type-II Dirac Points Research Articles

Emergence of Type-II Dirac Points in Graphynelike Photonic Lattices.

We theoretically demonstrate that a type-II class of tilted Dirac cones can emerge in generalized two-dimensional anisotropic lattice arrangements. This is achieved by introducing a special set of graphynelike exchange bonds by means of which the complete spectrum of the underlying Weyl Hamiltonian can be realized. Our abinitio calculations demonstrate a unique class of eigensolutions corresponding to a type-II class of Dirac fermionic excitations. Based on our approach, one can systematically synthesize a wide range of strongly anisotropic band diagrams having tilted Dirac cones with variable location and orientation. Moreover, we show that asymmetric conical diffraction, as well as edge states, can arise in these configurations. Our results can provide a versatile platform to observe, for the first time, optical transport around type-II Dirac points in two-dimensional optical settings under linear, nonlinear, and non-Hermitian conditions.

Manipulation of type-I and type-II Dirac points in PdTe2 superconductor by external pressure

A pair of type-II Dirac cones in PdTe$_2$ was recently predicted by theories and confirmed in experiments, making PdTe$_2$ the first material that processes both superconductivity and type-II Dirac fermions. In this work, we study the evolution of Dirac cones in PdTe$_2$ under hydrostatic pressure by the first-principles calculations. Our results show that the pair of type-II Dirac points disappears at 6.1 GPa. Interestingly, a new pair of type-I Dirac points from the same two bands emerges at 4.7 GPa. Due to the distinctive band structures compared with those of PtSe$_2$ and PtTe$_2$, the two types of Dirac points can coexist in PdTe$_2$ under proper pressure (4.7-6.1 GPa). The emergence of type-I Dirac cones and the disappearance of type-II Dirac ones are attributed to the increase/decrease of the energy of the states at $\Gamma$ and $A$ point, which have the anti-bonding/bonding characters of interlayer Te-Te atoms. On the other hand, we find that the superconductivity of PdTe$_2$ slightly decreases with pressure. The pressure-induced different types of Dirac cones combined with superconductivity may open a promising way to investigate the complex interactions between Dirac fermions and superconducting quasi-particles.

Coexistence of four-band nodal rings and triply degenerate nodal points in centrosymmetric metal diborides

Topological metals with protected band-crossing points have been attracting great interest. Here we report novel topological band features in a family of metal diboride materials. Using first- principles calculations, we show that these materials are metallic, and close to Fermi level, there appears coexistence of one pair of nodal rings and one pair of triply-degenerate nodal points (TNPs). The nodal ring here is distinct from the previously studied ones in that its formation requires four entangled bands, not just two as in previous cases, hence it is termed as a four-band nodal ring (FNR). Remarkably, we show that FNR features Dirac-cone-like surface states, in contrast to the usual drumhead surface states for two-band nodal rings. Due to the presence of inversion symmetry, the TNP here is also different from those discussed previously in inversion-asymmetric systems. Especially, when spin-orbit coupling is included, the TNP here transforms into a novel Dirac point that is close to the borderline between the type-I and type-II Dirac point categories. We discuss their respective symmetry protections, and construct effective models for their characterization. The large linear energy range (> 2 eV) in these materials should facilitate the experimental detection of the signatures of these nontrivial band crossings.

Tunable Type-I and Type-II Dirac Fermions in Graphene with Nitrogen Line Defects

Recently, type-II Dirac fermions characterized by strongly titled Dirac cones have been proposed. The new fermions exhibit unique physical properties different from the type-I Dirac fermions and thus attract tremendous attentions. To date, all type-II fermions are only found in the heavy compounds with strong spin obit coupling. Here, we propose that both type-I and type-II Dirac fermions can exist in the graphene embedding nitrogen line defects, and the types of Dirac fermions can be tuned by the size W of graphene nanoribbons between the line defects. By comparison of the two types of Dirac fermions, their different physical properties and originations are revealed directly. Remarkably, the type-I Dirac points induce one Fermi arc corresponding to edge states along the armchair direction, while the type-II Dirac points induce two Fermi arcs corresponding to two sets of edge states along the zigzag direction. These results not only expand our views on the Dirac fermions in two-dimensional structures but ...

Lifshitz transitions via the type-II dirac and type-II Weyl points

The type-II Weyl and type-II Dirac points emerge in semimetals and also in relativistic systems. In particular, the type-II Weyl fermions may emerge behind the event horizon of black holes. The type-II Weyl and Dirac points also emerge as the intermediate states of the topological Lifshitz transitions. In one case the type-II Weyl point connects the Fermi pockets, and the Lifshitz transition corresponds to the transfer of the Berry flux between the Fermi pockets. In the other case the type-II Weyl point connects the outer and inner Fermi surfaces. At the Lifshitz transition the Weyl point is released from both Fermi surfaces. They loose their Berry flux, which guarantees the global stability, and without the topological support the inner surface disappears after shrinking to a point at the second Lifshitz transition. These examples reveal the complexity and universality of topological Lifshitz transitions, which originate from the ubiquitous interplay of a variety of topological characters of the momentum-space manifolds.

Multiple unpinned Dirac points in group-Va single-layers with phosphorene structure

AbstractEmergent Dirac fermion states underlie many intriguing properties of graphene, and the search for them constitutes one strong motivation to explore two-dimensional (2D) allotropes of other elements. Phosphorene, the ultrathin layers of black phosphorous, has been a subject of intense investigations recently, and it was found that other group-Va elements could also form 2D layers with similar puckered lattice structure. Here, by a close examination of their electronic band structure evolution, we discover two types of Dirac fermion states emerging in the low-energy spectrum. One pair of (type-I) Dirac points is sitting on high-symmetry lines, while two pairs of (type-II) Dirac points are located at generic k-points, with different anisotropic dispersions determined by the reduced symmetries at their locations. Such fully-unpinned (type-II) 2D Dirac points are discovered for the first time. In the absence of spin-orbit coupling (SOC), we find that each Dirac node is protected by the sublattice symmetry from gap opening, which is in turn ensured by any one of three point group symmetries. The SOC generally gaps the Dirac nodes, and for the type-I case, this drives the system into a quantum spin Hall insulator phase. We suggest possible ways to realise the unpinned Dirac points in strained phosphorene.