Dirac Point Research Articles

Potential Application of 2D Haeckelite MoS2 as an Anode Material for Mg Ion Batteries.

The design and preparation of anode materials with structural stability, fast ion transmission, and low open-circuit voltage are critical to the development of magnesium ion batteries (MIBs). The feasibility of the unique phase Haeckelite MoS2 (Hae-MoS2) monolayer with Haeckelite structure as a potential anode material for MIBs was investigated using density functional theory (DFT) calculations. The Hae-MoS2 monolayer exhibits excellent structural stability and semimetallic characteristics with a Dirac cone located at the Gamma point of band structure. Mg ion is easily adsorbed on the Hae-MoS2 monolayer surface with an adsorption energy of -2.06 eV and can diffuse rapidly with a low diffusion energy barrier (0.3 eV), indicating excellent charge and discharge rates. Most importantly, the Hae-MoS2 monolayer exhibits a suitable open-circuit voltage, which falls within the desired voltage range and ensures the safety of battery performance. These exceptional properties indicate that the Hae-MoS2 monolayer can be proposed as a candidate for anode material for MIBs.

Quasi-Dirac points in electron-energy spectra of crystals

Specific properties, such as surface Fermi arcs, features of quantum oscillations and of various responses to a magnetic field, distinguish Dirac semimetals from ordinary materials. These properties are determined by Dirac points at which a contact of two electron-energy bands occurs and in the vicinity of which these bands disperse linearly in the quasimomentum. This work shows that almost the same properties are inherent in a wider class of materials in which the Dirac spectrum can have a noticeable gap comparable with the Fermi energy. In other words, the degeneracy of the bands at the point and their linear dispersion are not necessary for the existence of these properties. The only sufficient condition is the following: In the vicinity of such a quasi-Dirac point, the two close bands are well described by a two-band model that takes into account the strong spin-orbit interaction. To illustrate the results, the spectrum of ZrTe5 is considered. This spectrum contains a special quasi-Dirac point, similar to that in bismuth.

Single pair of charge-2 Dirac and charge-2Weyl phonons in GeO2

Abstract The presence of a pair of Weyl and Dirac points (WP–DP) in topological semimetal states is intriguing and sought after due to the effects associated with chiral topological charges. However, identifying these states in real materials poses a significant challenge. In this study, by means of first-principles calculations we predict the coexistence of charge-2 Dirac and charge-2 Weyl phonons at high-symmetry points within a noncentrosymmetric P41212 space group. Furthermore, we propose GeO2 as an ideal candidate for realizing these states. Notably, we observe two distinct surface arcs that connect the Dirac and Weyl points across the entire Brillouin zone, which could facilitate their detection in future experimental investigations. This study not only presents a tangible material for experimentalists to explore the topological properties of WP–DP states but also opens up new avenues in the quest for ideal platforms to study chiral particles.

Non-magnetic layers with a single symmetry-protected Dirac cone: Which additional dispersions must appear?

In two-dimensional (2D), non-magnetic materials, a single Dirac cone at high-symmetry point (HSP) of the Brillouin zone (BZ), akin to the one in graphenes’ band structure, cannot appear as the only quasiparticle at the Fermi level. Here we found two layer groups with time-reversal symmetry, among all possible both without and with spin-orbit coupling, that host one Dirac cone at HSP and we show which additional dispersions appear: a pair of Dirac lines on opposite BZ edges and a pair of Dirac cones that can be moved but not removed by symmetry preserving perturbations, on the other two BZ edges. We illustrate our theory by a tight-binding band structure and discuss real 2D materials that belong to one of the two symmetry groups. Finally, we single out smaller or bigger discrepancies among the published papers on the same or related topic.

Nernst effect of the dice lattice in a strong magnetic field

The dice lattice bears a similar honeycomb lattice structure to graphene but with a non-dispersive flat band intersecting the Dirac bands at the band center. In this work, we investigate Nernst effect of the dice lattice in a strong magnetic field, focusing on the role of the flat band. By using the Chebyshev polynomial Green’s function method, we show that no Nernst effect (Sxy=0) is around the Dirac point in the clean limit contrary to the graphene case because of the existence of a zero Hall conductivity platform. However, an unconventional negative Sxy of the double-peak structure emerges instead when the flat band is broadened by disorder and temperature. In addition, when a mass term of Dirac electrons is introduced in the system to open an energy gap, a negative single peak of Sxy appears at the Dirac point and this is due to the derivative quantum Hall effect of non-Dirac electrons in the flat band appearing in the energy gap.

Metallic nature of T-graphene sheet and nanotubes

The band structure, density of states (DOS), and Pauli magnetic susceptibility (PMS) of T-graphene nanotubes (TGNTs) with varying chiralities and diameters are investigated using the tight-binding Hamiltonian model and Green's function formalism. We analyze two edge types: zigzag (zTGNT) and armchair (aTGNT). Our findings reveal that both zTGNTs and aTGNTs exhibit metallic behavior regardless of diameter. Notably, aTGNTs feature Dirac points in their band structure, with their abundance increasing with nanotube diameter. As compared to graphene, when the diameter of the nanotube increases, aTGNTs reveal more Dirac points at the Fermi level. Additionally, increasing the diameter leads to the emergence of additional sub-bands in the band structure and van-Hove singularities in the DOS diagrams. Consequently, the PMS curves exhibit a crossover, dividing into distinct regimes at varying temperatures. The metallic properties of both TGNT types are apparent in the PMS curves, attributed to the proportional relationship between PMS and DOS. Furthermore, the DOS curves converge towards monolayer behavior as the TGNT diameter increases significantly.

Spin Space Groups: Full Classification and Applications

In this work, we exhaust all the spin space symmetries, which fully characterize collinear, noncollinear, and commensurate spiral as well as incommensurate spiral magnetism, etc., and investigate enriched features of electronic bands that respect these symmetries. We achieve this by systematically classifying the so-called spin space groups (SSGs)—joint symmetry groups of spatial and spin operations that leave the magnetic structure unchanged. Generally speaking, they are accurate (approximate) symmetries in systems where spin-orbit coupling (SOC) is negligible (finite but weaker than the energy scale of interest), but we also show that specific SSGs could remain valid even in the presence of strong SOC. In recent years, SSGs have played increasingly pivotal roles in various fields such as altermagnetism, topological electronic states, and topological magnon, etc. However, due to its complexity, a complete SSG classification has not been completed up to now. By representing the SSGs as O(N) representations, we—for the first time—obtain the complete classifications of 1421, 9542, and 56 512 distinct SSGs for collinear (N=1), coplanar (N=2), and noncoplanar (N=3) magnetism, respectively. SSG not only fully characterizes the symmetry of spin degrees of freedom, but also gives rise to exotic electronic states, which, in general, form projective representations of magnetic space groups (MSGs). Surprisingly, electronic bands in SSGs exhibit features never seen in MSGs, such as (i) nonsymmorphic SSG Brillouin zone, where SSG operations behave as a glide or screw when acting on momentum, (ii) effective π flux, where translation operators anticommute with each other and yield duplicate bands, (iii) higher-dimensional representations unexplained by MSGs, and (iv) unconventional spin texture on a Fermi surface, which is completely determined by SSGs, independent of Hamiltonian details. To apply our theory, we identify the SSG for each of the 1595 published magnetic structures in the MAGNDATA database on the Bilbao Crystallographic Server. Material examples exhibiting the novel features (i)–(iv) are discussed with emphasis. We also investigate new types of SSG-protected topological electronic states that are unprecedented in MSGs. In particular, we propose a 3D Z2 topological insulator state with a fourfold degenerate Dirac point on the surface and a new scenario of anomalous Z2 helical states that appear on magnetic domain walls. Published by the American Physical Society 2024

Rainbow trapping and concentration of surface waves on broad waveguide

Abstract In recent years, topological insulators have been widely designed to manipulate various types of classical waves. The topological edge states characterized by defect and backscattering immunity show great application potential in energy harvesting. This work reports a spin-locked topological surface wave channel, which consists of concrete-filled steel tubes (CFST) placed on foundation soil. Here, the distance between the lattice and the center of the CFST controls the hopping strength between adjacent atoms, determining the topological phase transition. Introducing the surface wave crystal with Dirac cones in the interface, then the robust broad waveguide modes of phononic heterostructure are explored. Notably, incorporating the rainbow effect allows for precise regulation and reliable concentration within the broad waveguide. The proposed broad waveguide surpasses traditional waveguides by simultaneously focusing and segregating energy, enabling applications in low-frequency energy harvesting, sensing, and logic gates. Our work will provide an efficient recovery platform for daily vibration energy, especially for vehicle loads.

Temperature tunability of topological phase transitions and edge states in two-dimensional acoustic topological insulators

Topological insulators are characterized by exhibiting an internal insulating state but a surface conductor state, which makes them advantageous for applications in novel devices. However, for most given acoustic topological metamaterials, the operating frequency is relatively fixed and the effect of temperature on their topological properties is rarely considered. Therefore, a temperature-tunable acoustic topological insulator is constructed in this paper. The quadruple degenerate Dirac cone formed at Γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma$$\\end{document} point can be opened by adjusting the temperature, causing topological band inversion between the doubly degenerate dipolar and quadrupole states, and achieving topological phase transition. The evolution of its topological state with temperature is numerically investigated and a novel topological acoustic waveguide is constructed. The switching effect of temperature on the waveguide device is verified by numerical simulation and experiment. Non-contact active modulation of edge states in the structure is achieved by temperature-controlled topological phases, exhibiting acoustic switching effects. This study can provide corresponding references for the intelligent control of acoustic topology in noise, vibration, and other aspects.

Transition metal atom on the two-dimensional Dirac structure RhB4/OsB4: A novel multifunctional electrocatalyst

The design of low-cost multifunctional electrocatalysts with high carrier mobility, high surface free energy and base surface activity facilitates hydrogen evolution reactions (HER) and oxygen reduction reactions (ORR), which are essential for the development of clean energy. Recent studies have shown significant progress in developing HER/ORR bifunctional catalysts, such as transition metal alloys, oxides, sulfides, and carbon-based composites. These materials are highly efficient in catalysis and help reduce costs. In this work, density functional theory is used to predict the performance of single atom catalysis (SACs) embedded with transition metal (TM) using two-dimensional (2D) Dirac node-ring semi-metal RhB4/OsB4 monolayer as substrate. Systematic calculations show that the TM@RhB4/OsB4 structure with thermodynamic and kinetic stability presents multiple active sites on the basal surface. Notably, Fe@RhB4 is an excellent hydrogen evolution reaction HER catalyst because Dirac cones occur near the Fermi level of this structure, providing high carrier densities and accelerating charge transfer between the catalyst and reaction intermediates. When the substrate RhB4/OsB4 is modified by Sc and Cu atoms, the band gap of the structure becomes small, which increases the conductivity of the original structure. The ΔGH* values of Sc@RhB4 and Cu@OsB4 were 0.118, and 9.38 meV, respectively, outperforming the ideal catalyst Pt. In addition, it is found that Fe@RhB4, and Mn@OsB4 exhibit outstanding catalytic properties for the oxygen reduction reaction (ORR), with overpotentials of 0.41V, and 0.40V, respectively, surpassing the performance of the reference catalyst Pt. It is exciting that the Fe@RhB4 exhibits ideal HER/ORR bifunctional electrocatalytic properties. This study will provide a theoretical basis for the development of multifunctional electrocatalysts in the field of Dirac nodal ring semi-metal materials by single atom doping technology.

Observation of monopole topological mode

Among the many far-reaching consequences of the potential existence of a magnetic monopole, it induces a topological zero mode in the Dirac equation, which was derived by Jackiw and Rebbi 48 years ago and has been elusive ever since. Here, we show that the monopole and multi-monopole solutions can be constructed in the band theory by gapping the three-dimensional Dirac points in hedgehog mass configurations. We then experimentally demonstrate such a monopole bound state in an optimized Dirac acoustic crystal structurally modulated in full solid angles. The monopole mode exhibits the optimal scaling behavior — whose modal spacing is inversely proportional to the cubic root of the modal volume. This work completes the kink-vortex-monopole zero-mode trilogy and paves the way for exploring higher-dimensional bulk-topological-defect correspondence.

Reconfigurable directional selective tunneling of p-type phonons in polarized elastic wave systems

There have been many studies on the ground state of phononic crystals, but few studies on the nature of the excited state. In this paper, we introduce the asymmetric Klein tunneling method in phononic systems, which enables selective direction and control of elastic waves by inducing polarization through an external field in an artificial barrier. Using tight-binding theory, we systematically studied phononics in a super-honeycomb structure, demonstrating the anisotropic transition properties of excited state phonons through a matrix model involving the ground state’s s-type and the first excited state’s p-type wave functions. Additionally, we exploit the thermal sensitivity of epoxy to achieve localized thermal field-induced distortion of the bottom flat band, forming a tiled Dirac cone, and thereby creating a reconfigurable polarized artificial barrier in the elastic wave system. Elastic waves propagate in these systems with topological charge conservation. Combining this with the theoretical of excited-state phonons, we demonstrate asymmetric Klein tunneling with directional selectivity in the elastic wave carriers, and systematically investigate the performance of this tunneling. Furthermore, we design a four-port elastic waveguide based on the principle of asymmetric tunneling, which achieves exceptional directional selectivity of elastic wave signals by adjusting the polarization direction of barriers at the junctions. These studies not only extend the application of Klein tunneling in elastic wave systems but also open new research avenues for the study of elastic wave devices controlled by various external fields, showing direct application potential in elastic wave signal processing.

Photon-assisted extrinsic Weyl orbits and three-dimensional quantum Hall effect in surface-doped topological Dirac semimetals

Photon-assisted extrinsic Weyl orbits and three-dimensional quantum Hall effect in surface-doped topological Dirac semimetals

A terahertz chiral metamaterial with tunable dual-band to broadband circular dichroism based on Dirac semimetals

Chiral metamaterials play a crucial role in manipulating the electromagnetic waves. This paper intoduces a three-dimensional Dirac semimetal materials (3D DSM) metamaterial structure tailored for tunable and broadband circular dichroism (CD) effects at terahertz (THz) frequencies. Using the Jones matrix, electromagnetic multipole resonance theory, and the atomic orbital hybridization model, the resonant performance for the DSM based metamaterials in reflection and transmission design is systematically analyzed, in terms of the resonant peak and bandwidth. Simulation results show that the bilayer DSM metamaterial supports the chiral response with dual-band resonance in transmitted spectra, and its CD and working frequency could be tuned by adjusting the rotation angle between the upper and lower DSM metamaterial layers and Fermi level of DSM. Therefore, the tunable CD from 0 to 0.51 could be achieved across a wide THz frequency from 3.56 THz to 4.02 THz. Additionlly, the resonant frequency is highly sensitive to the surrounding refractive index (RI), yielding a RI sensing sensitivity up to 308.6 GHz/RIU. The proposed DSM based chiral metamaterial features a tunable and broadband design, offering a universal design method and potential applications for the modulation of light polarization, chiral sensing and imaging, and communications.

Ti3O MOenes: Quantum Spin Hall Effect and Promising Semiconductors for Light-Harvesting.

The continuous pursuit of novel two-dimensional (2D) materials with intriguing properties has been a driving force in advancing various scientific and technological frontiers. Here, based on a wide range of first-principles calculations, we predicted the existence of a novel family of 2D transition-metal oxides, the Ti3O MOenes (MXene-like 2D transition oxides), and determined its distinctive electronic and topological properties. A pair of 2D antiferromagnetic (AFM) Dirac points precisely located at the Fermi level in the absence of spin-orbit coupling (SOC) is observed in the 1T-Ti3O monolayer. Moreover, upon halogenation on a bare monolayer, 1T-Ti3OCl3 and 1T-Ti3OBr3 monolayers display the quantum spin Hall (QSH) effect with nontrivial helical edge states within the gapless bulk states. Specifically, single layer 1T-Ti3OF3 behaves as an indirect semiconductor with a gap of 0.81 eV, exhibiting a strong light-harvesting capability. The indirect-gap feature can be switched to a direct one by only exerting a small tensile strain of 1.5%. These findings broaden emerging phenomena in a rich family of MOenes, suggesting a novel platform for the development of next-generation nanodevices.

Topological properties of C4zT-symmetric semimetals

Two-dimensional topological semimetals are typically characterized by the vorticity of gapless points, and can be classified according to the band representations. However, the topological properties involving the distribution of the Berry curvature in the entire Brillouin zone are often overlooked. In this study, we investigate a two-band two-dimensional topological semimetal protected by C4zT magnetic symmetry, exhibiting a two-fold band degeneracy at the Γ(0, 0) and M(π, π) points. Due to the presence of C4zT symmetry, the Brillouin zone is divided into two patches characterized by half-quantized Berry curvature fluxes with opposite signs. In multi-band case, the half-quantization deviates, indicating the fragile nature. The semimetal presents counter-propagating half-edge channels, accompanied by power-law decaying and oscillating edge currents. The band topology leads to unconventional Landau levels featuring anisotropic edge modes. Each massless Dirac cone, associated with the half-quantized Berry curvature flux, exhibits an integer quantum Hall conductance. Additionally, we calculate the local orbital magnetization with open boundary conditions in both the x and y directions. This reveals isolated magnetization islands, highlighting an experimentally observable magnetic phenomenon in this topological semimetal.

Half-quantum mirror Hall effect

We predict a half-quantized mirror Hall effect induced by mirror symmetry in strong topological insulator films. These films are known to host a pair of gapless Dirac cones in the first Brillouin zone associated with surface electrons. Our findings reveal that mirror symmetry assigns a unique mirror parity to each Dirac cone, resulting in a half-quantized Hall conductance of ±e22h\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pm \\! \\frac{{e}^{2}}{2h}$$\\end{document} for each cone. Despite the total electrical Hall conductance being null due to time-reversal invariance, the difference in the Hall conductance between the two cones yields a quantized Hall conductance of e2h\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\frac{{e}^{2}}{h}$$\\end{document} for the difference in mirror currents. The effect of helical edge mirror current - a crucial feature of this quantum effect - may, in principle, be determined by means of electrical measurements. The half-quantum mirror Hall effect reveals a type of mirror-symmetry induced quantum anomaly in a time-reversal invariant lattice system, giving rise to a topological metallic state of matter with time-reversal invariance.

Silicon Waveguide-Integrated Platinum Telluride Midinfrared Photodetector with High Responsivity and High Speed.

The detection of mid-infrared light, covering a variety of molecular vibrational spectra, is critical for both civil and military purposes. Recent studies have highlighted the potential of two-dimensional topological semimetals for mid-infrared detection due to their advantages, including van der Waals (vdW) stacking and gapless electronic structures. Among them, mid-infrared photodetectors based on type-II Dirac semimetals have been less studied. In this paper, we present a silicon waveguide integrated type-II Dirac semimetal platinum telluride (PtTe2) mid-infrared photodetector, and further improve detection performance by using PtTe2-graphene heterostructure. For the fabricated silicon waveguide-integrated PtTe2 photodetector, with an external bias voltage of -10 mV and an input optical power of 86 nW, the measured responsivity is 2.7 A/W at 2004 nm and a 3 dB bandwidth of 0.6 MHz is realized. For the fabricated silicon waveguide-integrated PtTe2-graphene photodetector, as the external bias voltage and input optical power are 0.5 V and 0.13 μW, a responsivity of 5.5 A/W at 2004 nm and a 3 dB bandwidth of 35 MHz are obtained. An external quantum efficiency of 119% can be achieved at an input optical power of 0.376 μW.

Frequency-selective valley-edge transmission and channeling in phononic-crystal plates with dual topological modulations

In this numerical study, we propose dual-modulated topological pillared phononic crystal (PnC) plates and demonstrate their application in achieving frequency-selective waveguiding of Lamb-wave valley-edge states. We show that both the radius and the height of the pillars in the honeycomb unit cell can be varied, allowing a generalized parameter space to obtain the complete topological bandgaps and two groups of distinct valley Hall phases for designing topological waveguides operating in different frequency ranges. Accordingly, we construct different types of phase domain walls to support valley-edge states using the dual-modulated PnC plates with a lattice constant of 2000 μm and with topological bandgaps opened around the Dirac cone frequency of 426 kHz. The numerical results show that the valley-edge states emerge to cover different frequency ranges and exhibit robust backscattering immunity when propagating along zigzag paths with sharp corners. Furthermore, the transport path of the valley-edge states can be designed to be highly dependent on the operating frequency in different domain walls. Consequently, we design a straight waveguide and three multichannel waveguides to demonstrate frequency-dependent switchable transmission and selective channeling of valley-edge states, respectively. The results of this study pave the way for the development and optimization of topological acoustic circuits using the generalized parameter space approaches and are expected to find promising applications in frequency-controlled and signal-division devices.

Material Design and Discovery in Full-Heusler Compounds: A Comprehensive First-Principles Analysis of XMg2Hg, XMgHg2, and X2MgHg (X = Sc, Li)

This study conducts a comprehensive first-principles analysis of the structural, mechanical, phonon dispersion, and electronic properties of XMg2Hg, XMgHg2, and X2MgHg (X = Sc and Li) compounds. Using energy-volume curves, cohesive and formation energy, and phonon dispersion analyses, we confirm the stability of these compounds. Our calculations reveal that Li2MgHg and ScMg2Hg are more stable in the cubic structure with space group F4¯3m (216), whereas other compounds are stable in the Fm3¯m (225) structure. Phonon dispersion calculations indicate dynamical stability for all compounds except Li2MgHg in the Fm3¯m structure and Sc2MgHg and LiMg2Hg in the cubic structure with space group F4¯3m (216). Mechanical stability is confirmed through the calculation of elastic constants, with Sc-based compounds showing higher bulk modulus, shear modulus, and Young's modulus compared to Li-based compounds. Electronic properties, analyzed through density of states and band structure calculations, confirm the metallic nature of these compounds, with significant contributions from Mg atoms at the Fermi energy. The study also identifies distinct electronic features such as flat electron bands and a Dirac point at the Gamma point for ScMgHg2​. Pressure-dependent studies indicate these materials are normal metals without topological phase transitions.