Dirac Nodes Research Articles

Tight-Binding Model and Electronic Property of Dirac Nodal Line in Single-Component Molecular Conductor [Pt(dmdt)2

Motivated by the recent discovery of Dirac nodal line in the single-component molecular conductor [Pt(dmdt)$_{2}$], we propose a three-orbital tight-binding model based on the Wannier fitting of the first-principles calculation, and address the problems of edge states, topological properties and magnetic susceptibility. We find that logarithmic peaks of the local density of states emerge near the Fermi energy, owing to pseudo-one-dimensional edge states that appear between the Dirac nodal lines. Magnetic susceptibility calculated in our model can explain the experimental result at a high temperature. In the presence of a realistic spin-orbit coupling, we show that [Pt(dmdt)$_{2}$] is a topological nodal line semimetal with isolated electron and hole pockets.

Quantum Hall effect of Weyl fermions in n-type semiconducting tellurene

Dirac and Weyl nodal materials can host low-energy relativistic quasiparticles. Under strong magnetic fields, the topological properties of Dirac/Weyl materials can directly be observed through quantum Hall states. However, most Dirac/Weyl nodes generically exist in semimetals without exploitable band gaps due to their accidental band-crossing origin. Here, we report the first experimental observation of Weyl fermions in a semiconductor. Tellurene, the two-dimensional form of tellurium, possesses a chiral crystal structure which induces unconventional Weyl nodes with a hedgehog-like radial spin texture near the conduction band edge. We synthesize high-quality n-type tellurene by a hydrothermal method with subsequent dielectric doping and detect a topologically non-trivial π Berry phase in quantum Hall sequences. Our work expands the spectrum of Weyl matter into semiconductors and offers a new platform to design novel quantum devices by marrying the advantages of topological materials to versatile semiconductors.

First-principles design of a Dirac semimetal: An NP monolayer

We report a two-dimensional (2D) Dirac semimetal in an orthorhombic $\mathit{Pmma}$ structure, an NP monolayer, based on first-principles calculations. The NP monolayer is found to be stable according to phonon dispersion and molecular dynamical simulations. It exhibits a pair of anisotropic Dirac cones exactly at the Fermi level, located along high symmetry lines in the Brillouin zone, and shows highly anisotropic in-plane stiffness. First-principles calculations show that Dirac cones are locally stable under strains along the $x$ or $y$ direction and electric fields perpendicular to the monolayer. The Dirac nodes are protected from gap opening by the mirror-reflection symmetry in the $x$ direction. We construct an effective two-band tight-binding model to characterize the Dirac states. Our result provides a promising 2D material for special electronics applications.

High pressure investigation of an organic three-dimensional Dirac semimetal candidate having a diamond lattice

$(\mathrm{ET}){\mathrm{Ag}}_{4}{(\mathrm{CN})}_{5}$ [ET = BEDT-TTF: bis(ethylenedithio)tetrathiafulvalene] is a rare example of organic conductors that crystallizes in a diamond structure due to the tetrahedral arrangement of neighboring ET molecules. Because each ET has a $+1$ site charge, the band is half filled, which in combination with strong Coulomb interactions, turn $(\mathrm{ET}){\mathrm{Ag}}_{4}{(\mathrm{CN})}_{5}$ into a Mott insulator. Recently, it was realized that this material may realize a nodal Dirac semimetal with a diamondlike lattice, whose state can be induced by suppressing the strong electron correlations. In this report, we present high pressure transport and optical studies on $(\mathrm{ET}){\mathrm{Ag}}_{4}{(\mathrm{CN})}_{5}$. Our transport study indicates that the activation energy is highly suppressed by the application of hydrostatic pressure. At high pressures, the system varies from activated behavior into Coulomb gap variable range hopping.

Magic-angle semimetals with chiral symmetry

We construct and solve a two-dimensional, chirally symmetric model of Dirac cones subjected to a quasiperiodic modulation. In real space, this is realized with a quasiperiodic hopping term. This hopping model, as we show, at the Dirac node energy has a rich phase diagram with a semimetal-to-metal phase transition at intermediate amplitude of the quasiperiodic modulation, and a transition to a phase with a diverging density of states and sub-diffusive transport when the quasiperiodic hopping is strongest. We further demonstrate that the semimetal-to-metal phase transition can be characterized by the multifractal structure of eigenstates in momentum space and can be considered as a unique "unfreezing" transition. This unfreezing transition in momentum space generates flat bands with a dramatically renormalized bandwidth in the metallic phase similar to the phenomena of the band structure of twisted bilayer graphene at the magic angle. We characterize the nature of this transition numerically as well as analytically in terms of the formation of a band of topological zero modes. For pure quasiperiodic hopping, we provide strong numerical evidence that the low-energy density of states develops a divergence and the eigenstates exhibit Chalker (quantum-critical) scaling despite the model not being random. At particular commensurate limits the model realizes higher-order topological insulating phases. We discuss how these systems can be realized in experiments on ultracold atoms and metamaterials.

Dirac Materials in a MatrixWay

Recent years have been the platform of discovery of a wide range of materials, like d-wave superconductors, graphene, and topological insulators. These materials do indeed share a fundamental similarity in their low-energy spectra namely the fermionic excitations. There carriers behave as massless Dirac particles rather than conventional fermions that obey the usual Schrodinger Hamiltonian. A surprising aspect of most Dirac materials is that many of their physical properties measured in experiments can be understood at the non-interacting level. In spite of the large effective coupling constant in case of graphene, it has been observed that the interactions do not seem to play a major key role. Controlling the electrons at Dirac nodes in the first Brillouin zone needs the interplay of sublattice symmetry, inversion symmetry and the time-reversal symmetry. In this article, we have used explicit fundamental symmetry to understand the basic features of Dirac materials occurring in three diverse systems in a compact 2 × 2 matrix way. Furthermore, the robustness of the Dirac cones has also been explored from the scientific notion of topological physics. In addition, an elementary introduction on the three dimensional (3D) topological insulators and d wave superconductors will shed light in their respective fields. Furthermore, we have also discussed the way to evaluate the effective mass tensor of the carriers in the two dimensional (2D) Dirac materials. This methodology has also been critically extended to three dimensional (3D) topological insulators and d wave superconductors.

Determination of the Fermi surface and field-induced quasiparticle tunneling around the Dirac nodal loop in ZrSiS

Unambiguous and complete determination of the Fermi surface is a primary step in understanding the electronic properties of topical metals and semi-metals, but only in a relatively few cases has this goal been realized. In this work, we present a systematic high-field quantum oscillation study up to 35 T on ZrSiS, a textbook example of a nodal-line semimetal with only linearly dispersive bands crossing the Fermi energy. The topology of the Fermi surface is determined with unprecedented precision and all pockets are identified by comparing the measured angle dependence of the quantum oscillations to density functional theory calculations. Comparison of the Shubnikov-de Haas and de Haas-van Alphen oscillations at low temperatures and analysis of the respective Dingle plots reveal the presence of significantly enhanced scattering on the electron pocket. Above a threshold field that is aligned along the c-axis of the crystal, the specific cage-like Fermi surface of ZrSiS allows for electron-hole tunneling to occur across finite gaps in momentum space leading to quantum oscillations with a complex frequency spectrum. Additional high-frequency quantum oscillations signify magnetic breakdown orbits that encircle the entire Dirac nodal loop. We suggest that the persistence of quantum oscillations in the resistivity to high temperatures is caused by Stark interference between orbits of nearly equal masses.

The giant planar Hall effect and anisotropic magnetoresistance in Dirac node arcs semimetal PtSn4

Topological semimetals (TSMs) present intriguing quantum states and have attracted much attention in recent years because of exhibiting various anomalous magneto-transport phenomena. Theoretical prediction shows that some novel phenomena, such as negative magnetoresistance (MR) and the planar Hall effect (PHE), originate from the chiral anomaly in TSMs. In this work, high-field (33 T) Shubnikov–de Haas (SdH) oscillations are obtained to reveal the topology of PtSn4. Giant PHE and anisotropic magnetoresistance (AMR) are observed in Dirac node arcs of semimetal PtSn4. First, a non-zero transverse voltage can be acquired while tilting the in-plane magnetic field. Moreover, the amplitude of PHE sharply increases at T* ∼ 50 K with decreasing temperature, which is suggested to be related to the Fermi surface reconstruction observed in PtSn4. Subsequently, the field-dependent amplitudes of the PHE show an abnormal behavior around 50 K, which is thought to stem from the complex correlation between the chiral charge and electric one in PtSn4 driving the system into different coupling states due to the complicated band structure. On the other hand, the relative AMR is negative and up to −98% at 8.5 T. Our work proves that the PHE measurements are a convincing transport fingerprint feature to confirm the chiral anomaly in TSMs.

Topological Dirac nodal loops in nonsymmorphic hydrogenated monolayer boron

The existence of a topological Dirac nodal loop is predicted for hydrogenated monolayer boron sheets with a nonsymmorphic symmetry. The three-center two-electron bonds in boron compounds restrict the electronic system to be insulating or semimetallic with a Dirac nodal loop. Two types of electronic structures are distinguished by the Z_2 topological index and confirmed by first-principles total-energy calculations. The topological taxonomy, developed in this research, can be applied to other two-dimensional materials and to seek novel Dirac fermions.

Planar Hypercoordinate Motifs in Two-Dimensional Materials.

ConspectusAs one of the most important and versatile elements, carbon renders itself as one of the most fundamental and cutting-edge topics in chemistry, physics, and materials science. Many carbon-based chemical rules were established accordingly. While the tetrahedral predilection of tetracoordinate carbon has been a cornerstone of organic chemistry since 1874, almost a century later tetracoordinate carbon was found to be able to adopt planar structures known as planar tetracoordinate carbon (ptC), which are stabilized electronically by good π-acceptor (delocalization of a lone electron pair of ptC) or σ-donor (promoting electron transfer to electron-deficient bonding) substituents or mechanically by appropriate steric enforcement. The experimental and theoretical achievements for the rule-breaking ptC species totally refreshed our understanding of chemical bonding and triggered exploration of peculiar molecules featuring planar pentacoordinate carbon (ppC) and planar hexacoordinate carbon (phC) as well as other outlandish species such as planar hypercoordinate silicon.While the planar hypercoordinate carbon chemistry has been gradually established for molecules in the past five decades, there is growing interest in pursuing their extension systems, especially in two-dimensional (2D) space as a result of the recent extensive studies of graphene and its analogues. Though the natural 2D layered crystals do not contain any planar hypercoordinate carbon or silicon, several 2D nanosheets featuring planar or quasi-planar hypercoordinate ones have been theoretically suggested. Encouragingly, these unique planar configurations possess decent stabilities, and some of them are even the global minimum structure, exhibiting great potential for experimental realization. As the nature of a material is mainly determined by its structural characteristics (e.g., dimensionality, crystallography, and bonding), the combination of planar hypercoordinate chemistry and 2D nanoscience not only endows these rule-breaking systems with the merits of 2D materials but also may offer various promising properties and applications. For example, an unusual negative Poisson's ratio can be found in ppC-containing Be5C2 and planar pentacoordinate silicon (ppSi)-containing CaSi monolayers, of which the former has an anisotropic Dirac cone and the latter is a semiconductor with a desirable band gap for the semiconductor industry. Specially, shortly after the theoretical prediction, a planar hexacoordinate silicon (phSi)-containing Cu2Si monolayer was experimentally synthesized and characterized with the 2D Dirac nodal line fermion, which offers a platform to achieve high-speed, low-dissipation nanodevices.In this Account, we review the recent progress, mostly by density functional theory (DFT) computations, in designing 2D materials with planar hypercoordinate motifs. We describe the key achievements in this field, paying special attention to the "bottom-up" and "isoelectronic substitution" design strategies. In addition, the fundamental stabilization mechanisms of planar hypercoordinate motifs in an infinite layer are discussed. We hope that this Account will inspire more experimental and theoretical efforts to explore nanomaterials with such unconventional chemical bonding.

BaHgSn: A Dirac semimetal with surface hourglass fermions

We proposed that BaHgSn is a Dirac semimetal (DSM) which can host hourglass-like surface states (HSSs) as protected by nonsymmorphic glide symmetry. Compared to KHgSb, an isostructural topological crystalline insulator with the same HSSs, BaHgSn has an additional band inversion at $\Gamma$ point. This band inversion is induced by the stronger interlayer coupling among Hg-Sn honeycomb layers than that among Hg-Sb-layers in KHgSb, which leads to bulk Dirac nodes in BaHgSn along the layer stacking direction $\Gamma$-$A$. In addition, the mirror Chern number $C_{i}$ protected by the mirror plane $\overline{M}_{z}$ ($k_z$=0) changes from 2 in KHgSb to 3 in BaHgSn. Therefore, when a compressive uniaxial strain is applied along the $y$ axis to break the rotation symmetry protecting the DSM state, BaHgSn becomes a strong topological insulator with $Z_{2}$ indices of $(1;000)$ and the topological surface Dirac cone co-exists with HSSs on the (010) surface. The Wilson-loop spectra have been calculated to verify these topological features. The calculated surface states, the Fermi surfaces and their quasiparticle interference patterns are ready to be compared with experimental measurements.

Tunable large spin Hall and spin Nernst effects in the Dirac semimetals ZrXY (X=Si,Ge;Y=S,Se,Te)

The ZrSiS-type compounds are Dirac semimetals and have been attracting considerable interest in recent years due to their topological electronic properties and possible applications. In particular, gapped Dirac nodes can possess large spin Berry curvatures and thus give rise to large spin Hall effect (SHE) and spin Nernst effect (SNE), which may be used to generate pure spin current for spintronics and spin caloritronics without applied magnetic field or magnetic material. In this paper we study both SHE and SNE in ZrXY (X = Si, Ge; Y = S, Se, Te) based on \textit{ab initio} relativistic band structure calculations. Our theoretical calculations reveal that some of these compounds exhibit large intrinsic spin Hall conductivity (SHC) and spin Nernst conductivity (SNC). The calculated SHC of ZrSiTe is as large as -755 ($\hbar$/e)(S/cm). Since the electric conductivity of these Dirac semimetals are much smaller than that of platinum which has the largest intrinsic SHC of $\sim$2200 ($\hbar$/e)(S/cm), this indicates that they will have a larger spin Hall angle than that of platinum. Remarkably, we find that both the magnitude and sign of the SHE and SNE in these compounds can be significantly tuned by changing either the electric field direction or spin current direction and may also be optimized by slightly varying the Fermi level via chemical doping. Analysis of the calculated band- and $k$-resolved spin Berry curvatures show that the large SHE and SNE as well as their remarkable tunabilities originate from the presence of many slightly spin-orbit coupling-gapped Dirac nodal lines near the Fermi level in these Dirac semimetals. Our findings suggest that the ZrSiS-type compounds are promising candidates for spintronic and spin caloritronic devices, and will certainly stimulate further experiments on these Dirac semimetals.

Catalytic activity of PtSn4: Insights from surface-science spectroscopies

Bulk PtSn4 has recently attracted the interest of the scientific community for the presence of electronic states exhibiting Dirac node arcs, enabling possible applications in nanoelectronics. Here, by means of surface-science experiments and density functional theory, we assess its suitability for catalysis by studying the chemical reactivity of the (0 1 0)-oriented PtSn4 surface toward CO, H2O, O2 molecules at room temperature and, moreover, its stability in air. We demonstrate that the catalytic activity of PtSn4 is determined by the composition of the outermost atomic layer. Specifically, we find that the surface termination for PtSn4 crystals cleaved in vacuum is an atomic Sn layer, which is totally free from any CO poisoning. In oxygen-rich environment, as well as in ambient atmosphere, the surface termination is a SnOx skin including SnO and SnO2 in comparable amount. However, valence-band states, including those forming Dirac node arcs, are only slightly affected by surface modifications. The astonishingly beneficial influence of surface oxidation on catalytic activity has been demonstrated by electrocatalytic tests evidencing a reduction of the Tafel slope, from 442 down to 86 mV dec−1, whose origin has been explained by our theoretical model. The use of surface-science tools to tune the chemical reactivity of PtSn4 opens the way toward its effective use in catalysis, especially for hydrogen evolution reaction and oxygen evolution reaction.

Creation of the Dirac Nodal Line by Extrinsic Symmetry Engineering.

The formation of the Dirac nodal line (DNL) requires intrinsic symmetry that can protect the degeneracy of continuous Dirac points in momentum space. Here, as an alternative approach, we propose an extrinsic symmetry protected DNL. On the basis of symmetry analysis and numerical calculations, we establish a general principle to design the nonsymmorphic symmetry protected 4-fold degenerate DNL against spin-orbit coupling in the nanopatterned 2D electron gas. Furthermore, on the basis of experimental measurements, we demonstrate the approximate realization of our proposal in the Bi/Cu(111) system, in which a highly dispersive DNL is observed at the boundary of the Brillouin zone. We envision that the extrinsic symmetry engineering will greatly enhance the ability for artificially constructing the exotic topological bands in the future.

Kagome Spinwaves: Spin Dynamics and Dirac Nodes in a Kagome Lattice (Ann. Phys. 2/2020)

Kagome Spinwaves: Spin Dynamics and Dirac Nodes in a Kagome Lattice (Ann. Phys. 2/2020)

Unique topological nodal line states and associated exceptional thermoelectric power factor platform in Nb3GeTe6 monolayer and bulk.

To date, ideal topological nodal line semimetal (TNLS) candidates in high dynamically stable and high thermally stable two-dimensional (2D) materials are still extremely scarce. Herein, by performing first-principles calculations, on the one hand, we found that three-dimensional Nb3GeTe6 bulk possesses a single closed TNL in the kx = 0 plane and a fourfold TNL in the S-R direction without considering spin-orbit coupling (SOC). Under the SOC effect, a new topological signature, i.e., hourglass-like Dirac nodal line, occurs in Nb3GeTe6 bulk. On the other hand, we found that the 2D Nb3GeTe6 monolayer features a doubly degenerate TNL along surface X-S paths. Importantly, this monolayer enjoys the following advantages: (i) it has high thermal stability at room temperature and above; (ii) its TNL is nearly flat in energy and is very close to the Fermi level (EF), which provides a fantastic maximum value platform of the thermoelectric power factor around the EF; and (iii) no extraneous bands are close to the TNL, near the Fermi level. Moreover, we explore the entanglement between the topological states and thermolectric properties for the 2D Nb3GeTe6 monolayer. Our work not only reports the discovery of a novel TNL material, but also builds the link between the TNL and thermoelectric properties.

Type-II Dirac states in full Heusler compounds XInPd2 ( X = Ti, Zr, and Hf)

We predict three full Heusler compounds XInPd2 (X = Zr, Hf and Ti) to be potential candidates for type-II Dirac semimetals. The crystal symmetry of these compounds have appropriate chemical environment with a unique interplay of inversion, time reversal and mirror symmetry. These symmetries help to give six pairs of type-II Dirac nodes on the C_4 rotation axis, closely located at/near the Fermi level. Using first principle calculations, symmetry arguments and crystal field splitting analysis, we illustrate the occurrence of such Dirac nodes in these compounds. Bulk Fermi surfaces have been studied to understand the Lorentz symmetry breaking and Lifshitz transition (LT) of Fermi surfaces. Bulk nodes are projected on the (001) and (111) surfaces which form the surface Fermi arcs, that can further be detected by probes such as angle resolved photo-emission and scanning tunneling spectroscopy. By analyzing the evolution of arcs with changing chemical potential, we prove the fragile nature and the absence of topological protection of the Dirac arcs. Our predicted compounds overcome the limitations of the previously reported PtTe2 class of compounds.

Bco-C24: A new 3D Dirac nodal line semi-metallic carbon honeycomb for high performance metal-ion battery anodes

Three-dimensional porous carbon materials play a significant role in gas separation and energy storage. However, their low performances in energy storage hamper their applications. Herein, we propose a new possible category of carbon honeycomb (CHC), i.e. CHCs with asymmetrical channels (denoted as asymmetrical CHCs), to increase their performance. As an example, by cross-linking graphene sheet with sp3–hybridized carbon chains, we prepare a new 3D porous asymmetrical CHC, i.e. bco-C24. It is dynamically, thermally, and mechanically stable. Our first-principles calculations and tight binding results demonstrate that it possesses a significant electronic band structure of Dirac nodal lines, which are ascribed to the px and py orbitals of α carbon atoms in the graphene ribbons that have both α and β carbon atoms. It provides high carrier mobility between 7.98 × 105 and 9.99 × 105 m/s. It has high theoretical capacities (743.8/495.9/991.8/743.8 mA h/g), low diffusion barriers (0.077/0.032/0.117/0.169 eV), low average voltages, and negligible volume changes for Na/K/Ca/Li-ion batteries. This study not only constructs a new concept of asymmetrical CHCs and provides a strategy of cross-linking graphene sheets to create its sample structures, but also suggests new carriers for ion storage in the superior next generation metal-ion battery anodes.

Spin Dynamics and Dirac Nodes in a Kagome Lattice

AbstractHerein, the spin dynamics for various magnetic configurations arranged on a Kagome lattice is investigated. Using a Holstein–Primakoff expansion of the isotropic Heisenberg Hamiltonian with multiple exchange parameters, the development and evolution of magnetic Dirac nodes with both anisotropy and magnetic field are examined. From the classical energies, the phase diagrams for the ferromagnetic (FM), antiferrimagnetic (AfM), and the 120° phases are shown as functions of J1, J2, J3, and anisotropy. Furthermore, the production of bosonic Dirac and Weyl nodes in the spin‐wave spectra is shown. Through frustration of the magnetic geometry, a connection to the asymmetric properties of the Kagome lattice and the various antiferromagnetic configurations is discerned. Most interesting is the 120° phase, which does not have Dirac nodes when considering only J1 due to the formation of an analogous antiferromagnetic honeycomb lattice, but gains Dirac symmetry with next‐nearest neighbor interactions. Additionally, the presence of flat modes that are characteristic of cluster excitations is shown. Further study of external frustrations from a magnetic field and anisotropy reveals a tunability of the exchange interactions and nodal points.

Two-dimensional Tunable Dirac/Weyl Semimetal in Non-Abelian Gauge Field

Three-dimensional(3D) Weyl semimetal(WSM) with linear energy spectra has attracted significant interest. Especially they have been observed experimentally in several solid materials with the breaking of inversion symmetry. Here we predict a new family of particle-hole({mathscr{C}}) invariant 2D WSMs in the non-Abelian gauge field, which can emerge in the low energy bands being close to Fermi energy (dubbed Weyl-I) and the high energy bands being away from Fermi energy (dubbed Weyl-II), only when the time-reversal symmetry({mathscr{T}}) of the 2D Dirac semimetal is broken in the presence of in-plane Zeeman fields. Moreover, a 2D Dirac node can split into a pair of Weyl nodes showing the same Berry phase, and the 2D WSM, being protected by {mathscr{T}} symmetry, exhibits four Weyl-I nodes, whose energies are invariant with the variation of the magnetic field. The corresponding Fermi velocity and Berry connection have been calculated. Based on the 2D WSMs, we also examine inhomogeneous pairings of attractive Fermi gases and find a new kind of the LO states with the beat frequency. This 2D WSM provides a realistic and promising platform for exploring and manipulating exotic Weyl physics, which may increase the experimental feasibility in the context of ultracold atoms.