal that quantum metric plays a crucial role in nonlinear electric spin response, leading to a quantum metric spin-orbit torque. We argue that enhanced quantum metric can occur at band (anti)crossings, so the nonlinear torque could be amplified in topological metals with nodal features close to Fermi level. By applying our theory to magnetic Kane-Mele model and monolayer CrSBr, which feature nodal lines and Weyl points, we demonstrate that the quantum metric torque dominates the response, and its magnitude is significantly enhanced by topological band structures, which even surpasses the previously reported linear torques and is sufficient to drive magnetic switching by itself.

In the field of symmetry-protected topological phases, a common wisdom is that the symmetries fix the topological classifications, but they alone cannot determine whether a system is topologically trivial or not. Here, we show that this is no longer true in cases where symmetries are projectively represented. Particularly, the Zak phase, a topological invariant of a one-dimensional system, can be entirely determined by the projective symmetry algebra (PSA). To demonstrate this remarkable effect, we propose a minimal model, termed as flux Su-Schrieffer-Heeger (SSH) model, where the bond dimerization in the original SSH model is replaced by a flux dimerization. We present experimental realization of our flux SSH model in an electric-circuit array, and our predictions are directly confirmed by experimental measurement. Our work refreshes the understanding of the relation between symmetry and topology, opens up new avenues for exploring PSA determined topological phases, and suggests flux dimerization as a novel approach for designing topological crystals., Comment: 6 pages, 3 figures

Time-reversal-odd ($\mathcal{T}$-odd) nonlinear current response has been theoretically proposed and experimentally confirmed recently. However, the role of disorder scattering in the response, especially whether it contributes to the $\sigma_{xx}$-independent term, has not been clarified. In this work, we derive a general scaling law for this effect, which accounts for multiple scattering sources. We show that the nonlinear conductivity is generally a quartic function in $\sigma_{xx}$. Besides intrinsic contribution, extrinsic contributions from scattering also enter the zeroth order term, and their values can be comparable to or even larger than the intrinsic one. Terms beyond zeroth order are all extrinsic. Cubic and quartic terms must involve skew scattering and they signal competition between at least two scattering sources. The behavior of zeroth order extrinsic terms is explicitly demonstrated in a Dirac model. Our finding reveals the significant role of disorder scattering in $\mathcal{T}$-odd nonlinear transport, and establishes a foundation for analyzing experimental result., Comment: 6 pages, 1 figure

Quadratic nodal point (QNP) in two dimensions has so far been reported only in nonmagnetic materials and in the absence of spin-orbit coupling. Here, by first-principles calculations and symmetry analysis, we predict stable QNP near Fermi level in a two-dimensional kagome metal-organic framework material, Cr$_3$(HAB)$_2$, which features noncollinear antiferromagnetic ordering and sizable spin-orbit coupling. Effective kp and lattice models are constructed to capture such magnetic QNPs. Besides QNP, we find Cr$_3$(HAB)$_2$ also hosts six magnetic linear nodal points protected by mirror as well as $C_{2z}T$ symmetry. Properties associated to these nodal points, such as topological edge states and quantized optical absorbance, are discussed.

Realizing topological semimetal states with novel emergent fermions in magnetic materials is a focus of current research. Based on first-principle calculations and symmetry analysis, we reveal interesting magnetic emergent fermions in an existing material MnB2. In the temperature range from 157 K to 760 K, MnB2 is a collinear antiferromagnet. We find the coexistence of eightfold nodal points and nodal net close to the Fermi level, which are protected by the spin group in the absence of spin-orbit coupling. Depending on the Neel vector orientation, consideration of spin-orbit coupling will either open small gaps at these nodal features, or transform them into magnetic linear and quadratic Dirac points and nodal rings. Below 157 K, MnB2 acquires weak ferromagnetism due to spin tilting. We predict that this transition is accompanied by a drastic change in anomalous Hall response, from zero above 157 K to 200 $\Omega\cdot \text{cm}^{-1}$ below 157 K., Comment: 5 figures and 7 pages

Two-dimensional (2D) ferrovalley semiconductor (FVSC) with spontaneous valley polarization offers an exciting material platform for probing Berry phase physics. How FVSC can be incorporated in valleytronic device applications, however, remain an open question. Here we generalize the concept of metal/semiconductor (MS) contact into the realm of valleytronics. We propose a half-valley Ohmic contact based on FVSC/graphene heterostructure where the two valleys of FVSC separately forms Ohmic and Schottky contacts with those of graphene, thus allowing current to be valley-selectively injected through the `Ohmic' valley while being blocked in the `Schottky' valley. We develop a theory of contact-limited valley-contrasting current injection and demonstrate that such transport mechanism can produce gate-tunable valley-polarized injection current. Using RuCl$_2$/graphene heterostructure as an example, we illustrate a device concept of valleytronic barristor where high valley polarization efficiency and sizable current on/off ratio, can be achieved under experimentally feasible electrostatic gating conditions. These findings uncover contact-limited valley-contrasting current injection as an efficient mechanism for valley polarization manipulation, and reveals the potential of valleytronic MS contact as a functional building block of valleytronic device technology., Comment: 9 pages, 5 figures

Chiral phonons have attracted increasing attention, as they play important roles in many different systems and processes. However, a method to control phonon chirality by external fields is still lacking. Here, we propose that in displacement-type ferroelectric materials, an external electric field can reverse the chirality of chiral phonons via ferroelectric switching. Using first-principles calculations, we demonstrate this point in the well known two-dimensional ferroelectric In$_2$Se$_3$. This reversal may lead to a number of electrically switchable phenomena, such as chiral phonon induced magnetization, phonon Hall effect, and possible interface phonon modes at ferroelectric domain boundaries. Our work offers a new way to control chiral phonons, which could be useful for the design of thermal or information devices based on them., Comment: 5 pages, 5 figures

The sustainable development of next-generation device technology is paramount in the face of climate change and the looming energy crisis. Tremendous efforts have been made in the discovery and design of nanomaterials that achieve device-level sustainability, where high performance and low operational energy cost are prioritized. However, many of such materials are composed of elements that are under threat of depletion and pose elevated risks to the environment. The role of material-level sustainability in computational screening efforts remains an open question thus far. Here we develop a general van der Waals materials screening framework imbued with sustainability-motivated search criteria. Using ultrawide bandgap (UWBG) materials as a backdrop -- an emerging materials class with great prospects in dielectric, power electronics, and ultraviolet device applications, we demonstrate how this screening framework results in 25 sustainable UWBG layered materials comprising only of low-risks elements. Our findings constitute a critical first-step towards reinventing a more sustainable electronics landscape beyond silicon, with the framework established in this work serving as a harbinger of sustainable 2D materials discovery., Comment: 17 pages, 8 figures

We theoretically investigate the nonlinear response current of a two-dimensional system under an in-plane magnetic field. Based on the extended semiclassical theory, we develop a unified theory including both longitudinal and transverse currents and classify contributions according to their scaling with the relaxation time. Besides time-reversal-even contributions, we reveal a previously unknown time-reversal-odd contribution to the Hall current, which occurs in magnetic systems, exhibits band geometric origin, and is linear in relaxation time. We show that the different contributions exhibit different symmetry characters, especially in their angular dependence on the field orientation, which can be used to distinguish them in experiment. The theory is explicitly demonstrated in the study of the Rashba model. Our work presents a deepened understanding of nonlinear planar transport, proposes approaches to distinguish different contributions, and sheds light on possible routes to enhance the effect in practice., Comment: 10 pages, 6 figures

Topological phases of matter are classified based on symmetries, with nonsymmorphic symmetries like glide reflections and screw rotations being of particular importance in the classification. In contrast to extensively studied glide reflections in real space, introducing space-dependent gauge transformations can lead to momentum-space glide reflection symmetries, which may even change the fundamental domain for topological classifications, e.g., from a torus to a Klein bottle. Here we discover a new class of three-dimensional (3D) higher-order topological insulators, protected by a pair of momentum-space glide reflections. It supports gapless hinge modes, as dictated by the quadrupole moment and Wannier Hamiltonians defined on a Klein bottle manifold, and we introduce two topological invariants to characterize this phase. Our predicted topological hinge modes are experimentally verified in a 3D-printed acoustic crystal, providing direct evidence for 3D higher-order Klein bottle topological insulators. Our results not only showcase the remarkable role of momentum-space glide reflections in topological classifications, but also pave the way for experimentally exploring physical effects arising from momentum-space nonsymmorphic symmetries., Comment: 37 pages, 14 figures

Over the past decades, context sensitivity has been considered as one of the most effective ideas for improving the precision of pointer analysis for Java. However, despite great precision benefits, as each method is equivalently cloned and analyzed under each context, context sensitivity brings heavy efficiency costs. In this work, we present a fundamentally different approach called Cut-Shortcut for fast and precise pointer analysis for Java. Its insight is simple: the main effect of cloning methods under different contexts is to filter spurious object flows that have been merged inside a callee method; from the view of a typical pointer flow graph (PFG), such effect can be simulated by cutting off (Cut) the edges that introduce precision loss to certain pointers and adding Shortcut edges directly from source pointers to the target ones circumventing the method on PFG. As a result, we can achieve the effect of context sensitivity without contexts. We identify three general program patterns and develop algorithms based on them to safely cut off and add shortcut edges on PFG, formalize them and formally prove the soundness. To comprehensively validate Cut-Shortcut's effectiveness, we implement two versions of Cut-Shortcut for two state-of-the-art pointer analysis frameworks for Java, one in Datalog for the declarative Doop and the other in Java for the imperative Tai-e, and we consider all the large and complex programs used in recent literatures that meet the experimental requirements. The evaluation results are extremely promising: Cut-Shortcut is even able to run faster than context insensitivity for most evaluated programs while obtaining high precision that is comparable to context sensitivity (if scalable) in both frameworks. This is for the first time that we have been able to achieve such a good efficiency and precision trade-off for those hard-to-analyze programs., Comment: Accepted paper at PLDI 2023

Real Chern insulators have attracted great interest, but so far, their material realization is limited to nonmagnetic crystals and to systems without spin-orbit coupling. Here, we reveal magnetic real Chern insulator (MRCI) state in a recently synthesized metal-organic framework material Co3(HITP)2. Its ground state with in-plane ferromagnetic ordering hosts a nontrivial real Chern number, enabled by the C2zT symmetry and robust against spin-orbit coupling. Distinct from previous nonmagnetic examples, the topological corner zero-modes of MRCI are spin-polarized. Furthermore, under small tensile strains, the material undergoes a topological phase transition from MRCI to a magnetic double-Weyl semimetal phase, via a pseudospin-1 critical state. Similar physics can also be found in closely related materials Mn3(HITP)2 and Fe3(HITP)2, which are also existing. Possible experimental detections and implications of an emerging magnetic flat band in the system are discussed., Comment: 6 pages,5 figures

A two-dimensional (2D) Weyl semimetal featuring a spin-polarized linear band dispersion and a nodal Fermi surface is a new topological phase of matter. It is a solid-state realization of Weyl fermions in an intrinsic 2D system. The nontrivial topology of 2D Weyl cones guarantees the existence of a new form of topologically protected boundary states, Fermi string edge states. In this work, we report the realization of a 2D Weyl semimetal in monolayer-thick epitaxial bismuthene grown on SnS(Se) substrate. The intrinsic band gap of bismuthene is eliminated by the space-inversion-symmetry-breaking substrate perturbations, resulting in a gapless spin-polarized Weyl band dispersion. The linear dispersion and spin polarization of the Weyl fermion states are observed in our spin and angle-resolved photoemission measurements. In addition, the scanning tunneling microscopy/spectroscopy reveals a pronounced local density of states at the edge, suggesting the existence of Fermi string edge states. These results open the door for the experimental exploration of the exotic properties of Weyl fermion states in reduced dimensions., Comment: 5 figures

Band structure for a crystal generally consists of connected components in energy-momentum space, known as band complexes. Here, we explore a fundamental aspect regarding the maximal number of bands that can be accommodated in a single band complex. We show that in principle a band complex can have no finite upper bound for certain space groups. It means infinitely many bands can entangle together, forming a connected pattern stable against symmetry-preserving perturbations. This is demonstrated by our developed inductive construction procedure, through which a given band complex can always be grown into a larger one by gluing a basic building block to it. As a by-product, we demonstrate the existence of arbitrarily large accordion type band structures containing $N_C=4n$ bands, with $n\in\mathbb{N}$., Comment: 6 pages, 4 figures

The real Chern insulator state, featuring nontrivial real Chern number and second-order boundary modes, has been revealed in a few two-dimensional systems. The concept can be extended to three dimensions (3D), but a proper material realization is still lacking. Here, based on first-principles calculations and theoretical analysis, we identify the recently synthesized bulk ${\gamma}$-graphyne as a 3D real Chern insulator. Its nontrivial bulk topology leads to topological hinge modes spreading across the 1D edge Brillouin zone. Under compression of the interlayer distance, the system can undergo a topological phase transition into a real nodal-line semimetal, which hosts three bulk nodal rings and topological boundary modes on both surfaces and hinges. We also develop a minimal model which captures essential physics of the system.

A peculiar feature of quantum states is that they may embody so-called projective representations of symmetries rather than ordinary representations. Projective representations of space groups-the defining symmetry of crystals-remain largely unexplored. Despite recent advances in artificial crystals, whose intrinsic gauge structures necessarily require a projective description, a unified theory is yet to be established. Here, we establish such a unified theory by exhaustively classifying and representing all 458 projective symmetry algebras of time-reversal-invariant crystals from 17 wallpaper groups in two dimensions-189 of which are algebraically non-equivalent. We discover three physical signatures resulting from projective symmetry algebras, including the shift of high-symmetry momenta, an enforced nontrivial Zak phase, and a spinless eight-fold nodal point. Our work offers a theoretical foundation for the field of artificial crystals and opens the door to a wealth of topological states and phenomena beyond the existing paradigms., Comment: 62 pages, 11 pages for main text + 51 pages for supplementary information

Berry curvature dipole plays an important role in various nonlinear quantum phenomena. However, the maximum symmetry allowed for nonzero Berry curvature dipole in the transport plane is a single mirror line, which strongly limits its effects in materials. Here, via probing the nonlinear Hall effect, we demonstrate the generation of Berry curvature dipole by applied dc electric field in WTe2, which is used to break the symmetry constraint. A linear dependence between the dipole moment of Berry curvature and the dc electric field is observed. The polarization direction of the Berry curvature is controlled by the relative orientation of the electric field and crystal axis, which can be further reversed by changing the polarity of the dc field. Our Letter provides a route to generate and control Berry curvature dipole in broad material systems and to facilitate the development of nonlinear quantum devices.

Recent experiments have demonstrated interesting physics in a family of two-dimensional (2D) composition-tunable materials Nb$_{2n+1}$Si$_n$Te$_{4n+2}$. Here, we show that owing to its intrinsic low symmetry, metallic nature, tunable composition, and ambient stability, these materials offer a good platform for studying Berry curvature dipole (BCD) and nonlinear Hall effect. Using first-principles calculations, we find that BCD exhibits pronounced peaks in monolayer Nb$_{3}$SiTe$_{6}$ ($n=1$ case). Its magnitude decreases monotonically with $n$ and completely vanishes in the $n\rightarrow\infty$ limit. This variation manifests a special hidden dimensional crossover of the low-energy electronic states in this system. The resulting nonlinear Hall response from BCD in these materials is discussed. Our work reveals pronounced geometric quantities and nonlinear transport physics in Nb$_{2n+1}$Si$_n$Te$_{4n+2}$ family materials, which should be readily detected in experiment., Comment: 8 pages, 7 figures and 1 table

Short-range (SR) magnetic orders such as magnetic glass orders or fluctuations in a quantum system usually host exotic states or critical behaviors. As the long-range (LR) magnetic orders, SR magnetic orders can also break time-reversal symmetry and drive the non-zero Berry curvature leading to novel transport properties. In this work, we report that in EuZn$_2$As$_2$ compound, besides the LR A-type antiferromagnetic (AF) order, the SR magnetic order is observed in a wide temperature region. The magnetization measurements and electron spin resonance (ESR) measurements reveal the ferromagnetic (FM) correlations for this SR magnetic order which results in an obvious anomalous Hall effect above the AF transition. Moreover the ESR results reveal that this FM SR order coexists with LR AF order exhibiting anisotropic magnetic correlations below the AF transition. The interactions of LR and SR magnetism evolving with temperature and field can host non-zero spin charility and berry curvature leading the additional topological Hall contribution even in a centrosymmetric simple AF system. Our results indicate that EuZn$_2$As$_2$ is a fertile platform to investigate exotic magnetic and electronic states., Comment: 6 pages, 4 figures

Recent breakthroughs in Josephson diodes dangle the possibility of extending conventional non-reciprocal electronics into the realm of superconductivity. While a strong magnetic field is recognized for enhancing diode efficiency, it concurrently poses a risk of undermining the essential superconductivity required for non-dissipative devices. To circumvent the need for magnetic-based tuning, we propose a field-effect Josephson diode based on the electrostatic gate control of finite momentum Cooper pairs in asymmetric spin-momentum-locking states. We propose two possible implementations of our gate-controlled mechanism: (i) a topological field-effect Josephson diode in time-reversal-broken quantum spin Hall insulators; and (ii) semiconductor-based field-effect Josephson diodes attainable in current experimental setups involving a Zeeman field and spin-orbit coupling. Notably, the diode efficiency is highly enhanced in the topological field-effect Josephson diode because the current carried by the asymmetric helical edge states is topologically protected and can be tuned by local gates. In the proposed Josephson diode, the combination of gates and asymmetric spin-momentum-locking nature is equivalent to that of a magnetic field, thus providing an alternative electrical operation in designing nonreciprocal superconducting devices., Comment: 24 pages, 14 figures

Recent experiments reported an antisymmetric planar Hall effect, where the Hall current is odd in the in-plane magnetic field and scales linearly with both electric and magnetic fields applied. Existing theories rely exclusively on a spin origin, which requires spin-orbit coupling to take effect. Here, we develop a general theory for the intrinsic planar Hall effect (IPHE), highlighting a previously unknown orbital mechanism and connecting it to a band geometric quantity -- the anomalous orbital polarizability (AOP). Importantly, the orbital mechanism does not request spin-orbit coupling, so sizable IPHE can occur and is dominated by orbital contribution in systems with weak spin-orbit coupling. Combined with first-principles calculations, we demonstrate our theory with quantitative evaluation for bulk materials $\mathrm{TaSb_{2}}$, $\mathrm{NbAs_{2}}$, and $\mathrm{SrAs_{3}}$. We further show that AOP and its associated orbital IPHE can be greatly enhanced at topological band crossings, offering a new way to probe topological materials.

Recent experiments have established a type of nonsymmorphic symmetry protected nodal lines in the family of two-dimensional (2D) composition tunable materials NbSi$_x$Te$_2$. Here, we theoretically study the plasmonic properties of such nonsymmorphic nodal-line semimetals. We show that the nonsymmorphic character endows the plasmons with extremely strong anisotropy. There exist both intraband and interband plasmon branches. The intraband branch is gapless and has a $q^{1/2}$ dispersion. It is most dispersive and is independent of carrier density in direction normal to the nodal line, whereas along the nodal line, its dispersion is largely suppressed and its frequency scales linearly with carrier density. The interband branches are gapped and their long wavelength limits are connected with van Hove singularities of the band structure. We find that the single particle excitations are strongly suppressed in such systems, which decreases the Landau damping of plasmons. These characters are further verified by first-principles calculations on 2D NbSi$_x$Te$_2$. Interesting features in static screening of charged impurity are also discussed. Our result reveals characteristic plasmons in a class of nonsymmorphic topological semimetals and offers guidance for its experimental detection and possible applications., Comment: 10 pages, 8 figures

Two-dimensional (2D) niobium oxydihalide NbOI$_2$ has been recently demonstrated as an excellent in-plane piezoelectric and nonlinear optical materials. Here we show that Janus niobium oxydihalide, NbO$XY$ (X, Y = Cl, Br, I and X$\neq$Y), is a multifunctional anisotropic semiconductor family with exceptional piezoelectric, electronic, photocatalytic and optical properties. NbO$XY$ are stable and mechancially flexible monolayers with band gap around the visible light regime of $\sim 1.9$ eV. The anisotropic carrier mobility of NbO$XY$ lies in the range of $10^3 \sim 10^4$ cm$^2$V$^{-1}$s$^{-1}$, which represents some of the highest among 2D semiconductors of bandgap $\gtrsim 2$ eV. Inversion symmetry breaking in Janus NbO$XY$ generates sizable out-of-plane $d_{31}$ piezoelectric response while still retaining a strong in-plane piezoelectricity. Remarkably, NbO$XY$ exhibits an additional out-of-plane piezoelectric response, $d_{32}$ as large as 0.55 pm/V. G$_0$W$_0$-BSE calculation further reveals the strong linear optical dichroism of NbO$XY$ in the visible-to-ultraviolet regime. The optical absorption peaks with $14\sim18$ \% in the deep UV regime ($5\sim6$ eV), outperforming the vast majority of other 2D materials. The high carrier mobility, strong optical absorption, sizable built-in electric field and band alignment compatible with overall water splitting further suggest the strengths of NbO$XY$ in energy conversion application. We further propose a directional stress sensing device to demonstrate how the out-of-plane piezoelectricity can be harnessed for functional device applications. Our findings unveil NbO$XY$ as an exceptional multifunctional 2D semiconductor for flexible electronics, optoelectronics, UV photonics, piezoelectric and sustainable energy applications., Comment: 16 Pages, 7 Figures, 3 Tables

We present a systematic classification of emergent particles in all 528 magnetic layer groups and 394 magnetic rod groups, which describe two-dimensional and one-dimensional crystals respectively. Our approach is via constructing a correspondence between a given magnetic layer/rod group and one of the magnetic space group, such that all irreducible representations of the layer/rod group can be derived from those of the corresponding space group. Based on these group representations, we explicitly construct the effective models for possible band degeneracies and identify all emergent particles, including both spinless and spinful cases. We find that there are six kinds of particles protected by magnetic layer groups and three kinds by magnetic rod groups. Our work provides a useful reference for the search and design of emergent particles in lower dimensional crystals., Comment: 7 pages, 2 figures, 4 tables