Dirac-like Cone Research Articles

Two-dimensional bilayer blue phosphorus Dirac-like material: a multi-orbital tight-binding investigation.

This study presents a theoretical examination of the electronic band structure of AA (AB) stacked bilayer blue phosphorus system within the fifth intralayer (5NN) and second interlayer nearest-neighbor (2NN) multi-orbital tight-binding (MOTB) approach. The variation of energy levels has been investigated through the symmetrical tensile strain of the low-buckled honeycomb lattice. Here, the primary objective is to examine the existence of Dirac electronic features in hexagonal stacked bilayer geometry. Our theoretical calculations predict that the AA bilayer is a new hexagonal two-dimensional material with px,y-orbital Dirac-like states at the high-symmetry K point. Consequently, these systems can host massless (massive) Dirac fermions. In particular, the AA bilayer exhibits zero-gap Dirac-like properties and manifests distinguishable Dirac-like cones in the presence of weak spin-orbit coupling when a modest stretch of 2.30% is achieved with a remarkably high Fermi velocity of approximately vf ≈ 0.12 × 105 m s-1. The behavior of the dispersion bands aligns reasonably well with recent experimental observations. Moreover, a stretch of 7.17% breaks some of the sublattice equivalence and enhances the spin-orbit interaction, resulting in the emergence of an electronic band gap of approximately ≈ 0.27 eV in the proximity of the high-symmetry K point. Furthermore, the tiny gap induced by the spin-orbit interaction implies topological nontriviality in the electronic state (quantum anomalous Hall state) of the honeycomb lattice. These findings categorize the AA bilayer as a rare two-dimensional Dirac-like material. This work provides, to the extent of our knowledge, a pioneering investigation into the existence of Dirac electronic properties in bilayer blue phosphorus. In addition, we present the first derivation of the MOTB model. However, the identified electronic characteristics designate this two-dimensional system as an ideal candidate for high-performance nanoelectronic devices.

Hidden symmetry-induced effective moving double-zero-index metamaterials.

Materials possessing an effective zero refractive index are often associated with Dirac-like cone dispersion at the center of the Brillouin zone (BZ). It has been reported the presence of hidden symmetry-enforced triply degenerate points [nexus points (NP)] away from the Brillouin zone center with the stacked dielectric photonic crystals. The spin-1 Dirac-like dispersion in the xy plane near the nexus point suggests a method for achieving zero refractive index materials. The stacked photonic crystals at the nexus points can be deemed as an effective moving double-zero-index medium (MDZIM) traveling with a speed relative to the laboratory reference. The ability of this moving double-zero-index medium to enable perfect wave tunneling across barriers without reflection has been demonstrated, dependent on the incident waves' specific angular orientations.

Graphsene as a novel porous two-dimensional carbon material for enhanced oxygen reduction electrocatalysis

Graphene allotropes with varied carbon configurations have attracted significant attention for their unique properties and chemical activities. This study introduces a novel two-dimensional carbon-based material, termed Graphsene (GrS), through theoretical study. Comprising tetra-, penta-, and dodeca-carbon rings, GrS’s cohesive energy calculations demonstrate its superior structural stability over existing graphene allotropes, including graphyne and graphdiyne families. Phonon dispersion analysis confirms GrS’s dynamic stability and its relatively low thermal conductivity. All calculated GrS elastic constants meet the Born criteria, ensuring mechanical stability. Ab-initio molecular dynamic simulations show GrS maintains its structure at 300 K. HSE06 calculations reveal a narrow electronic bandgap of 20 meV, with the electronic band structure featuring a highly anisotropic Dirac-like cone due to its intrinsic structural anisotropy along armchair and zigzag directions. Notably, GrS is predicted to offer exceptional catalytic performance for the oxygen reduction reaction, favoring the four-electron reduction pathway with high selectivity under both acidic and alkaline conditions. This discovery opens promising avenues for developing metal-free catalyst materials in clean energy production.

Spin resolved topological bulk state in acoustics

Extremely rare topologically protected acoustic energy sink is presented in this article. Acoustic topological phenomena are generally described using quantum anomalous hall effects (QAHE), quantum valley hall effects (QVHE), and quantum spin hall effects (QSHE) where spin orbit coupling is predominant. Topological edge states are demonstrated by bulk-boundary distinction when the bulk is insulated. In this article topological acoustic conductor and its phenomena are theoretically demonstrated where the boundaries are insulated. This is exactly opposite to the behavior of a topological acoustic insulator. Phenomena presented in this article could not be explained by any of the trio Quantum Hall effects. To explain the phenomenon phononic crystals or PnCs were designed to obtain accidental triple degeneracies, resulting a Dirac-like cone at the Γ point (k→=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\overrightarrow{k}=0$$\\end{document}). The phenomenon is microarchitecture and microrotation field independent. Here time reversal symmetry or the space inversion symmetry is not broken, and the degenerated ‘Deaf band’ dominates the local dispersion with a syncline top band. This scenario results in continuously changing ‘up spin’ and ‘down spin’ of the wave energy in the media and remain trapped without specific preferential direction of wave transport. The spin was found to generate the spin angular momentum, causing the switching in geometric phase from 0-2π\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0-2\\pi$$\\end{document} in cyclic pattern, keeping the energy trapped inside the bulk media.

Dirac cones in three-layered plates

The proper Dirac-like cones are observed in dispersion portraits of guided waves propagating in isotropic three-layered traction-free plates. It is revealed that if both layers have equal Poisson’s ratios and satisfy Wiechert condition, the Dirac-like cones appear regardless of the Poisson’s ratio value. This phenomenon opens a new approach for the creation of the layered plates possessing Dirac-like cones. The analysis is based on the Cauchy sextic formalism combined with the exponential fundamental matrix method.

Wave dispersion in a phononic metaplate with Boater-like cells

Meta-structure based on acoustic-mismatch among different materials shows distinct properties and also leads potential damage at the multi-material interfaces under complex loading conditions. In this paper, a phononic metaplate with Boater-like cells is proposed based on the concept of acoustic black hole and vibrator-plate models with the aim to explore the possibility of multi-acoustic meta-phenomena in a mono metaplate. Firstly, the proposed model is introduced and the governing equations for wave dispersion are formulated. Then the band structures are investigated. The wave dispersion at the double degeneracy points, Dirac-like cone, as well as bi-refraction are explored. At last, parameter dependence of band gaps is analyzed. The results indicate that multi-acoustic meta-phenomena could be realized in this phononic metaplate with Boater like cells, including bi-refraction and formation of band gaps. Considering low-cost and easily manufactured, the prototype in this paper provides a simpler but effective pattern for the metaplate design.

Inverse design of polymorphic Dirac-like cone dispersion relationship in photonic crystals

Dirac-like cone linear dispersion relations in photonic crystals (PhCs) often endow them with unique properties, yet searching for such relations can be challenging. We introduce a generalized inverse design system that, given the dielectric constants and lattice of two-dimensional PhCs, can efficiently determine its structural parameters to obtain its Dirac-like cone dispersion. Employing this inverse design strategy, we design three types of Dirac cone PhCs, including triple degenerate, quadruple degenerate, and triple degenerate under dual polarization with the same frequency. Further investigations reveal a systematic relationship between the radius of the dielectric rods in these PhCs and their corresponding Dirac frequencies across varying dielectric constants. The zero refractive index characteristic is validated in two of the three PhCs studied, as confirmed through numerical simulations. Additionally, by leveraging our proposed inverse design method, we introduce an innovative shell dielectric rod model, which encapsulates a dielectric material, achieving a quadruple degenerate dispersion structure with dual Dirac cones. This research provides a potent tool for the inverse design of PhCs and expands its application in Dirac cone dispersion design.

Bilayer Kagome Borophene with Multiple van Hove Singularities.

The appearance of van Hove singularities near the Fermi level leads to prominent phenomena, including superconductivity, charge density wave, and ferromagnetism. Here a bilayer Kagome lattice with multiple van Hove singularities is designed and a novel borophene with such lattice (BK-borophene) is proposed by the first-principles calculations. BK-borophene, which is formed via three-center two-electron (3c-2e) σ-type bonds, is predicted to be energetically, dynamically, thermodynamically, and mechanically stable. The electronic structure hosts both conventional and high-order van Hove singularities in one band. The conventional van Hove singularity resulting from the horse saddle is 0.065eV lower than the Fermi level, while the high-order one resulting from the monkey saddle is 0.385eV below the Fermi level. Both the singularities lead to the divergence of electronic density of states. Besides, the high-order singularity is just intersected to a Dirac-like cone, where the Fermi velocity can reach 1.34 × 106m s-1. The interaction between the two Kagome lattices is critical for the appearance of high-order van Hove singularities. The novel bilayer Kagome borophene with rich and intriguing electronic structure offers an unprecedented platform for studying correlation phenomena in quantum material systems and beyond.

Topological design of optical dirac-like cones by manipulating multiple local density of states

Topological design of optical dirac-like cones by manipulating multiple local density of states

Exotic quantum states in multilayer phosphorene nanoribbons in electric and magnetic fields

Using the tight-binding method, we modeled the energy spectra of multilayer phosphorene nanoribbons in a perpendicular electric field and in-plane magnetic field. Phosphorene nanosheets have a highly anisotropic honeycomb-like lattice. Their band gap is wider than that of their bulk counterparts, and armchair and zigzag edges of either skewed or regular type terminate the nanowire edges. Zigzag and various skewed edges support states whose wave functions decay exponentially from an edge. These states are virtually dispersionless and split the band gap. In principle, regular armchair edges do not host edge states. Thus, the energy spectrum in this case has a wide band gap. Here, we consider nanoribbons composed of multilayer phosphorene with regular armchair edges. A wide direct energy band gap exists when external fields are absent, but its width decreases when a perpendicular electric field is applied. The Dirac-like cones cross-section emerges at the zone center for a particular field value, named the lowest critical field. Although spin–orbit coupling was not included in the model, there is a small gap at the anticrossing site. The local density of states shows that the conduction- and valence-band states near the anticrossing are localized on the top and bottom surfaces of the nanoribbon. A thorough analysis of the interlayer coupling integrals indicates that for sufficiently thin phosphorene slabs, the electron and hole states at the opposite sides of the slab couple mutually strongly, despite the tendency of an external electric field to separate them. A further increase in the electric field induces an inversion between the conduction and valence band states in the zone center, which is inherent to topological insulators. However, sharp anticrossings at the zone center emerged for certain higher field values, named higher critical fields. Furthermore, when an in-plane magnetic field is applied, the conduction and valence band states shift, causing the dispersion to twist around the center of the k-space. Therefore, the band gap is indirect and closes for a sufficiently large magnetic field. A similar effect is observed in quantum spin Hall insulators, in which an in-plane magnetic field induces a semiconductor-to-semimetal transition. We conclude that the band inversion and topological-like features induced by external fields can be attributed to the strong interlayer coupling inherent to multilayered materials with anisotropic honeycomb lattices.

Bulk and surface electronic structure of NiBi3

We present a high-resolution, angle-resolved photoemission spectroscopy study of the normal electronic state of the superconducting ${\mathrm{NiBi}}_{3}$. Our experimental results show a complex Fermi surface structure with many sheets along the $\mathrm{\ensuremath{\Gamma}}\text{\ensuremath{-}}X$ and $\mathrm{\ensuremath{\Gamma}}\text{\ensuremath{-}}Y$ directions of the Brillouin zone. The band structure presents a topological surface state (TSS) at the high symmetry $\mathrm{\ensuremath{\Gamma}}$ point with a surface Dirac point at the energy $\ensuremath{-}0.185$ eV. The Dirac-like cone presents a linear dispersion along ${\mathrm{k}}_{x}$ while it presents saddle-like states along ${\mathrm{k}}_{y}$ located in the vicinity of the surface Dirac point. Our results are in good agreement with results of density functional theory band structure calculations. We also discuss the topological band structure of the ${\mathrm{NiBi}}_{3}$ compound.

Tuning Band Gaps in Twisted Bilayer Borophene

Two-dimensional (2D) materials have captured considerable attention owing to their different properties compared to those of three-dimensional (3D) structures. The participation of rotation angles allows 2D bilayer materials to show more diverse physical properties. Here, we investigated the structural and electronic properties of bilayer borophene with four different rotation angles using first-principles calculations based on the density functional theory method. We found that the cohesive energy shows the same trend as the interlayer spacing, where the system with 83.1° is the most stable and its partial charge density shows the formation of apparent interlayer π-bonds. Meanwhile, the rotation angles alter the energy band structures and reduce the band gap sizes. It is worth noting that when 83.1°, a Dirac-like cone exists in Γ-Y. Finally, 31.4 and 83.1° bilayer borophene with initial band gaps exhibit the same band gap change behavior under external electric fields. These results extend the understanding of the interlayer interactions of twisted bilayer borophene with van der Waals interactions and provide a new and effective approach to precisely tune the band structure in bilayer materials.

Interplay of electronic structure, magnetism, strain, and defects in carbide MXenes

The two-dimensional (2D) magnetic and semiconducting materials, including carbide MXenes, are in high demand for magneto-electronic devices and applications. Here, we report a first-principles study of electronic structure and magnetism of a Ti2C MXene, its derivatives Ti2CT2 (T = -F, -O, -OH, -H), and the effect of single vacancy defects (25% C, 12.5% O, and 12.5% and 5.5% Ti) and transition metal (V, Cr, Mn, and Co) dopings. The MAX phase Ti2AlC is a non-magnetic (NM) metal which upon removal of Al layer forms a pristine Ti2C MXene with A-type antiferromagnetic (AFM) semiconductor having reliable transition temperature (TN=41K) predicted by the Heisenberg model. All the functionalized MXenes are stable as NM metal except for Ti2CO2 which remains semiconducting with NM ground state. The significant effect of spin–orbit coupling (SOC) is evident in the band structure forming Dirac-like cones and band inversions near the Fermi level. Depending upon the type of vacancy defects Ti2CO2 is NM metal and ferromagnetic (FM) metal. The transition metal (TM) doped MXenes fulfill FM Stoner criterion. The V- and Co-doped MXenes are metals, whereas Cr- and Mn-doped are half-metal and semiconductor.

Acoustic computing: At tunable pseudospin-1 Hermitian Dirac-like cone.

Hermitian Dirac-like cones are proposed for creating acoustic logic gates herein. The predictive phenomenon of creating Dirac-like cones near a bipolar antisymmetric deaf band was found to be useful for acoustic computing of Boolean algebra. Unlike previous approaches, Dirac-like cone creates exclusive opportunity to perform all possible Boolean algebra computation with valid inputs. The phenomenon is demonstrated in two-dimensional phononic crystals (PnCs), consisting of tunable square columns in air media. By predictive tuning of the deaf bands, a triply to doubly degenerated Dirac-like cone is reported to form and is particularly useful for acoustic computing. It is only possible when a bottom band has a negative curvature that is lifted from a nearby doubly degenerated band with positive curvature, which is again degenerated with a deaf band. On the contrary, similar computing possibilities are difficult when the bottom band degenerates with the deaf band and the top band is lifted. Using these phenomena, acoustic logic gates are designed to perform Boolean algebra through AND, NAND, OR, and NOR gate operations. A simple one degree of freedom system and a complex six degrees of freedom system are proposed and demonstrated in which simple rotation of the PnCs activates a specific gate.

Dipolar spin-waves and tunable band gap at the Dirac points in the 2D magnet ErBr3

Topological magnon insulators constitute a growing field of research for their potential use as information carriers without heat dissipation. We report an experimental and theoretical study of the magnetic ground-state and excitations in the van der Waals two-dimensional honeycomb magnet ErBr3. We show that the magnetic properties of this compound are entirely governed by the dipolar interactions which generate a continuously degenerate non-collinear ground-state on the honeycomb lattice with spins confined in the plane. We find that the magnon dispersion exhibits Dirac-like cones when the magnetic moments in the ground-state are related by time-reversal and inversion symmetries associated with a Berry phase π as in single-layer graphene. A magnon band gap opens when the dipoles are rotated away from this state, entailing a finite Berry curvature in the vicinity of the K and K’ Dirac points. Our results illustrate that the spin-wave dispersion of dipoles on the honeycomb lattice can be reversibly controlled from a magnetic phase with Dirac cones to a topological antiferromagnetic insulator with non-trivial valley Chern number.

Dual-insensitive zero refraction based on annular photonic crystals

Over the past few years, zero refraction (ZR) represents an important breakthrough in field of distinctive dynamic optical beam tuning for double-zero-index (media with zero relative permittivity and permeability) photonic crystals (PCs). Because accidental ZR effects for conventional PCs is sensitive to the structural or refractive index parameters, how to enhance the robustness of ZR design is vital for applications. Here, we report a pioneering wave property that reveals a non-accidental Dirac-like cone dispersion composed of low- or high-energy bands, corresponding to dual-insensitive ZR effects for both transverse magnetic and transverse electric polarizations based on the same annular PCs. The performance of non-accidental ZR is simultaneously based on refractive index-insensitivity and structural- insensitivity, attributed to a satisfactory filling ratio.

Tunable transmission near Dirac-like point in the designed plasma photonic crystal

The ingenious combination of gaseous plasma and alumina columns forms a plasma photonic crystal with the advantage of dynamic tunability to control the transmission of electromagnetic waves. Plasma density as another degree of freedom is used to realize the Dirac-like cone, which degenerates accidentally at the first Brillouin zone in a square lattice. The investigations of transmission spectrum and phase variation demonstrate that the Dirac-like cone formed in a plasma photonic crystal still possess the zero-refractive-index property, and the cloaking effect for obstacles can be turned on or off by adjusting the electron density. Based on the feature of dynamic tunability, the dual-channel optical switch is designed, and the transmission path of electromagnetic waves can be controlled dynamically.

Hermitian and Non-Hermitian Dirac-Like Cones in Photonic and Phononic Structures

Accidental degeneracy plays an important role in the generation of novel band dispersions. Photonic structures that exhibit an accidental Dirac-like conical dispersion at the center of the Brillouin zone can behave like a zero-index material at the Dirac-point frequency, leading to a number of unique features, such as invariant phase in space, wave tunneling, photonic doping and anti-doping, etc. Such a phenomenon has been explored in on-chip structures or three dimensions recently. The introduction of non-Hermiticity into the system via loss or gain could transform the accidental Dirac-like cone into a spawning ring of exceptional points, a complex Dirac-like cone or other unique dispersions. Similar Dirac-like cones and related physics are also observed in phononic structures. This review presents an overview of the accidental-degeneracy-induced Dirac-like cones at the center of the Brillouin zone in both photonic and phononic structures, including the fundamental physics, effective-medium description and experimental demonstration, as well as current challenges and future directions.

Structural and electronic properties of nonconventional α -graphyne nanocarbons

In this work, we propose a set of nonconventional graphyne lattices inspired by previously studied $s{p}^{2}$ nanocarbon sheets, known as haeckelites, and we study their electronic properties by density functional theory methods. Two of these systems are solely composed of five- and seven-membered rings in rectangular lattices, while a third system features a mixture of five-, six-, and seven-polygonal rings in a hexagonal network. We show that these systems exhibit dynamical, thermal, and mechanical stability as demonstrated by phonon band structures, molecular dynamics simulations, and by the computation of their elastic constants. The three lattices exhibit a metallic nature similar to their full-$s{p}^{2}$ counterparts. However, the graphynes' electronic properties are strongly different from those of the original haeckelites, as the largest contribution to their frontier states comes from the $sp$ hybridized atoms. Furthermore, the three proposed systems feature different electronic signatures from each other, as their frontier states feature different energy ranges for forbidden electronic states, and one of them features a set of Dirac-like cones.

Dirac cones with zero refractive indices in phoxonic crystals.

In this paper, simultaneous zero refractive indices (ZRIs) for both sound and light are realized on the basis of a 2D triangular lattice phoxonic crystal (PxC) with C6v symmetry. For the phononic mode, accidental phononic Dirac degeneracy at the center of Brillouin zone (BZ) occurs at a relatively high frequency which leads to the failure of the efficient medium theory; hence, it is no longer applicable to the realization of acoustic ZRI. We thus turn to a low-frequency phononic Dirac cone located at K point, the corner of the BZ, which shows in-phase pressure field oscillations in expanded unit cells. Using zone folding, we further reveal the cause for the characteristic of acoustic ZRI. For the photonic mode, a low-frequency photonic Dirac-like cone can be achieved by adjusting the geometric parameter due to the high contrast permittivity between scatterers and the matrix. When the phononic and photonic low-frequency Dirac dispersions coexist, the PxC can be mapped into a zero-index material for both sound and light at the same time. The new mechanism for simultaneously controlling sound and light helps to achieve acousto-optic synchronous cloaking and unidirectional transmission, which are numerically demonstrated.