Dirac Nodes Research Articles

Dirac fermions and spin transport in the SrVO3/SrTiO3 quantum well

The type-II Dirac fermions are characterized by a tilted Dirac cone and sustain exotic quantum transport phenomena. Here, we show the emergence of a type-II Dirac nodal loop in the SrVO3/SrTiO3 quantum well structure by density functional theory calculations and symmetry arguments. When the spin–orbit coupling (SOC) is neglected, the unavoidable crossing between two t2g bands gives rise to a nodal loop in the Brillouin zone, which is protected by the mirror symmetry. Such a nodal loop is fully gapped by including SOC, which results in a large spin Hall effect due to large spin Berry curvatures. Our findings add the unexplored functionality to oxide quantum wells and offer a practical platform to explore the interplay between topological fermions and spin transport phenomena.

Topological phase engineering of rutile GeO2 with strain

Nodal-line semimetals serve as the parent phase for various topological states. By manipulating spin-orbit coupling (SOC), time-reversal symmetry, or spatial inversion symmetry, a Dirac nodal-line semimetal can transition into a 3D Dirac semimetal, Weyl semimetal, or topological insulator.In this study, we present the topological phase engineering of rutile GeO2 under strain through first-principles calculations. Without considering SOC effect, applying tensile strain to GeO2 induces a transformation from a trivial insulator to a Dirac nodal-line semimetal, characterized by two orthogonal and interconnected Dirac nodal rings protected by mirror symmetry. When SOC is taken into account, the band degeneracy persists only at two points, resulting in a 3D Dirac semimetal. Nonetheless, due to the negligible strength of SOC in GeO2, its nodal-line semimetal properties remain largely intact even after including SOC effects.Our findings provide valuable insights for the topological phase engineering and potential spintronics applications of GeO2.

Dimensionality-mediated type-II Dirac semimetal to quantum spin Hall insulator phase transition in TiC

We present first-principles results on monolayer (ML) and bulk titanium carbide (TiC) exhibiting dual topological characteristics: a quantum spin Hall insulator state in two-dimensional ML and a type-II Dirac semimetal state in its three-dimensional bulk form. The nontrivial nature of ML TiC is confirmed through the calculation of a Z2 invariant, spin Hall conductivity, and edge states. The edge band structure of ML TiC displays a single pair of gapless edge states at the M point. The insulating topological phase in ML TiC is driven by a band inversion around the M point involving Ti-d orbitals, with a nontrivial band gap of 0.47 eV. Our findings also indicate that ML TiC possesses excellent dynamical and thermal stability. Moreover, the bulk, ML hollow sphere arrays, and a 4-nm-thick film of TiC have already been synthesized, suggesting the high feasibility of the experimental synthesizing of ML TiC. On the other hand, we demonstrate that the bulk TiC hosts both a type-II Dirac cone and a topological nodal surface without spin-orbit coupling, protected by a combined symmetry of inversion and time reversal. The presence of spin-orbit coupling removes the nodal surface while preserving the type-II Dirac cone. Surface states connecting bulk Dirac nodes in bulk TiC can be readily observed, making the surface characteristics easily detectable in experiments. Published by the American Physical Society 2024

Breaking new ground in metal-ion battery anodes: First principles design of Dirac nodal line semimetallic carbon materials

With the rapid development of electronic devices, the demand for batteries has gradually increased, and existing batteries can no longer satisfy it. In this paper, a three-dimensional honeycomb carbon material is designed and termed pmma-C32. The mechanical stability, dynamic stability, thermal stability, and mechanical stability were investigated through first-principles molecular dynamics, phonon spectrum, and the Born-Huangkun criterion. The calculation results show that pmma-C32 not only has good thermodynamic stability, but also has static stability. Similar to graphene, pmma-C32 exhibits semi-metallic characteristics, featuring two Dirac node lines with high Fermi velocity, indicating a high capacity for electron transport. As a metal-ion battery material, pmma-C32 exhibits higher theoretical capacity(836.8, 732.2, and 418.4 mA h/g for Li, Na, and K), lower diffusion barrier (0.06–0.12 eV for Li, 0.10–0.11 eV for Na, and 0.05–0.06 eV for K), and lower open circuit voltage (0.34 V for Li, 0.37 V for Na, and 0.74 V for K). These remarkable properties endow semimetallic pmma-C32 as a promising anode material for metal-ion batteries, providing fast charge and discharge rates. This research not only broadens the family of three-dimensional carbon materials, but also greatly improves the performance for universal metal-ion battery anode materials through material structure design.

Ultrahigh Néel Temperature Antiferromagnetism and Ultrafast Laser-Controlled Demagnetization in a Dirac Nodal Line MoB3 Monolayer.

Two-dimensional (2D) antiferromagnetic (AFM) materials boasting a high Néel temperature (TN), high carrier mobility, and fast spin response under an external field are in great demand for efficient spintronics. Herein, we theoretically present the MoB3 monolayer as an ideal 2D platform for AFM spintronics. The AFM MoB3 monolayer features a symmetry-protected, 4-fold degenerate Dirac nodal line (DNL) at the Fermi level. It demonstrates a high magnetic anisotropy energy of 865 μeV/Mo and an ultrahigh TN of 1050 K, one of the highest recorded for 2D AFMs. Importantly, we reveal the ultrafast demagnetization of AFM MoB3 under laser irradiation, which induces a rapid transition from a DNL semimetallic state to a metallic state on the time scale of hundreds of femtoseconds. This work presents an effective method for designing advanced spintronics using 2D high-temperature DNL semimetals and opens up a new idea for ultrafast modulation of magnetization in topological semimetals.

A topological Hund nodal line antiferromagnet

The interplay of topology, magnetism, and correlations gives rise to intriguing phases of matter. In this study, through state-of-the-art angle-resolved photoemission spectroscopy, density functional theory, and dynamical mean-field theory calculations, we visualize a fourfold degenerate Dirac nodal line at the boundary of the bulk Brillouin zone in the antiferromagnet YMn2Ge2. We further demonstrate that this gapless, antiferromagnetic Dirac nodal line is enforced by the combination of magnetism, space-time inversion symmetry, and nonsymmorphic lattice symmetry. The corresponding drumhead surface states traverse the whole surface Brillouin zone. YMn2Ge2 thus serves as a platform to exhibit the interplay of multiple degenerate nodal physics and antiferromagnetism. Interestingly, the magnetic nodal line displays a d-orbital dependent renormalization along its trajectory in momentum space, thereby manifesting Hund’s coupling. Our findings offer insights into the effect of electronic correlations on magnetic Dirac nodal lines, leading to an antiferromagnetic Hund nodal line.

Dual Dirac Nodal Line in Nearly Freestanding Electronic Structure of β-Sn Monolayer.

Two-dimensional topological insulators (2D TIs) have distinct electronic properties that make them attractive for various applications, especially in spintronics. The conductive edge states in 2D TIs are protected from disorder and perturbations and are spin-polarized, which restrict current flow to a single spin orientation. In contrast, topological nodal line semimetals (TNLSM) are distinct from TIs because of the presence of a 1D ring of degeneracy formed from two bands that cross each other along a line in the Brillouin zone. These nodal lines are protected by topology and can be destroyed only by breaking certain symmetry conditions, making them highly resilient to disorder and defects. However, 2D TNLSMs do not possess protected boundary modes, which makes their investigation challenging. There have been several theoretical predictions of 2D TNLSMs, however, experimental realizations are rare. β-Sn, a metallic allotrope of tin with a superconducting temperature of 3.72 K, may be a candidate for a topological superconductor that can host Majorana Fermions for quantum computing. In this work, single layers of α-Sn and β-Sn on a Cu(111) substrate are successfully prepared and studied using scanning tunneling microscopy, angle-resolved photoemission spectroscopy, and density functional theory calculations. The lattice and electronic structure undergo a topological transition from 2D topological insulator α-Sn to 2D TNLSM β-Sn, with two types of nodal lines coexisting in monolayer β-Sn. Such a realization of two types of nodal lines in one 2D material has not been reported to date. Moreover, we also observed an unexpected phenomenon of freestanding-like electronic structures of β-Sn/Cu(111), highlighting the potential of ultrathin β-Sn films as a platform for exploring the electronic properties of 2D TNLSM and topological superconductors, such as few-layer superconducting β-Sn in lateral contact with topological nodal line single-layer β-Sn.

Classification of interacting Dirac semimetals

Topological band theory predicts a Z classification of three-dimensional (3D) Dirac semimetals (DSMs) at the single-particle level. Namely, an arbitrary number of identical bulk Dirac nodes will always remain locally stable and gapless in the single-particle band spectrum, as long as the protecting symmetry is preserved. In this work we find that this single-particle classification for Cn-symmetric DSMs will break down to Zn/gcd(2,n) in the presence of symmetry-preserving electron interactions. Our theory is based on a dimensional reduction strategy which reduces a 3D Dirac fermions to one-dimensional building blocks, i.e., vortex-line modes, while respecting all the key symmetries. Using bosonization technique, we find that there exists a minimal number N=n/gcd(2,n) such that the collection of vortex-line modes in N copies of DSMs can be symmetrically eliminated via four-fermion interactions. While this gapping mechanism does not have any free-fermion counterpart, it yields an intuitive “electron-trion coupling” picture. By developing a topological field theory for DSMs and further checking the anomaly-free condition, we independently arrive at the same classification results. Our theory paves the way for understanding topological crystalline semimetallic phases in the strongly correlated regime. Published by the American Physical Society 2024

Higher-order topological Dirac phase in Y3InC: a first-principles study

Higher-order topological insulators hosting intriguing topologically protected hinge or corner states are of significant research interest. However, materials that possess higher-order topological hinge states associated with gapless bulk Dirac phases still need to be explored. Using first-principles calculations with hybrid exchange functional, we explore the electronic structure and topological properties of Y3InC and a few of its sister compounds, totaling 16 bulk materials. A symmetry-protected triple point phase, with dominated d-t 2g character, is observed in Y3InC without spin–orbit coupling (SOC). Interestingly, the SOC induces a twin Dirac node phase in the bulk Y3InC. Furthermore, the computed Z 4 topological invariant reveals the higher-order topological nature of investigated materials. To demonstrate the gapless hinge states, we conduct edge state calculations using a rod-shaped geometry of Y3InC. Remarkably, Y3InC is identified to host multi-Dirac nodes in the bulk and surface phases together with the higher-order hinge states. These results lay the groundwork for further experimental and theoretical investigations into cubic antiperovskite materials for higher-order topological phases.

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.

Synthesis and characterisation of Cu2Ge, a new two-dimensional Dirac nodal line semimetal

Dirac nodal line (DNL) semimetals are a novel class of topological materials in which the valence and conduction bands touch along lines in the reciprocal space, with linear dispersion. These materials attract a growing attention, but the experimental realizations for two-dimensional systems are sparse. This article reports the first experimental realization of a two-dimensional hexagonal monolayer Cu2Ge, grown by evaporation of Ge on a Cu(111) substrate. Through a combination of low-energy electron diffraction XPS and ARPES measurements, it is shown that the surface presents all characteristics expected from calculations for a free-standing Cu2Ge monolayer. More specifically, the preservation of the two concentric nodal lines around the Γ point indicates weak interactions between the Cu2Ge surface and its Cu(111) substrate, making it an ideal system for the study of DNL materials.

Hydrogenation-controlled band engineering of dumbbell graphene

The stability of the dumbbell structure has been confirmed by previous theory and experiment. Based on first-principles calculations, we proposed hexagonal dumbbell graphene (HDB C10) and rectangular dumbbell graphene (RDB C10) monolayers containing periodically raised C (CR) atoms. They turn out to have high mobility semiconductor properties. By adsorbing H atoms on these CR atoms, their band structures can be widely tuned from semiconductor to semimetal. When considering adsorption of two/four H atoms on the unit cell of the dumbbell structure, the bandgap can be increased, and isolated flat band structures can be obtained by further adding or removing H atoms. Remarkably, two different Dirac band structures can be found in the HDB/RDB C10H2-I monolayers. The HDB C10H2-I shows a Dirac cone with isotropic Fermi velocities, while the RDB C10H2-I monolayer exhibits a quasi-one-dimensional Dirac nodal line with varying Fermi velocities along the XS path. Tight-binding (TB) models are constructed including nearest neighbor (NN) and next NN hopping in order to understand our DFT results. These TB models are related to the Su-Schrieffer-Heeger model, and are able to explain the tunable topological properties of the RDB C10H2-I monolayer. They not only are able to explain the different kinds of Fermi velocity, but also can predict the emergence of topological edge states, providing a good platform for research on Dirac fermions. The HDB/RDB C10 monolayer exhibits more freedom of tunable band structures and more stable hydrogen storage capacity, making it superior to graphene. Finally, possible experimental synthesis paths of these DB monolayers are provided.

Photoinduced Floquet higher-order Weyl semimetal in C6 symmetric Dirac semimetals

Abstract Topological Dirac semimetals are a parent state from which other exotic topological phases of matter, such as Weyl semimetals and topological insulators, can emerge. In this study, we investigate a Dirac semimetal possessing sixfold rotational symmetry and hosting higher-order topological hinge Fermi arc states, which is irradiated by circularly polarized light. Our findings reveal that circularly polarized light splits each Dirac node into a pair of Weyl nodes due to the breaking of time-reversal symmetry, resulting in the realization of the Weyl semimetal phase. This Weyl semimetal phase exhibits rich boundary states, including two-dimensional surface Fermi arc states and hinge Fermi arc states confined to six hinges. Furthermore, by adjusting the incident direction of the circularly polarized light, we can control the degree of tilt of the resulting Weyl cones, enabling the realization of different types of Weyl semimetals.

Strain-induced modulation of electronic structure in correlated Dirac semimetal Pv-CaIrO3 epitaxial thin films

Perovskite CaIrO3 is theoretically predicted to be a Dirac node semimetal near the Mott transition, which possesses a considerable interplay between electron correlations and spin–orbit coupling. Electron correlations can significantly tune the behavior of relativistic Dirac fermions. Here, we have grown high-quality perovskite CaIrO3 thin films on different substrates using oxide molecular beam epitaxy to modulate both electron correlations and Dirac electron states. Through in situ angle-resolved photoemission spectroscopy, we demonstrate a systematic evolution of the bandwidth and effective mass of Jeff=1/2 band in perovskite CaIrO3 induced by strain. The bandwidth of the Jeff=1/2 band undergoes an evident increase under in-plane compressive strain, which could be attributed to the weakening of electron correlations. The compressive strain can potentially shift the position of the Dirac node relative to the Fermi level and play a vital role in the transition from hole-type to electron-type transport characteristics. Our work provides a feasible approach for manipulating the topological Dirac electron states by engineering the strength of electron correlations.

Twist-Angle Tuning of Electronic Structure in Two-Dimensional Dirac Nodal Line Semimetal Au2Ge on Au(111).

Topological semimetals have emerged as quantum materials including Dirac, Weyl, and nodal line semimetals, and so on. Dirac nodal line (DNL) semimetals possess topologically nontrivial bands crossing along a line or a loop and are considered precursor states for other types of semimetals. Here, we combine scanning tunneling microscopy/spectroscopy (STM/S) measurements and density functional theory (DFT) calculations to investigate a twist angle tuning of electronic structure in two-dimensional DNL semimetal Au2Ge. Theoretical calculations show that two bands of Au2Ge touch each other in Γ-M and Γ-K paths, forming a DNL. A significant transition of electronic structure occurs by tuning the twist angle from 30° to 24° between monolayer Au2Ge and Au(111), as confirmed by STS measurements and DFT calculations. The disappearing of DNL state is a direct consequence of symmetry breaking.

Observation of Dirac nodal line states in topological semimetal candidate PrSbTe

Observation of Dirac nodal line states in topological semimetal candidate PrSbTe

Variations of topological surface states of nodal line semimetal AlB<sub>2</sub> after adsorption in aqueous environment

Topological semimetals have aroused great research interest due to their intrinsic topological physics and potential applications in devices. A key feature for all topological materials is the so-called bulk-boundary correspondence, which means that if there is non-trivial band topology in the bulk, then we can expect unique topologically protected conducting states in the surface, i.e. the topological surface state (TSS). Previously, the studies of the surface states of topological materials mainly focused on the pristine surfaces, while the topological nodal line semimetal surface states with adsorbates are rarely systematically studied. In this paper, the topological properties of the topological semimetal AlB<sub>2</sub> are studied by first-principles calculations, and the TSS position is calculated by constructing the Al- and B-terminated slab models. Observing the topological surface state, it is found that the drumhead-like TSS connects two Dirac nodes with no energy gaps on the node line, and the TSS of the Al end-terminated slab has a smaller energy dispersion than that of the B-terminated slab. The adsorption characteristics of AlB<sub>2</sub> (010) surface are studied, and it is found that the Gibbs free energy (<inline-formula><tex-math id="M2">\begin{document}$ {\Delta }{G}_{{{\mathrm{H}}}^{*}} $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20240404_M2.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20240404_M2.png"/></alternatives></inline-formula>) for hydrogen adsorption on the surface of Al is only –0.031 eV, demonstrating excellent hydrogen evolution reaction (HER) performance. The changes of TSS after H, OH and H<sub>2</sub>O are adsorbed on the surface of AlB<sub>2</sub> in aqueous solution environment are observed. The TSS change is the most significant when H is adsorbed, followed by OH adsorption. And the influence of H<sub>2</sub>O on TSS due to its electrical neutrality and weak surface adsorption is very weak. Before and after adsorption, because the topology protection TSS still exists, only the energy changes, which confirms its robustness in the environment. The results of this work provide a systematic understanding of the effects of different adsorbents on the TSS of AlB<sub>2</sub>, paving the way for future theoretical and experimental research in related fields, and alsopresent theoretical support for putting the topological materials into practical applications .

Coexistence of multiple dirac nodal points and nodal lines in two-dimensional carbon nanotube arrays

Seeking for novel fermions in two-dimensional (2D) materials is of practical significance for devices with extraordinary transport properties. In this work, 2D carbon nanotube arrays (CNTAs) formed by ‘fusible’ connection of uniform CNTs are studied based on first-principles calculations. We find the coexistence of multiple Dirac points and diverse nodal lines (including type I, type II, and type III in band crossing modes, and both open and closed in forms) formed by four entangled bands near the Fermi levels. Such kind of coexistence, which can be regarded as the splitting of eight-fold degeneracy or double Dirac nodal lines, is the results of the interaction between the upper and lower surfaces of CNTAs, and leads to the nontrivial arc-like, drumhead-like, and torus edge states in their nanoribbons concurrently. Our study suggests that CNTAs can be excellent platforms to study the entanglements between different states, and excellent candidates for quantum devices.

Rational design of large anomalous Nernst effect in Dirac semimetals

Anomalous Nernst effect generates a transverse voltage perpendicular to the temperature gradient. It has several advantages compared with the longitudinal thermoelectricity for energy conversion, such as decoupling of electronic and thermal transports, higher flexibility, and simpler lateral structure. However, a design principle beyond specific materials systems for obtaining a large anomalous Nernst conductivity (ANC) is still absent. In this work, we theoretically demonstrate that a pair of Dirac nodes under a Zeeman field manifests an odd-distributed, double-peak anomalous Hall conductivity curve with respect to the chemical potential and a compensated carrier feature, leading to an enhanced ANC compared with that of a simple Weyl semimetal with two Weyl nodes. Based on first-principles calculations, we then provide two Dirac semimetal candidates, i.e., Na3Bi and NaTeAu, and show that under a Zeeman field, they exhibit a sizable ANC value of 0.4 {rm{A}}{{rm{m}}}^{-1}{{rm{K}}}^{-1} and 1.3 {rm{A}}{{rm{m}}}^{-1}{{rm{K}}}^{-1}, respectively, near the Fermi level. Such an approach is also applicable to ferromagnetic materials with intrinsic Zeeman splitting, as exemplified by a hypothetical alloy NaFeTe2Au2, exhibiting an ANC as high as 3.7 {rm{A}}{{rm{m}}}^{-1}{{rm{K}}}^{-1} at the Fermi level. Our work provides a design principle with a prototype band structure for enhanced ANC pinning at the Fermi level, shedding light on the inverse design of other specific functional materials based on electronic structure.

Visualizing near-coexistence of massless Dirac electrons and ultra-massive saddle point electrons

Strong singularities in the electronic density of states amplify correlation effects and play a key role in determining the ordering instabilities in various materials. Recently high order van Hove singularities (VHSs) with diverging power-law scaling have been classified in single-band electron models. We show that the 110 surface of Bismuth exhibits high order VHS with an usually high density of states divergence \sim (E)^{-0.7}∼(E)−0.7. Detailed mapping of the surface band structure using scanning tunneling microscopy and spectroscopy combined with first-principles calculations show that this singularity occurs in close proximity to Dirac bands located at the center of the surface Brillouin zone. The enhanced power-law divergence is shown to originate from the anisotropic flattening of the Dirac band just above the Dirac node. Such near-coexistence of massless Dirac electrons and ultra-massive saddle points enables to study the interplay of high order VHS and Dirac fermions.