Pair Of Dirac Points Research Articles

Topological Dirac semimetal phase in GexSny alloys

Recently, two stable allotropes (germancite and stancite) for the group IV elements (Ge and Sn) with a staggered layered dumbell structure were proposed to be three-dimensional (3D) topological Dirac semimetals [Phys. Rev. B 93, 241117 (2016)]. A pair of Dirac points is on the rotation axis away from the time-reversal invariant momentum, and the stability of the 3D bulk Dirac points is protected by the C3 rotation symmetry. Here, we use the first principles calculations to investigate GexSny alloys which share the same rhombohedral crystal structure with the space group of D3d6. Six GexSny alloys are predicted to be energetically and dynamically stable, where (x, y) = (8, 6) and (6, 8) and the α and β phases of (10, 4) and (4, 10). Our results demonstrate that all the six GexSny alloys are topological Dirac semimetals. The different nontrivial surface states and surface Fermi arcs are identified. Our work will substantially enrich the family of 3D Dirac semimetals which are within the reach of experimental realization.

Tuning topological phase transitions in hexagonal photonic lattices made of triangular rods

In this paper, we study topological phases in a 2D photonic crystal with broken time ($\mathcal{T}$) and parity ($\mathcal{P}$) symmetries by performing calculations of band structures, Berry curvatures, Chern numbers, edge states and also numerical simulations of light propagation in the edge modes. Specifically, we consider a hexagonal lattice consisting of triangular gyromagnetic rods. Here the gyromagnetic material breaks $\mathcal{T}$ symmetry while the triangular rods breaks $\mathcal{P}$ symmetry. Interestingly, we find that the crystal could host quantum anomalous Hall (QAH) phases with different gap Chern numbers ($C_g$) including $|C_g| > 1$ as well as quantum valley Hall (QVH) phases with contrasting valley Chern numbers ($C_v$), depending on the orientation of the triangular rods. Furthermore, phase transitions among these topological phases, such as from QAH to QVH and vice versa, can be engineered by a simple rotation of the rods. Our band theoretical analyses reveal that the Dirac nodes at the $K$ and $K'$ valleys in the momentum space are produced and protected by the mirror symmetry ($m_y$) instead of the $\mathcal{P}$ symmetry, and they become gapped when either $\mathcal{T}$ or $m_y$ symmetry is broken, resulting in a QAH or QVH phase, respectively. Moreover, a high Chern number ($C_g = -2$) QAH phase is generated by gapping triply degenerate nodal points rather than pairs of Dirac points by breaking $\mathcal{T}$ symmetry. Our proposed photonic crystal thus provides a platform for investigating intriguing topological phenomena which may be challenging to realize in electronic systems, and also has promising potentials for device applications in photonics such as reflection-free one-way waveguides and topological photonic circuits.

A New Dirac Semimetal in Hexagonal BaGaSnH

By first-principles calculations, we find that BaGaSnH is a topological Dirac semimetal with a pair of Dirac points at \((0,0, \pm 0.45\frac{2\pi }{c})\) when spin–orbit coupling (SOC) is considered. The Dirac points are exactly at the Fermi energy, which makes the experimental measurement easy. The Dirac semimetal state as well as the topological properties are sensitive to the strain, which makes the compound enter the trivial semiconductor state. The finding of a Dirac semimetal phase in BaGaSnH may stimulate further research on the topological properties of hexagonal materials and promote new practical applications.

Dirac semimetal phase in hexagonal LiZnBi

Based on first-principles calculations, we find that LiZnBi, a metallic hexagonal $ABC$ compound, can be driven into a Dirac semimetal with a pair of Dirac points by strain. The nontrivial topological nature of the strained LiZnBi is directly demonstrated by calculating its $\mathbb{Z}_2$ index and the surface states, where the Fermi arcs are clearly observed. The low-energy states as well as topological properties are shown to be sensitive to the strain configurations. The finding of Dirac semimetal phase in LiZnBi may intrigue further researches on the topological properties of hexagonal $ABC$ materials and promote new practical applications.

CaTe: a new topological node-line and Dirac semimetal

Combining first-principles calculations and effective model analysis, we predict that CaTe is a topological node-line semimetal in the absence of the spin-orbit coupling. Using a slab model, we obtain the nearly flat drumhead surface state near the Fermi level. When the spin-orbit coupling is included, three node lines will evolve into a pair of Dirac points along the M−R line. These Dirac points are robust and protected by the C4 rotation symmetry. Once this crystal symmetry is broken, the Dirac points will be eliminated, and the system becomes a strong topological insulator.

Topological Dirac semimetal phase in Pd and Pt oxides

Topological Dirac semimetals (DSMs) exhibit nodal points through which energy bands disperse linearly in three-dimensional (3D) momentum space, a 3D analogue of graphene. The first experimentally confirmed DSMs with a pair of Dirac points (DPs), Na$_{3}$Bi and Cd$_{3}$As$_{2}$, show topological surface Fermi arc states and exotic magneto-transport properties, boosting the interest in the search for stable and nontoxic DSM materials. Here, based on the {\it ab-initio} band structure calculations we predict a family of palladium and platinum oxides as robust 3D DSMs. The novel topological properties of these compounds are distinct from all other previously reported DSMs, they are rendered by the multiple number of DPs in the compounds. We show that along three unit axes of the cubic lattice there exist three pairs of DPs, which are linked by Fermi arcs on the surface. The Fermi arcs display a Lifshitz transition from a heart- to a diamond-shape upon varying the chemical potential. Corresponding oxides are already available as high-quality single crystals, which is an excellent precondition for the verification of our prediction by photoemission and magneto-transport experiments. Our findings not only predict a number of much robust 3D DSM candidates but also extend DSMs to transition metal oxides, a versatile family of materials, which opens the door to investigate the interplay between DSMs and electronic correlations that is not possible in the previously discovered DSM materials.

Stable Dirac semimetal in the allotropes of group-IV elements

Three dimensional topological Dirac semi-metals represent a novel state of quantum matter with exotic electronic properties, in which a pair of Dirac points with the linear dispersion along all momentum directions exist in the bulk. Herein, by using the first principles calculations, we discover a new metastable allotrope of Ge and Sn in the staggered layered dumbbell structure, named as germancite and stancite, to be Dirac semi-metals with a pair of Dirac points on its rotation axis. On the surface parallel to the rotation axis, a pair of topologically non-trivial Fermi arcs are observed and a Lifshitz transition is found by tuning the Fermi level. Furthermore, the quantum thin film of germancite is found to be an intrinsic quantum spin Hall insulator. These discoveries suggest novel physical properties and future applications of the new metastable allotrope of Ge and Sn.

Multiple Dirac Points and Hydrogenation-Induced Magnetism of Germanene Layer on Al (111) Surface.

A continuous germanene layer grown on the Al (111) surface has recently been achieved in experiment. In this work, we investigate its structural, electronic, and hydrogenation-induced properties through first-principles calculations. We find that despite having a different lattice structure from its free-standing form, germanene on Al (111) still possesses Dirac points at high-symmetry K and K' points. More importantly, there exist another three pairs of Dirac points on the K(K')-M high-symmetry lines, which have highly anisotropic dispersions due to the reduced symmetry. These massless Dirac Fermions become massive when spin-orbit coupling is included. Hydrogenation of the germanene layer strongly affects its structural and electronic properties. Particularly, when not fully hydrogenated, ferromagnetism can be induced due to unpaired local orbitals from the unsaturated Ge atoms. Remarkably, we discover that the one-side semihydrogenated germanene turns out to be a two-dimensional half-semimetal, representing a novel state of matter that is simultaneously a half-metal and a semimetal.

Topological Node-Line Semimetal and Dirac Semimetal State in Antiperovskite Cu3PdN.

Based on first-principles calculation and effective model analysis, we propose that the cubic antiperovskite material Cu3PdN can host a three-dimensional (3D) topological node-line semimetal state when spin-orbit coupling (SOC) is ignored, which is protected by the coexistence of time-reversal and inversion symmetry. There are three node-line circles in total due to the cubic symmetry. Drumheadlike surface flat bands are also derived. When SOC is included, each node line evolves into a pair of stable 3D Dirac points as protected by C4 crystal symmetry. This is remarkably distinguished from the Dirac semimetals known so far, such as Na3Bi and Cd3As2, both having only one pair of Dirac points. Once C4 symmetry is broken, the Dirac points are gapped and the system becomes a strong topological insulator with (1;111) Z2 indices.

From Dia- to Paramagnetic Orbital Susceptibility of Massless Fermions

We study the orbital susceptibility of multiband systems with a pair of Dirac points interpolating between honeycomb and dice lattices. Despite having the same zero-field energy spectrum, these different systems exhibit spectacular differences in their orbital magnetic response, ranging from dia- to paramagnetism at Dirac points. We show that this striking behavior is related to a topological Berry phase varying continuously from π (graphene) to 0 (dice). The latter strongly constrains interband effects, resulting in an unusual dependence of the magnetic response also at finite doping.

Searching for topological density-wave insulators in multiorbital square-lattice systems

We study topological properties of density-wave states with broken translational symmetry in two-dimensional multiorbital systems with particular focus on ${\text{t}}_{2g}$ orbitals in a square lattice. Due to the distinct symmetry properties of $d$-orbitals, a nodal charge or spin-density-wave state with Dirac points protected by lattice symmetries can be achieved. When an additional order parameter with opposite reflection symmetry is introduced to a nodal density-wave state, the system can be fully gapped leading to a band insulator. Among those, topological density-wave insulators can be realized when an effective staggered on-site potential generates a gap to a pair of Dirac points connected by inversion symmetry which have the same topological winding numbers. We also present a mean-field phase diagram for various density-wave states and discuss the experimental implications of our results.

Semi-Dirac point in the Hofstadter spectrum

The spectrum of tight binding electrons on a square lattice with half a magnetic flux quantum per unit cell exhibits two Dirac points at the band center. We show that, in the presence of an additional uniaxial staggered potential, this pair of Dirac points may merge into a single one, with a topological transition towards a gapped phase. At the transition, the spectrum is linear in one direction and quadratic in the other one (a spectrum recently named "hybrid" or "semi-Dirac"). This transition is studied in the framework of a general Hamiltonian describing the merging of Dirac points. The possibility of creating gauge fields for cold atoms in optical lattices may offer the first opportunity to observe this merging of Dirac points and the hybrid dispersion relation.

Induced chiral Dirac fermions in graphene by a periodically modulated magnetic field

The effect of a modulated magnetic field on the electronic structure of neutral graphene is examined in this paper. It is found that application of a small staggered modulated magnetic field does not destroy the Dirac-cone structure of graphene and so preserves its 4-fold zero-energy degeneracy. The original Dirac points (DPs) are just shifted to other positions in k space. By varying the staggered field gradually, new DPs with exactly the same electron-hole crossing energy as that of the original DPs, are generated, and both the new and original DPs are moving continuously. Once two DPs are shifted to the same position, they annihilate each other and vanish. The process of generation and evolution of these DPs with the staggered field is found to have a very interesting patten, which is examined carefully. Generally, there exists a corresponding branch of anisotropic massless fermions for each pair of DPs, resulting in that each Landau level (LL) is still 4-fold degenerate except the zeroth LL which has a robust $4n_t$-fold degeneracy with nt the number of pairs of DPs. As a result, the Hall conductivity $\sigma_{xy}$ shows a step of size $4n_te^2/h$ across zero energy.