Nontrivial Topological States Research Articles

Phononic Weyl nodal lines and Weyl pairs in van der Waals heavy fermion material CeSiI

Abstract Topological phonon is a new frontier in the field of topological materials. Different from electronic structures, phonons are bosons and most topological phonons are metallic form. Previous studies about topological phonon states were focused on threedimensional (3D) materials. Owing to the lack of material candidates, two-dimensional (2D) and van der Waals f-electron-related topological phonons were rarely reported. Based on first-principles calculations, we investigated the topological phononic state in the heavy fermion material CeSiI with a layered structure. Both three-dimensional (3D) bulk and two-dimensional (2D) monolayers have topological nontrivial states in the rarely seen f-electron dominated van der Waals metal. Owing to the PT and C 3z symmetries, Weyl nodal lines with non-zero Chern numbers exist on the hinge of the Brillouin zone (BZ). Protected by C 3z rotation symmetry, three pairs of Weyl points with ±π Berry phase exist at point K near the Frequency of 8 and 10 THz. In addition to the bulk topological charges, corresponding surface/edge states were also systematically analyzed, which gives a consistent understanding. Our results proposed another interesting point in the newly discovered rear earth heavy fermion material CeSiI and are helpful for future experimental study of its topological phonons.

Janus monolayers Fe2SSeX2(X = Ga, In, and Tl): Robust nontrivial topology with high Chern-number

Abstract High-performance quantum anomalous Hall (QAH) systems are the crucial materials to explore emerging quantum physics and magnetic topological phenomena. Inspired by layered FeSe materials with excellent superconducting properties, the Janus monolayers Fe2SSeX2 (X = Ga, In, and Tl) are built by the decoration of Ga, In, and Tl atoms in monolayer Fe2SSe. Using the first-principles calculations, the Fe2SSeX2 have stable structures and prefer ferromagnetic (FM) orders, which belong to the Weyl semimetal without spin-orbit coupling (SOC). For the out-of-plane (OOP) magnetic anisotropy, the large nontrivial gaps are opened, and the Fe2SSeX2 are predicted to be large-gap QAH insulators with high Chern-number C = 2, proved by two chiral edge states and Berry curvatures. When the magnetization is flipped, two chiral edge states can be simultaneously changed and C = -2 can be obtained, revealing one fascinating behavior of chiral spin-edge-state locking. It is found that the QAH properties of the Fe2SSeX2 are robust against the strain. Especially, the nontrivial topological quantum states can spontaneously appear for the Fe2SSeGa2 and Fe2SSeIn2, because the easy magnetic axis orientations are adjusted from in-plane to OOP by the biaxial strain. Our studies provide excellent candidate systems to realize the QAH properties with high Chern-number, and advocate more experimental explorations in the combination of superconductivity and topology.

Hierarchical bound states in heat transport

Higher-order topological phases in non-Hermitian photonics revolutionize the understanding of wave propagation and modulation, which lead to hierarchical states in open systems. However, intrinsic insulating properties endorsed by the lattice symmetry of photonic crystals fundamentally confine the robust transport only at explicit system boundaries, letting alone the flexible reconfiguration in hierarchical states at arbitrary positions. Here, we report a dynamic topological platform for creating the reconfigurable hierarchical bound states in heat transport systems and observe the robust and nonlocalized higher-order states in both the real- and imaginary-valued bands. Our experiments showcase that the hierarchical features of zero-dimension corner and nontrivial edge modes occur at tailored positions within the system bulk states instead of the explicit system boundaries. Our findings uncover the mechanism of non-localized hierarchical non-trivial topological states and offer distinct paradigms for diffusive transport field management.

The de Haas–van Alphen quantum oscillations in the kagome metal RbTi3Bi5

Abstract The kagome system has attracted great interest in condensed matter physics due to its unique structure that can host various exotic states such as superconductivity (SC), charge density waves (CDWs) and nontrivial topological states. The topological semimetal RbTi3Bi5 consisting of a Ti kagome layer shares a similar crystal structure to the topological correlated materials AV3Sb5 (A = K, Rb, Cs) but without the absence of CDW and SC. Systematic de Haas–van Alphen oscillation measurements are performed on single crystals of RbTi3Bi5 to pursue nontrivial topological physics and exotic states. Combining this with theoretical calculations, the detailed Fermi surface topology and band structure are investigated. A two-dimensional Fermi pocket β is revealed with a light effective mass, consistent with the semimetal predictions. The Landau fan diagram of RbTi3Bi5 reveals a zero Berry phase for the β oscillation in contrast to that of CsTi3Bi5. These results suggest that kagome RbTi3Bi5 is a good candidate for exploring nontrivial topological exotic states and topological correlated physics.

Revealing the nontrivial topological surface states of catalysts for effective photochemical carbon dioxide conversion

Topological semimetals with protected surface states mark a new paradigm of research beyond the early landmarks of band-structure engineering, allowing fabrication of efficient catalyst to harness the rich metallic surface states to activate specific chemical processes. Herein, we demonstrate a facile solid-phase method for in-situ doping of Ir at the Os sites in the Os3Sn7, an alloy with topological states, which significantly improves the photocatalytic performance for the reduction of CO2 to CO and CH4. Experimental evidence combined with theoretical calculations reveal that the nontrivial topological surface states greatly accelerate charge-separation/electron-enrichment and adsorption/activation of CO2 molecules, rendering highly efficient reaction channels to stimulate the formation of *COOH and *CO, as well CHO*. This work shows the promise of achieving high photocatalytic performances with synthesizing topological catalysts and provides hints on the design of novel topological catalysts with superior photoactivity towards the CO2 reduction reaction.

Extended Berry Curvature Tail in Ferromagnetic Weyl Semimetals NiMnSb and PtMnSb.

Heusler compounds belong to a large family of materials and exhibit numerous physical phenomena with promising applications, particularly ferromagnetic Weyl semimetals for their use in spintronics and memory devices. Here, anomalous Hall transport is reported in the room-temperature ferromagnets NiMnSb (half-metal with a Curie temperature (TC) of 660 K) and PtMnSb (pseudo half-metal with a TC of 560 K). They exhibit 4 µB/f.u. magnetic moments and non-trivial topological states. Moreover, NiMnSb and PtMnSb are the first half-Heusler ferromagnets to be reported as Weyl semimetals, and they exhibit anomalous Hall conductivity (AHC) due to the extended tail of the Berry curvature in these systems. The experimentally measured AHC values at 2 K are 1.8×102Ω-1cm-1 for NiMnSb and 2.2×103Ω-1 cm-1 for PtMnSb. The comparatively large value between them can be explained in terms of the spin-orbit coupling strength. The combined approach of using ab initio calculations and a simple model shows that the Weyl nodes located far from the Fermi energy act as the driving mechanism for the intrinsic AHC. This contribution of topological features at higher energies can be generalized.

Higher-order topological states in T-graphene and their realization in photonic crystals

Higher-order topological states extend the power of nontrivial topological states beyond the bulk-edge correspondence. Here we study the higher-order topological states (corner states) in an open-boundary two-dimensional T-graphene lattice. Unlike the common zero-energy corner states, our findings reveal non-zero energy corner states in such lattice systems, and the energy could be controlled by modifying the hopping parameters. Moreover, the corner states could be transferred away from the lattice corners by designing the position-specific vacancy defects. The strong robustness of the corner states is also demonstrated against the uniaxial strain and vacancy defects, respectively. A plasmonic crystal is constructed to testify to the theory, in which the corner states are realized in optical modes and their higher-order topological properties are verified. Our results open the avenue of corner-states engineering, which holds significant physical implications of higher-order topological states for the design of photonic and electronic devices with specialized functionalities.

First‐Principles Investigation of Electronic and Thermodynamic Properties of Honeycomb CuSe

AbstractIn the realm of materials science, a fascinating class of substances known as topological nodal line semimetals have garnered significant attention. These materials possess distinctive quantum states, characterized by topologically nontrivial conduction and valence bands that intricately intersect with the Fermi level. Such unique band structures give these materials a plethora of surprising properties, including the emergence of flat Landau levels and the appearance of long‐range Coulomb interactions. Notably, certain bulk materials, namely PbTaSe2, ZrSiS, PtSn4, and Cu2Si, exhibit these intriguing topological nodal lines. However, the theoretical investigation pertaining to CuSe and its Dirac nodal line properties remains relatively limited. In this work, we have employed simulations on CuSe to elucidate its distinctive physical properties such as a Dirac matter. There exist Dirac bands and band inversion in the vicinity of Fermi levels, and Fermi surface holds a Horn‐like structure. We pointed out the occurrence of mirror reflection symmetry‐protected Dirac nodal line fermions in copper selenide (CuSe) that make CuSe a candidate for Dirac nodal line fermion started by the Se 4p and Cu 3d orbitals. The nontrivial topological edge states further verify our proposal of the mirror reflection symmetry is broken by spin‐orbit coupling. These findings provide a new perspective that advances our comprehension of the remarkable properties exhibited by these materials, thereby paving the way for the development of high‐speed and low‐dissipation devices in the future.

Topological phase transition and tunable surface states in YBi

A unique co-existence of extremely large magnetoresistance (XMR) and topological characteristics in non-magnetic rare-earth monopnictides has stimulated intensive research on these materials. Yttrium monobismuthide (YBi) has been reported to exhibit XMR up to 105% but its topological properties still need clarification. Here we use the hybrid density functional theory to probe the structural, electronic, and topological properties of YBi in detail. We observe that YBi is topologically trivial semimetal at ambient pressure which is in accordance with reported experimental results. The topological phase transitions i.e. trivial to non-trivial are obtained with volumetric pressure of 6.5 GPa and 3% of epitaxial strain. These topological phase transitions are well within the structural phase transition of YBi (24.5 GPa). The topological non-trivial state is characterized by band inversions among Y-d band and Bi-p band at Γ- and X-point which is further verified with the help of surface band structure along (001) plane. The Z2 topological invariants are calculated with the help of product of parities and evolution of Wannier charge centers. The occurrence of non-trivial phase in YBi with a relatively small epitaxial strain, which a thin film geometry can naturally have, make it an ideal candidate to probe inter-relationship between XMR and non-trivial topology.

Magnetic topological phases in the double exchange model with spin–orbit coupling

The double exchange model with the spin–orbit coupling is studied by the dynamical mean field theory. It reveals a competition between the magnetic, charge orderings and the non-trivial topology of the ground state. The spin exchange tends to maintain the magnetic ordering, and at the same time it tries to suppress the charge ordering. The spin–orbit coupling maintains nontrivial topology of the ground state, whereas the magnetic ordering tries to destroy it. As a result, a rich phase diagram is obtained. The competition leads to a half topological ground state, where spin-up electrons form a nontrivial topological state, while spin-down electrons are in the topological trivial insulating state.

Two-dimensional Sb net generated nontrivial topological states in SmAgSb2 probed by quantum oscillations

Abstract The REAgSb2 (RE = rare earth and Y) family has drawn considerable research interest because the two-dimensional Sb net in their crystal structure hosts topological fermions and hence rich topological properties. We report herein the magnetization and magnetotransport measurements of SmAgSb2 single crystal, which unveil very large magnetoresistance and high carrier mobility up to 6.2×103% and 5.58×103 cm2V-1s-1, respectively. The analysis of both Shubnikov-de Haas and de Haas-van Alphen quantum oscillations indicates nontrivial Berry phases in the paramagnetic state while trivial Berry curvature in the antiferromagnetic state, indicating a topological phase transition induced by the antiferromagnetic order. It is also supported by the first-principles calculations. The results not only provide a new interesting topological material but also offer valuable insights into the correlation between magnetism and nontrivial topological states.

Evolution of anomalous Hall effect in ferromagnetic Weyl semimetal NbxZr1–xCo2Sn

Abstract Magnetic topological semimetal can host various topological non-trivial states leading to exotic novel transport properties. Here we report the systematic magneto-transport studies on the Heusler alloy Nb x Zr1−x Co2Sn considered as a ferromagnetic (FM) Weyl semimetal. The cusp anomaly of temperature-dependent resistivity and large isotropic negative magneto-resistivity (MR) emerge around the FM transition consistent with the theoretical half-metallic predictions. The prominent anomalous Hall effect (AHE) has the same behavior with the applied field along various crystal directions. The Nb doping introduces more disorder resulting in the enhancement of the upturn for the temperature-dependent resistivity in low temperatures. With Nb doping, the AHE exhibits systemic evolution with the Fermi level lifted. At the doping level of x = 0.25, the AHE mainly originates from the intrinsic contribution related to non-trivial topological Weyl states.

Multiple topological states within a common bandgap of two non-trivial photonic crystals.

Topological photonic crystals (PCs) provide an effective method for controlling how light propagates and concentrates through their topological states. However, it remains unclear whether topological states can be obtained by combining two different two-dimensional (2D) PCs with topological non-trivial states. In this Letter, two types of 2D Penrose-square (P-S) PCs are proposed. These PCs can generate topological edge states (TESs) and topological corner states (TCSs) within the low-frequency part of the bandgap. Moreover, by combining these two non-trivial PCs, a total of two groups of TESs and four groups of TCSs can be generated in both the high-frequency and low-frequency parts of the common bandgap. To the best of our knowledge, the two proposed P-S PCs offer a new platform for investigating topological photonics and related devices, providing novel approaches and perspectives for generating topological states in 2D PCs.

Engineering the topological states of Weyl ferromagnetic CoxMnGay films grown by molecular beam epitaxy

Due to its nontrivial topological state, a magnetic Weyl semimetal often exhibits exotic transport properties that are important for both fundamental physics and potential spintronics applications. In this Letter, we investigate the composition dependences of the structural order, magnetism, and transport properties for the epitaxial Heusler alloy CoxMnGay (CMG) topological Weyl semimetal films grown via molecular beam epitaxy. Our results show that the saturated magnetization, anomalous Hall conductivity, and anomalous Hall angle of CMG are influenced by its composition and structural order. Specifically, we observed that the optimized L21–Co2MnGa alloy exhibits a high intrinsic anomalous Hall conductivity of approximately 913 Ω−1 cm−1 at its maximum, which is attributed to the substantial Berry curvature within its electronic band structures. This study provides valuable insights into how to engineer the topological ferromagnetic state of the Weyl semimetals for future applications.

Non-trivial topological surface states regulation of 1 T-OsCoTe2 enables selective C―C coupling for highly efficient photochemical CO2 reduction toward C2+ hydrocarbons

Despite ongoing research, the rational design of non-trivial topological semimetal surface states for the selective photocatalytic CO2 conversion into valuable products remains full of challenges. Herein, we present the synthesis of lattice-matched 1 T-OsCoTe2 for the photoreduction upgrading of CO2 to tri-carbon (C3) alkane (propane, C3H8) by the integration of experimental work and theory prediction/calculation. Experimental studies suggested a high electron-based selectivity of 71.2 % for C3H8 and an internal quantum efficiency of 54.6 % at 380 nm. In-situ X-ray photoelectron spectroscopy and X-ray absorption fine structure spectroscopy demonstrated that Co and Os atoms coordinated with Te atoms enable an efficient Os―Te―Co electron transfer to activate the generation of *CH3, *CHOCO and *CH2OCOCO. Density functional theory calculations further confirmed Os―Te―Co electron bridging on the improved CO2 conversion kinetics. To our knowledge, this is the first report suggesting the role of Os atoms in accelerating the photocatalytic CO2 conversion activity of the topological semimetal 1 T-OsCoTe2.

Skyrmion based universal logic gates and computation operation

Swirling spin configurations with a non-trivial topological state are popularly known as magnetic skyrmions. They are often observed in magnetic thin films with perpendicular magnetic anisotropy and Dzyaloshinskii–Moriya interaction (DMI). Due to their small size and non-collinear spin texture, they are being considered as a potential candidate for spintronic devices such as data storage devices, and logic-based devices. These skyrmions have distinct properties and interactions, that can be utilized to control their movement by applying an external electric current. In this work, we have successfully demonstrated the operation of skyrmion-based universal NAND and NOR logic gates. We have further performed arithmetic addition of two and three single-bit by using a half and full adder, fabricated based on the XOR and AND gates. We have observed that the presence of only uniform DMI is not enough to achieve all logic operations. The presence of a negative DMI at the edges is crucial in achieving proper logic operations. The findings are very important for the realization of skyrmion-based logic and computational operations.

Magnons in a two-dimensional Weyl magnet

The discovery of topological states of matter has led to a revolution in condensed-matter science. While a non-trivial band topology in a material is often associated with intriguing transport properties, much less attention has been given to the impact on spin dynamics and non-equilibrium magnetization states. Here, we provide evidence that a chiral asymmetric magnon dispersion in the two-dimensional Weyl magnet Fe/W(110) is related to the presence of Weyl fermions close to the Fermi energy and surface Fermi arcs. We find that the large anomalous Hall conductivity and the Dzyaloshinskii–Moriya interaction are attributed to the non-trivial band topology in the composite momentum-magnetization space. Our results show the direct impact of Weyl fermions on both the charge and spin dynamics in a two-dimensional magnet. Unveiling these principles can promote innovative technologies in magnonics by utilizing topological materials, where magnons and non-trivial topological electronic states can be manipulated through magnetization.

Coexistence of topological node surface and Dirac fermions in phonon-mediated superconductor YB2C2.

The interaction between nontrivial topology and superconductivity in condensed matter physics has attracted tremendous research interest as it could give rise to exotic phenomena. Herein, based on first-principles calculations, we investigate the electronic structures, mechanical properties, topological properties, dynamic stability, electron-phonon coupling (EPC), and superconducting properties of the synthesized real material YB2C2. It is a tetragonal structure with P4/mbm symmetry and exhibits excellent stability. The calculated electronic band structures reveal that a zero-dimension (0D) Dirac point and two-dimensional (2D) nodal surface coexist near the Fermi level. A spin-orbit coupling (SOC) Dirac point with the topological Fermi arc is observed on the (001) surface. These nodal surfaces are protected by a two-fold screw axis and time-reversal symmetry. Based on the Bardeen-Cooper-Schrieffer theory, the superconducting transition temperature (Tc) in the range 1.25-4.45 K with different Coulomb repulsion constant μ* for YB2C2 is estimated to be consistent with previous experimental results. In addition, the EPC is mainly from the coupling between the dx2-y2 and dz2 orbitals of the Y atom and low-energy phonon modes. The presence of superconductivity and nontrivial topological surface state in YB2C2 suggests that it may be a candidate material for topological superconductors.

Topological boundary states in micropolar gyroelastic continua

The study of topology in elastic media has been primarily focused on achieving non-trivial topological states in discrete elastic lattices through active or chiral microscopic interactions. Realization of such topological states in continuous elastic media remains largely unexplored. In this study, a new continuum theory of micropolar gyroelasticity is developed and applied to attain non-trivial topological boundary states in elastic continua. According to the new theory, an elastic continuum is composed of elastically interacting micro-volume elements that can translate and rotate and are connected at their mass centers to gyroscopes, which contribute to the linear and orbital angular momenta but not to the spin angular momentum of the continuum. By applying this micropolar gyroelasticity theory to elastic media with both periodic and finite domains, the emergence of topological boundary states in 2D micropolar gyroelastic continua is demonstrated. Through using the Floquet–Bloch method for periodic domains, the bulk-boundary correspondence is analytically established, and the emergence of non-trivial topological bulk states characterized by Mexican-hat band structures is observed. In addition, by employing an asymptotic analytical model based on the extended Bloch theorem and performing numerical analyses of micropolar gyroelastic continua with finite domains of different geometries, it is shown that the non-trivial Mexican-hat band structure is associated with and provides protection for topological boundary states confined at the boundaries. Finally, the application of the newly developed micropolar gyroelasticity theory to Zinc-blende structured materials (including ZnTe, GaP, InP and ZnS) reveals that the emergence of the topological boundary states in an elastic continuum is not triggered solely by the gyroscopic effect but also depends on the material properties of the micropolar continuum. This study provides new insights into extending notions and methods of topology to analyze elastic continua, paving the way for the practical implementation of topological mechanical systems in various engineering applications.

Non-trivial topological phases in transition metal rich half-Heusler oxides

Topological insulators with gapless surface states and insulating bulk in non-centrosymmetric cubic systems have been extensively explored following the discovery of two-dimensional quantum spin hall effect in zincblende HgTe. In such systems the negative band inversion strength E (= E E 0) governs the robustness of the non-trivial topological states at ambient conditions. Hence, realizing large negative values of E has been a guiding motivation of several investigations reported in literature. Here, we present a material design approach which can be employed to realize large negative values of E in cubic materials such as half-Heusler (HH) oxides with 18 valence electron configurations. We explore 27 HH oxides of the form ABO (A = Li, K, Rb; B = Cu, Ag, Au) in α-, β-, and γ-phase (by placing transition metal atom at different Wyckoff positions) for their non-trivial topological phase. Off these three phases, we found that, the α-phase of nine HH oxides (wherein the transition metal atoms occupy 4a Wyckoff positions in the crystal structure) is the most promising with non-trivial topological phase which is governed by the mass-Darwin fully-relativistic effects enhancing E. Whereas the other phases were found to be either trivial semiconductors or semimetals or metals and most of them being dynamically unstable. We focus on RbAuO in α-phase with E of −1.29 eV and the effect of strain fields on the topological surface states of this compound. We conclude that the α-phase of HH oxide presented here can be synthesized experimentally for diverse room temperature applications in spintronics and nanoelectronics.