Dirac Nodal Line Research Articles

Rectangular Carbon Nitrides C4N Monolayers with a Zigzag Buckled Structure: Quasi‐1D Dirac Nodal Lines and Weak Topological Properties with Flat Edge States

AbstractUsing first‐principles calculations, two C4N monolayers with a zigzag buckled (ZB) structure are proposed. The ZB C4N monolayers contain raised‐C (raised‐N) atoms with sp3 hybridization, different from the traditional 2D graphene‐like carbon nitride materials with sp2 hybridization. Interestingly, the band structures of the ZB C4N monolayers exhibit quasi‐1D Dirac nodal line resulting from the corresponding quasi‐1D structure of the zigzag carbon chains, which is essentially different from the conventional ring‐shaped nodal line. The quasi‐1D Dirac nodal line exhibits the following features: i) gapless Dirac points, ii) varying Fermi velocity, and iii) a slightly curved band along the high‐symmetry path. All these features are successfully explained by the proposed tight‐binding model that includes interactions up to the third nearest neighbor. The Fermi velocity of the 2D system can reach 105 m s−1, which is promising for applications in high‐speed electronic devices. The topological flat band structure of the corresponding 1D system determined by the Zak phase and band inversion is edge‐dependent, which is a weak topological state and can be explained by the 2D Su‐Schrieffer‐Heeger (SSH) model. The quasi‐1D Dirac Fermions and SSH edge states make the ZB C4N monolayers promising for nanoelectronics applications.

Growth and electronic structure of the nodal line semimetal in monolayer Cu2Si on Cu(111)

Cu2Si, a single-layer two-dimensional material with a honeycomb structure, has been proposed to have Dirac nodal line fermions. In this study, the synchrotron radiation X-ray photoelectron spectroscopy, ultraviolet photoelectron spectroscopy, and angle-resolved photoemission spectroscopy (SR-XPS, SR-UPS, and SR-ARPES) techniques were used to investigate the dynamic process of in situ deposition of single-layer Cu2Si on a Cu(111) crystal surface via molecular beam epitaxy (MBE). Cu2Si existed as a monolayer (ML) alloy, and there were competing mechanisms of distinct chemical states of silicon in different growth periods, according to a detailed examination of the experimental SR-XPS and SR-UPS spectra. Additionally, a weak interaction between the Cu2Si ML and Cu(111) was demonstrated via SR-ARPES and first-principles computations. The unique electronic structure of the Cu2Si ML was not destroyed by either this weak interaction or the disordered silicon produced on the surface during the growth process. The study of the Cu2Si growth kinetics provides a guarantee and a basis for the future exploration of the exotic properties of Cu2Si.

Correlated topological flat bands in rhombohedral graphite

Flat bands and nontrivial topological physics are two important topics of condensed matter physics. With a unique stacking configuration analogous to the Su-Schrieffer-Heeger model, rhombohedral graphite (RG) is a potential candidate for realizing both flat bands and nontrivial topological physics. Here, we report experimental evidence of topological flat bands (TFBs) on the surface of bulk RG, which are topologically protected by bulk helical Dirac nodal lines via the bulk-boundary correspondence. Moreover, upon in situ electron doping, the surface TFBs show a splitting with exotic doping evolution, with an order-of-magnitude increase in the bandwidth of the lower split band, and pinning of the upper band near the Fermi level. These experimental observations together with Hartree-Fock calculations suggest that correlation effects are important in this system. Our results demonstrate RG as a platform for investigating the rich interplay between nontrivial band topology, correlation effects, and interaction-driven symmetry-broken states.

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.

Realization of Two-Dimensional Intrinsic Polar Metal in a Buckled Honeycomb Binary Lattice.

Structural topology and symmetry of a two-dimensional (2D) network play pivotal roles in defining its electrical properties and functionalities. Here, a binary buckled honeycomb lattice with C3v symmetry, which naturally hosts topological Dirac fermions and out-of-plane polarity, is proposed. It is successfully achieved in a group IV-V compound, namely monolayer SiP epitaxially grown on Ag(111) surface. Combining first-principles calculations with angle-resolved photoemission spectroscopy, the degeneration of the Dirac nodal lines to points due to the broken horizonal mirror symmetry is elucidated. More interesting, the SiP monolayer manifests metallic nature, which is mutually exclusive with polarity in conventional materials. It is further found that the out-of-plane polarity is strongly suppressed by the metallic substrate. This study not only represents a breakthrough of realizing intrinsic polarity in 2D metallic material via ingenious design but also provides a comprehensive understanding of the intricate interplay of many exotic low-dimensional quantum phenomena.

Effects of electronic correlation on topological properties of Kagome semimetal Ni3In2S2.

Kagome metals gain attention as they manifest a spectrum of quantum phenomena such as superconductivity, charge order, frustrated magnetism, and allied correlated states of condensed matter. With regard to electronic band structure, several of them exhibit non-trivial topological characteristics. Here, we present a thorough investigation on the growth and the physical properties of single crystals of Ni3In2S2 which is established to be a Dirac nodal line Kagome semimetal. Extensive characterization is attained through temperature and field-dependent resistivity, angle-dependent magnetoresistance and specific heat measurements. The central question we seek to address is the effect of electronic correlations in suppressing the manifestation of topological characteristics. In most metals, the Fermi liquid behaviour is restricted to a narrow range of temperatures. Here we show that Ni3In2S2 follows the Fermi-liquid behaviour up to 86K. This phenomenon is further supported by a high Kadowaki-Woods ratio obtained through specific heat analysis. Different interpretations of the magneto-transport study reveal that magnetoresistance exhibits linear behavior, suggesting the presence of Dirac semi-metallic signatures at lower temperatures. The angle-dependent magneto-transport study obeys the Voigt-Thomson formula. This, on the contrary, implies the classical origin of magnetoresistance. Thus, the effect of strong electron correlation in Ni3In2S2 manifests itself in the anisotropic magneto-transport. Furthermore, the magnetization measurement shows the presence of de-Haas van Alphen oscillations. Calculations of Berry phase provide insights into the topological features in the Kagome semimetal Ni3In2S2.&#xD.

Insights into electron and phonon topology: multi-fold fermions and Dirac nodal-line net bosons in SiX2 (X=P and As)

There has been a notable increase in enthusiasm for delving into new (quasi) particles within the domains of condensed matter and materials. Particularly, a distinctive excitement has arisen over a recently theorized exotic excitation found in a three-dimensional material, showcasing linear dispersion and the possibility of multi-fold degeneracy. In this article, we embark on an extensive investigation into the multi-fold degenerate exotic fermions beyond Dirac and Weyl in the pyrite-structured SiX2 compounds (with X as P and As). We delve into the topological attributes of band-touching nodes in fermions, featuring four- and six-fold degeneracy positioned at the Γ and R points in the first Brillouin zone, analyzing them through symmetry analysis. Regarding bosons, employing symmetry analysis, this study identifies distinctive properties where three-nodal surfaces (NSs) and phononic Dirac nodal-line (DNL) nets coexist. These phononic DNL nets comprise three phononic DNLs that share a common nodal point in momentum space, positioned at the intersection of two out of the three k i planes (i = x, y, z). The presence of observable phononic surface states in these materials may facilitate their experimental detection, suggesting these materials’ potential as prime candidates for realizing such phononic states in solid-state materials. Our investigation highlights the pyrite-structured SiX2 as a promising platform for studying multi-fold fermions and delving into their potential applications.

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.

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

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

Two-dimensional platinum borides: A Dirac nodal line quantum electrocatalyst for efficient hydrogen evolution reaction

Two-dimensional (2D) catalysts exhibiting high carrier mobility, near-zero Gibbs free energy (ΔGH*), and an active basal plane are highly desirable for optimizing the hydrogen evolution reaction (HER). However, fusing these attributes within a solitary material encounters profound difficulties. Utilizing density functional theory (DFT) calculations, we have identified the PtB2 monolayer is such a candidate, demonstrating exceptional dynamical, thermal, and mechanical stability. The band structure analysis reveals that the PtB2 monolayer features double Dirac points along its high-symmetry lines. The estimated Fermi velocity of the PtB2 monolayer is as high as 7.8×105m/s, close to that of graphene. By scanning the Dirac points in the first Brillouin Zone, the Dirac points constitute a nodal-line semimetal with a loop centered at the Γ point. This nodal line is anticipated to facilitate charge transfer between the catalyst surfaces and reaction intermediates, potentially enhancing catalytic efficiency. Importantly, PtB2 monolayer boasts superior HER performance, with a nearly zero ΔGH* of 0.057 eV at its boron-dominant sites. The application of a subtle 1% strain serves to reduce its ΔGH* to an even more favorable −0.003 eV, suggesting significantly improved HER capabilities. When layered in a bilayer form, the PtB2 exhibits van der Waals (vdW) type interlayer interactions. Remarkably, we found that varying the stacking order can effectively alter the nodal line's shape and, accordingly, the PtB2 layer's catalytic properties. The distinctive combination of a Dirac nodal line, ideal Gibbs free energy, and expansive active sites positions the PtB2 monolayer as a competitive 2D quantum catalyst for hydrogen production.

Illuminating the Bragg intersections as roots of Dirac nodal lines and high-order van Hove singularities

We theoretically reexamine nearly uniform electron models with weak crystalline potentials. In particular, we theorize the modulation of the plane-wave branches at linear regions where multiple Bragg planes intersect. Any such linear intersections involve three or more plane-wave branches diffracted by the periodic potential. Small interbranch interactions can yield various crossing and anticrossing singularities with promised breakdown of the quadratic approximation, extending alongside the intersection lines. Most of the intersections run in low-symmetric paths in the Brillouin zone and therefore we cannot completely characterize their electronic states with standard band-structure plotting methods. The present theory reveals a general mechanism in nearly uniform systems to induce the Dirac nodal lines and van Hove singularities with broken quadratic band approximation in three dimensions, which may host a variety of anomalous low-energy electronic properties. We apply the theory to a recently discovered high-temperature superconductor H3S to interpret the enigmatic density-of-state (DOS) peaking therein. The results show how and the continuous saddle points–the source of the peaked DOS–emerge, as well as reveal the companion Dirac nodal lines hidden in the conduction bands. Published by the American Physical Society 2024

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.

A novel and promising Penta-Octa-Based silicon carbide semiconductor

Penta-octa-graphene (POG) consists of pentagonal and octagonal carbon rings, hosting type-I and type-II Dirac line nodes due to its sp2 and sp3 mixed bonds. Inorganic analogs of 2D carbon lattices have increased the potential applications and changed the main properties of carbon-based structures. Therefore, this work proposes penta-octa-graphene based on silicon carbide using DFT simulations. With a cohesive energy of −5.22 eV/atom, POG-Si5C4 is energetically viable in comparison with other silicon carbide-based monolayers. Phonon dispersion analysis confirms the POG-Si5C4 dynamical stability. MD simulations demonstrate that this new monolayer can withstand temperatures up to 1020 K. Electronic analysis indicates it is a semiconductor with an indirect band gap transition of 2.02 eV. The mechanical properties exhibit anisotropy, with Young’s modulus ranging from 38.65 to 99.47 N/m and an unusual negative Poisson’s ratio of −0.09. The band edge alignment suggests that POG-Si5C4 holds potential for hydrogen generation through photocatalytic water splitting. This research opens possibilities for designing inorganic penta-octa-based structures and provides insights for future experimental and theoretical studies focused on exploring and optimizing advanced silicon-carbide 2D materials.

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.

Double Dirac nodal lines enforced by multiple nonsymmorphic symmetries

Double Dirac nodal lines enforced by multiple nonsymmorphic symmetries

Stability of 2D Crystals from Tessellation

AbstractReticular chemistry has been a cornerstone in the design of novel 2D materials. Despite numerous possibilities for topological arrangements, only a few with high symmetry can form stable networks. Here, starting from 2D carbons, four types of highly stable tessellations are discovered, which consist of chains of non‐hexagonal rings separated by hexagonal ribbons. A modified Read–Shockley model is established to perfectly describe the stability of these highly stable frameworks, which is based on the interaction between non‐hexagonal rings. Moreover, these four types of tessellations and the modified Read–Shockley model are found to be of general validity in designing highly stable 2D materials, which is verified by the calculations on polymorphs of boron nitride and molybdenum disulfide. Besides, among the studied 2D carbon allotropes, two semi‐metallic structures with highly anisotropic Dirac cones and one semimetal with a Dirac nodal line at the Fermi level are discovered, as protected by their D2h symmetry. Spin‐orbital coupling is further found to open small bandgaps for these three Dirac structures, making them nontrivial topological insulators. The in‐depth understanding of the stability of 2D crystals in this study provides a new way for rational design of 2D crystals that may show peculiar electronic structures.

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.