Dirac Point Research Articles

Active multi-focus vortex beam terahertz encoding metasurface based on Dirac semimetals.

An electromagnetic wavefront can be flexibly manipulated by discrete phase coding on the coding unit. In this paper, we designed two coding metasurfaces with 1-bit and 3-bit based on active tuning of Dirac semimetals by controlling the Fermi level (E F) with an external polarization voltage. The size and structure of the metasurface remain unchanged with this strategy. Both designs were found to be dynamically tunable. The 1-bit coding metasurface enables beam conversion, single-focus switching, and switching between single-focus and multi-focus. On the other hand, the 3-bit coding metasurface enables the switching between vortex beams and single-beam mirror reflections. These proposed structures have potential applications in terahertz (THz) communications and terahertz-focused imaging, opening up new possibilities for the dynamic modulation of THz waves.

Quantum spin Hall effect and emergence of conducting edge states in silicene supported by MX (M=Ga, In; X=S, Se, Te) monolayer

The electronic structure of silicene supported by monolayer of different monochalcogenide MX (GaS, GaSe, GaTe and InSe) substrates has been investigated by first principle density functional theory. By calculating the formation energies and phonons, it has been seen that silicene supported by monolayer of MX remains stable. The systems retain their almost [Formula: see text] planner configurations with small buckling as that of the free standing silicene and also the Bader charge analysis shows that silicene hardly interacts with any of the MX substrates. The Dirac cone with a small gap ([Formula: see text] [Formula: see text]meV) has been observed in each of the cases. All the systems show quantum spin Hall effect and the quantum spin Hall conductivities have been estimated to be within the range [Formula: see text]S/cm, which are larger than that of the free standing silicene. Our calculations show that even if the systems have bulk band gaps but the edge states are conducting in nature.

Second order topology in a band engineered Chern insulator

Haldane model is a celebrated tight binding toy model of a Chern insulator in a 2D honeycomb lattice that exhibits quantized Hall conductance in the absence of an external magnetic field. In our work, we deform the bands of the Haldane model smoothly by varying one of its three nearest neighbour hopping amplitudes (t1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$t_1$$\\end{document}), while keeping the other two (t) fixed. This breaks the C3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C_3$$\\end{document} symmetry of the Hamiltonian, while the Mx∗T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_x*T$$\\end{document} symmetry is preserved. The symmetry breaking causes the Dirac cones to shift from the K and the K′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$'$$\\end{document} points in the Brillouin zone (BZ) to an intermediate M point. This is evident from the Berry curvature plots which show a similar shift in the corresponding values as a function of the deformation parameter, namely t1t\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\frac{t_1}{t}$$\\end{document}. We observe two different topological phases of which, one is a topological insulator (TI) and the other is a second order topological insulator (SOTI). The Chern number (C) remains perfectly quantized at a value of C=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C=1$$\\end{document} for the TI phase and it goes to zero in the SOTI phase. Furthermore, the evolution of the Wannier charge center (WCC) as the band is smoothly deformed shows a jump in the TI phase indicating the presence of conducting edge modes. We also study the SOTI phase and diagonalize the real space Hamiltonian on a rhombic supercell which shows the presence of in-gap zero energy corner modes. The polarization of the system, namely px\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p_x$$\\end{document} and py\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p_y$$\\end{document}, are evaluated, along the x and the y directions, respectively. We see that both px\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p_x$$\\end{document} and py\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p_y$$\\end{document} are quantized in the SOTI phase owing to the presence of the inversion symmetry of the system. Finally we establish the SOTI phase as an example of a topological phase with zero Berry curvature and provide an analogy with the two dimensional Su–Schrieffer–Heeger model.

Strain-tunable Dirac semimetal phase transition and emergent superconductivity in a borophane

A two-dimensional (2D) Dirac semimetal with concomitant superconductivity has been long sought but rarely reported. It is believed that light-element materials have the potential to realize this goal owing to their intrinsic lightweight and metallicity. Here, based on the recently synthesized β12 hydrogenated borophene, we investigate its counterpart named β12-B5H3. Our first-principles calculations suggest it has good stability. β12-B5H3 is a scarce Dirac semimetal demonstrating a strain-tunable phase transition from three Dirac cones to a single Dirac cone. Additionally, β12-B5H3 is also a superior phonon-mediated superconductor with a superconducting critical temperature of 32.4 K and can be further boosted to 42 K under external strain. The concurrence of Dirac fermions and superconductivity, supplemented with dual tunabilities, reveals β12-B5H3 is an attractive platform to study either quantum phase transition in 2D Dirac semimetal or the superconductivity or the exotic physics brought about by their interplay.

Optical conductivity of anisotropic Dirac semimetals: The relaxation-time approximation

Optical conductivity of anisotropic Dirac semimetals: The relaxation-time approximation

Research on electronic and optical properties of pristine and Ag/Au/Cu-doped graphene/MoS2 heterostructures

The Dirac cone in the single-layer graphene limits its application in electronic devices such as Schottky barrier diodes and field-effect transistors. Thus, we make the novel heterostructures based on graphene to solve this problem. The electronic and optical properties of pristine and Ag/Au/Cu-doped graphene/MoS2 heterostructures are investigated by using the density functional theory. For the Ag/Au/Cu-doped MoS2 monolayer, the results show that they are magnetic. Their bands across the Fermi level, which indicates these systems are metallic. For the Ag/Au/Cu-doped graphene/MoS2 heterostructures, they are metallic and nonmagnetic. Especially in the Au-doped graphene/MoS2, the Dirac cone opens about 66 meV. It means that Au-doped graphene/MoS2 has the potential to be a candidate material for high speed electronic devices. Compared with pristine heterostructure, the probability of electron transition in the low energy region is the enhanced in Ag/Au/Cu-doped systems. The optical absorption coefficient of doped heterostructure is enhanced in the range of 0–0.4 eV and 1.7–2.7 eV. This work indicates that these heterostructures have a certain potential in the application of nanodevices.

Tight-binding model with sublattice-asymmetric spin-orbit coupling for square-net nodal line Dirac semimetals

Tight-binding model with sublattice-asymmetric spin-orbit coupling for square-net nodal line Dirac semimetals

Evaluation of the structural, electronic and magnetic properties of modified 8-16-4 graphyne by 3d transition metals: A DFT-D2 study

A new two-dimensional carbon allotrope called 8-16-4 graphyne (GY) has been recently introduced (in 2021). This allotrope consists of sp. and sp2 hybridized carbon atoms. To investigate the adsorption behavior of single atom of 3d transition metals (TM) on 8-16-4 GY, corrected density functional theory (DFT-D2) was employed. The results reveal that single TM atoms prefer to bind tightly in the center of the 16-carbon ring of GY, and the adsorption energy of TMs decreases from Sc to Zn with a reducible trend from −9.282 to −1.158 eV, respectively. These high adsorption energies show that diffusion of TM atoms and clustering of them are prevented on the surface of the carbon frame. Pristine and 3d TM decorated GY have some Dirac points, zero band gap, and conductivity properties. Also, pristine and all of TM decorated GY except Cr, Mn, and Fe-decorated GY haven't magnetic properties. These findings suggest that 8-16-4 GY is a suitable carbonic substrate to prevent the clustering of TM atoms that is essential for some applications such as effective single-atom catalysts, hydrogen storage, CO2 capture, etcetera.

Discovery of the First 3D Dirac Semimetal in Organics

Discovery of the First 3D Dirac Semimetal in Organics

Quantum oscillations revealing topological band in kagome metal ScV6Sn6

Compounds with kagome lattice structure are known to exhibit Dirac cones, flatbands, and van Hove singularities, which host numerous versatile quantum phenomena. Inspired by these intriguing properties, we investigate the temperature and magnetic field-dependent electrical transports along with the theoretical calculations of ScV6Sn6, a nonmagnetic charge-density wave (CDW) compound. At low temperatures, the compound exhibits Shubnikov–de Haas quantum oscillations, which help to design the Fermi-surface (FS) topology. This analysis reveals the existence of several small FSs in the Brillouin zone, combined with a large FS. Among them, the FS-possessing Dirac band is nontrivial and generates a nonzero Berry phase. In addition, the compound also shows the anomalous Hall-like behavior up to the CDW phase transition, and they might be correlated. Combining these interesting physical properties with the CDW phase, ScV6Sn6 presents a unique material example of the versatile HfFe6Ge6 family and provides various promising opportunities to explore the series further. Published by the American Physical Society 2024

Electronic properties, interface contact and transport properties of strain-modulated MS2/borophosphene and MSeS/borophosphene (M = Cr, Mo, W) heterostructure: Insights from first-principles

Controlling the interface contact performance to form low-resistance ohmic contact is of great importance in designing low-power two-dimensional (2D) devices. Here, we explore a 2D semi-metal with Dirac cones, borophosphene, for different types of contact with MS2, MSeS/borophosphene (M = Cr, Mo, W) using density functional theory (DFT) and non-equilibrium Green's function (NEGF) methods. The results indicate that under no strain, different van der Waals heterojunctions (vdWHs) exhibit an n-type (p-type) Schottky contact type, with the CrS2/borophosphene vdWHs exhibiting a lower barrier height (Φn = 0.08 eV). Next, we find that the in-plane strain is more efficient than the vertical strain. Under in-plane strain modulation, the contact type will change from Schottky to Ohmic contacts as the tensile strain increases. Similarly, the contact type will change from Schottky to semiconductor as the compressive strain increases. Under the influence of vertical strain, the CrS2/borophosphene vdWHs transition into ohmic contact only when the interlayer spacing increases to above 0.4 Å. Finally, we study the ohmic contact formation and transport characteristics based on the device angle. These findings demonstrate that interface contact types can be effectively regulated by strain, which is crucial for the design and manufacturing of novel nano electronic devices composed of borophosphene based vdWHs.

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.

Angular Engineering Strategy for Enhanced Surface Nonlinear Frequency Conversion in Centrosymmetric Topological Semimetal HfGe0.92Te.

Surface nonlinear optics are essential for developments in integrated photonics and micro/nano optoelectronics. However, the nonlinear optical conversion efficiency on a surface is restricted by the finite nonlinear susceptibility of matter and the intrinsic atomic-layered interaction length between light and matter. In this work, based on an angular engineering strategy, it is demonstrated that the centrosymmetric topological semimetal HfGe0.92Te crystal has a giant and anisotropic surface second-order nonlinear susceptibility up to 5535 ± 308pm V-1 and exhibits efficient and unprecedented second-harmonic generation (SHG). The maximum optical conversion efficiency is found to be up to 3.75‰, which is 104 times higher than that obtained from a silicon surface. Because of the linear dispersion over a wide range of energies around the Dirac points, this high conversion efficiency can be maintained with SHG wavelengths ranging from the visible region (779nm) to the deep-UV region (257.5nm). This study can facilitate the development of topological photonics and integrated nonlinear photonics based on topological semimetals.

Hosohedral nodal-line superconductivity in hexagonal ABC Dirac semimetals

The recently identified hexagonal non-polar phase of KZnBi, an archetypal topological semimetal, has been found to cohost superconductivity on the surface. We propose that KZnBi can realize an unconventional topological superconductor featuring the hosohedral formation of nodal lines and Bogoliubov Fermi surface emerging under a magnetic field. Our density functional theory (DFT)-based low-energy model shows that the nonsymmorphic band degeneracy of the Dirac bands generically triggers topological nodal line superconductivity fostered by inter-band Coulomb interaction. In particular, the nodal lines of the gap resemble a hexagonal hosohedron with the Schläfli symbol of {2, 6}. Remarkably, the holohedral nodal line superconductor defines the topological phase boundary of the Bogoliubov Fermi surface in the limit where time-reversal symmetry is restored. Our results demonstrate that line nodes readily inflate to the Bogoliubov Fermi surface under an external magnetic field. We provide an experimentally verifiable explanation for the observed superconductivity and suggest a feasible platform for observing topological superconductivity in the hexagonal ABC ternary systems class.

Emergence of symmetric and asymmetric Dirac points under periodic electric and vector potentials in ABA-trilayer graphene superlattice.

We have theoretically investigated the impact of both periodic electric and vector potentials on the low energy spectrum of ABA-trilayer graphene superlattice. Finite energy Dirac points appear in the energy spectrum due to the application of the vector potential. These extra Dirac points are symmetric about k y = 0 plane for equal barrier and well widths. For different barriers and well widths, one Dirac point shifts away and the second Dirac point shifts towards the k y = 0 plane. The extra Dirac points are not only generated from the original Dirac point but also emerge from the valleys developed in the energy spectrum. The application of both electric and vector potentials with identical barrier and well widths breaks the symmetry of the spectrum about the Fermi level. When the electric and vector potentials are asymmetric with all three layers having the same electric potentials, the energy spectrum becomes asymmetric about the Fermi level, and this asymmetric behavior of both potentials annihilates the original Dirac point from the spectrum. When all the layers have different electric potentials and both electric and vector potentials are asymmetric, the spectrum becomes asymmetric again, but this time the asymmetry of the spectrum occurs across the k y = 0 plane.

First-principles prediction of superconducting properties of monolayer 1T'-WS2 under biaxial tensile strain.

High-purity 1T'-WS2 film has been experimentally synthesized [Nature Materials, 20, 1113-1120 (2021)] and theoretically predicted to be a two-dimensional (2D) superconducting material with Dirac cones [arXiv:2301.11425]. In the present work, we further study the superconducting properties of monolayer 1T'-WS2 by applying biaxial tensile strain. It is shown that the superconducting critical temperature Tc firstly increases and then decreases with respect to tensile strains, with the highest superconducting critical temperature Tc of 7.25 K under the biaxial tensile strain of 3%. In particular, we find that Dirac cones also exist in several tensile strained cases. Our studies show that monolayer 1T'-WS2 may provide a good platform for understanding the superconductivity of 2D Dirac materials.

Electronic phase transition in bilayer P6mmm borophene.

In this study, using the tight-binding model and Green's function technique, we investigate potential electronic phase transitions in bilayer P6mmm borophene under the influence of external stimuli, including a perpendicular electric field, electron-hole coupling between sublayers (excitonic effects), and dopants. Our focus is on key electronic properties such as the band structure and density of states. Our findings reveal that the pristine lattice is metal with Dirac cones around the Fermi level, where their intersection forms a nodal line. The system undergoes transitions to a semiconducting state - elimination of nodal line - with a perpendicular electric field and a semimetallic state - transition from two Dirac cones to a single Dirac cone - with combined electric field and excitonic effects. Notably, with these, the system retains its massless Dirac-like bands characteristic at finite energy. However, introducing a dopant still leads to a metallic phase, but the Dirac-like bands become massive. Considering all these effects, the system ultimately reaches a semiconducting phase with massive Dirac-like bands. These results hold significance for optoelectronic applications.

Electronic Lieb lattice signatures embedded in two-dimensional polymers with a square lattice.

Exotic band features, such as Dirac cones and flat bands, arise directly from the lattice symmetry of materials. The Lieb lattice is one of the most intriguing topologies, because it possesses both Dirac cones and flat bands which intersect at the Fermi level. However, the synthesis of Lieb lattice materials remains a challenging task. Here, we explore two-dimensional polymers (2DPs) derived from zinc-phthalocyanine (ZnPc) building blocks with a square lattice (sql) as potential electronic Lieb lattice materials. By systematically varying the linker length (ZnPc-xP), we found that some ZnPc-xP exhibit a characteristic Lieb lattice band structure. Interestingly though, fes bands are also observed in ZnPc-xP. The coexistence of fes and Lieb in sql 2DPs challenges the conventional perception of the structure-electronic structure relationship. In addition, we show that manipulation of the Fermi level, achieved by electron removal or atom substitution, effectively preserves the unique characteristics of Lieb bands. The Lieb Dirac bands of ZnPc-4P shows a non-zero Chern number. Our discoveries provide a fresh perspective on 2DPs and redefine the search for Lieb lattice materials into a well-defined chemical synthesis task.

Coexistence of topological node surface and Dirac fermions in phonon-mediated superconductor YB2C2.

The interaction between nontrivial topology and superconductivity in condensed matter physics has attracted tremendous research interest as it could give rise to exotic phenomena. Herein, based on first-principles calculations, we investigate the electronic structures, mechanical properties, topological properties, dynamic stability, electron-phonon coupling (EPC), and superconducting properties of the synthesized real material YB2C2. It is a tetragonal structure with P4/mbm symmetry and exhibits excellent stability. The calculated electronic band structures reveal that a zero-dimension (0D) Dirac point and two-dimensional (2D) nodal surface coexist near the Fermi level. A spin-orbit coupling (SOC) Dirac point with the topological Fermi arc is observed on the (001) surface. These nodal surfaces are protected by a two-fold screw axis and time-reversal symmetry. Based on the Bardeen-Cooper-Schrieffer theory, the superconducting transition temperature (Tc) in the range 1.25-4.45 K with different Coulomb repulsion constant μ* for YB2C2 is estimated to be consistent with previous experimental results. In addition, the EPC is mainly from the coupling between the dx2-y2 and dz2 orbitals of the Y atom and low-energy phonon modes. The presence of superconductivity and nontrivial topological surface state in YB2C2 suggests that it may be a candidate material for topological superconductors.

Coexistence of giant Goos-Hänchen shift and high reflectance in Dirac semimetal based multilayered structure.

Bulk Dirac semimetals (BDSs) possess Fermi energy dependent optical parameters, providing unprecedented opportunities for the study of the controllable Goos-Hänchen (GH) shift. However, the enhancement of GH shifts often comes at the cost of the reflectance in the previous BDS-based structures, which hinders their practical application. In this work, we theoretically present the investigation of the GH shift in a multilayered structure composed of one BDS film and a symmetric one-dimensional photonic crystal (1DPC) with a defect layer. We demonstrate that this well-designed structure supports a large GH shift at the specific working wavelength, whose magnitude can be enhanced up to 3883 times the incident wavelength. In particular, such an enhanced GH shift achieved in this structure is associated with high reflectance (0.94) and these remarkable features can be attributed to the sharp change in the reflective phase and the destructive interference that occurs between the simultaneously excited optical Tamm state (OTS) at the BDS/1DPC interface and the defect state at the 1D defected PC. In addition, we also explore the manipulation of the GH shift by adjusting the Fermi energy of the BDS as well as the geometrical parameter of the multilayered structure. Our results provide a new approach for realizing an enhanced and controllable GH shift in a BDS-based multilayered structure, which endows it with promising prospects for application in optical sensors, optical detectors and beam controllers.