No Arabic abstract
Theoretical evidence of the existence of 12 inequivalent Dirac cones at the vicinity of the Fermi energy in monolayered ZrB$_2$ is presented. Two-dimensional ZrB$_2$ is a mechanically stable d- and p-orbital compound exhibiting a unique electronic structure with two Dirac cones out of high-symmetry points in the irreducible Brillouin zone with a small electron-pocket compensation. First-principles calculations demonstrate that while one of the cones is insensitive to lattice expansion, the second cone vanishes for small perturbation of the vertical Zr position. Internal symmetry breaking with external physical stimuli, along with the relativistic effect of SOC, is able to remove selectively the Dirac cones. A rational explanation in terms of d- and p-orbital mixing is provided to elucidate the origin of the infrequent amount of Dirac cones in a flat structure. The versatility of transition metal d-orbitals combined with the honeycomb lattice provided by the B atoms yields novel features never observed in a two-dimensional material.
Using evolutionary algorithm for crystal structure prediction, we present a new stable two-dimensional (2D) carbon allotrope composed of polymerized as-indacenes (PAI) in a zigzag pattern, namely PAI-graphene whose energy is lower than most of the reported 2D allotropes of graphene. Crucially, the crystal structure realizes a nonsymmorphic layer group that enforces a nontrivial global topology of the band structure with two Dirac cones lying perfectly at the Fermi level. The absence of electron/hole pockets makes PAI-graphene a pristine crystalline topological semimetal having anisotropic Fermi velocities with a high value of $7.0 times 10^{5}$ m/s. We show that while the semimetallic property of the allotrope is robust against the application of strain, the positions of the Dirac cone and the Fermi velocities can be modified significantly with strain. Moreover, by combining strain along both the x- and y-directions, two band
Realization of conically linear dispersion, termed as Dirac cones, has recently opened up exciting opportunities for high-performance devices that make use of the peculiar transport properties of the massless carriers. A good example of current fashion is the heavily studied graphene, a single atomic layered graphite. It not only offers a prototype of Dirac physics in the field of condensed matter and materials science, but also provides a playground of various exotic phenomena. In the meantime, numerous routes have been attempted to search for the next graphene. Despite these efforts, to date there is still no simple guideline to predict and engineer such massless particles in materials. Here, we propose a theoretical recipe to create Dirac cones into anyones favorite materials. The method allows to tailor the properties, such as anisotropy and quantity, in any effective one-band two-dimensional lattice. We demonstrate the validity of our theory with two examples on the square lattice, an unlikely candidate hosting Dirac cones, and show that a graphene-like low-energy electronic structure can be realized. The proposed recipe can be applied in real materials via introduction of vacancy, substitution or intercalation, and also extended to photonic crystal, molecular array, and cold atoms systems.
We present a framework to elucidate the existence of accidental contacts of energy bands, particularly those called Dirac points which are the point contacts with linear energy dispersions in their vicinity. A generalized von-Neumann-Wigner theorem we propose here gives the number of constraints on the lattice necessary to have contacts without fine tuning of lattice parameters. By counting this number, one could quest for the candidate of Dirac systems without solving the secular equation. The constraints can be provided by any kinds of symmetry present in the system. The theory also enables the analytical determination of k-point having accidental contact by selectively picking up only the degenerate solution of the secular equation. By using these frameworks, we demonstrate that the Dirac points are feasible in various two-dimensional lattices, e.g. the anisotropic Kagome lattice under inversion symmetry is found to have contacts over the whole lattice parameter space. Spin-dependent cases, such as the spin-density-wave state in LaOFeAs with reflection symmetry, are also dealt with in the present scheme.
Atomic scale engineering of two-dimensional materials could create devices with rich physical and chemical properties. External periodic potentials can enable the manipulation of the electronic band structures of materials. A prototypical system is 3x3-silicene/Ag(111), which has substrate-induced periodic modulations. Recent angle-resolved photoemission spectroscopy measurements revealed six Dirac cone pairs at the Brillouin zone boundary of Ag(111), but their origin remains unclear [Proc. Natl. Acad. Sci. USA 113, 14656 (2016)]. We used linear dichroism angle-resolved photoemission spectroscopy, the tight-binding model, and first-principles calculations to reveal that these Dirac cones mainly derive from the original cones at the K (K) points of free-standing silicene. The Dirac cones of free-standing silicene are split by external periodic potentials that originate from the substrate-overlayer interaction. Our results not only confirm the origin of the Dirac cones in the 3x3-silicene/Ag(111) system, but also provide a powerful route to manipulate the electronic structures of two-dimensional materials.
By band engineering the iron chalcogenide Fe(Se,Te) via ab-initio calculations, we search for topological surface states and realizations of Majorana bound states. Proposed topological states are expected to occur for non-stoichiometric compositions on a surface Dirac cone where issues like disorder scattering and charge transfer between relevant electronic states have to be addressed. However, this surface Dirac cone is well above the Fermi-level. Our goal is to theoretically design a substituted crystal in which the surface Dirac cone is shifted towards the Fermi-level by modifying the bulk material without disturbing the surface. Going beyond conventional density functional theory (DFT), we apply the coherent potential approximation (BEB-CPA) in a mixed basis pseudo-potential framework to scan the substitutional phase-space of co-substitutions on the Se-sites. We have identified iodine as a promising candidate for intrinsic doping. Our specific proposal is that FeSe$_{0.325}$I$_{0.175}$Te$_{0.5}$ is a very likely candidate to exhibit a Dirac cone right at the Fermi energy without inducing strong disorder scattering.