We have investigated several strong spin-orbit coupling ternary chalcogenides related to the (Pb,Sn)Te series of compounds. Our first-principles calculations predict the low temperature rhombohedral ordered phase in TlBiTe2, TlBiSe2, and TlSbX2 (X=Te, Se, S) to be topologically Kane-Mele Z2 = -1 nontrivial. We identify the specific surface termination that realizes the single Dirac cone through first-principles surface state computations. This termination minimizes effects of dangling bonds making it favorable for photoemission (ARPES) experiments. Our analysis predicts that thin films of these materials would harbor novel 2D quantum spin Hall states, and support odd-parity topological superconductivity. For a related work also see arXiv:1003.2615v1. Experimental ARPES results will be published elsewhere.
We theoretically predict that a large variety of Dirac-cone materials can be constructed in Bi${}_{1-x}$Sb${}_{x}$ thin films, and we here show how to construct single-, bi- and tri- Dirac-cone materials with various amounts of wave vector anisotropy. These different types of Dirac cones can be of special interest to electronic devices design, quantum electrodynamics and other fields.
Combining first-principles calculations and spin- and angle-resolved photoemission spectroscopy measurements, we identify the helical spin textures for three different Dirac cone states in the interfaced systems of a 2D topological insulator (TI) of Bi(111) bilayer and a 3D TI Bi2Se3 or Bi2Te3. The spin texture is found to be the same for the intrinsic Dirac cone of Bi2Se3 or Bi2Te3 surface state, the extrinsic Dirac cone of Bi bilayer state induced by Rashba effect, and the hybridized Dirac cone between the former two states. Further orbit- and atom-resolved analysis shows that s and pz orbit…
We validate the linear dispersion relation and resolve the Dirac cone on the surface of a single Bi2Te3 nanowire via a combination of field-effect and magnetoresistance measurements by which we unambiguously prove the topological insulator nature of the nanowire surface states. Moreover we show that the experimentally determined carrier concentration, mobility and cyclotron mass of the surface states are in excellent agreement with relativistic models. Our method provides a facile way to identify topological insulators that too small for angle-resolved photo emission spectroscopy.
We investigate generation of new Dirac cones in graphene under double-periodic and quasiperiodic superlattice potentials. We first show that double-periodic potentials generate the Dirac cones sporadically, following the Diophantine equation, in spite of the fact that double-periodic potentials are also periodic ones, for which previous studies predict consecutive appearance of the cones. The sporadic appearance is due to the fact that the dispersion relation of graphene is linear only up to an energy cutoff. We then show that quasiperiodic potentials generate the new Dirac cones densely with …
We theoretically demonstrate how competition between band inversion and spin-orbit coupling (SOC) results in nontrivial evolution of band topology, taking antiperovskite Ba$_3$SnO as a prototype material. A key observation is that when the band inversion dominates over SOC, there appear "twin" Dirac cones in the band structure. Due to the twin Dirac cones, the band shows highly peculiar structure in which the upper cone of one of the twin continuously transforms to the lower cone of the other. Interestingly, the relative size of the band inversion and SOC is controlled in this series of antipe…
We describe the fine structure of Dirac states in HgTe/CdHgTe quantum wells of critical and close-to-critical thickness and demonstrate the formation of an anticrossing gap between the tips of the Dirac cones driven by interface inversion asymmetry. By combining symmetry analysis, atomistic calculations, and k-p theory with interface terms, we obtain a quantitative description of the energy spectrum and extract the interface mixing coefficient. The zero-magnetic-field splitting of Dirac cones can be experimentally revealed in studying magnetotransport phenomena, cyclotron resonance, Raman scat…
Anisotropic bulk Dirac (or Weyl) cones in three dimensional systems have recently gained intense research interest as they are examples of materials with tilted Dirac (or Weyl) cones indicatig the violation of Lorentz invariance. In contrast, the studies on anisotropic surface Dirac cones in topological materials which contribute to anisotropic carrier mobility have been limited. By employing angle-resolved photoemission spectroscopy and first-principles calculations, we reveal the anisotropic surface Dirac dispersion in a tetradymite material Ti2Te2P on the (001) plane of the Brillioun zone. …
We present a short pedagogical introduction to the physics of Dirac materials, restricted to graphene and two- dimensional topological insulators. We start with a brief reminder of the Dirac and Weyl equations in the particle physics context. Turning to condensed matter systems, semimetallic graphene and various Dirac insulators are introduced, including the Haldane and the Kane-Mele topological insulators. We also discuss briefly experimental realizations in materials with strong spin-orbit coupling.
Nodal line in single-component molecular conductor [Pd(dddt)_2] has been examined to understand the tilted Dirac cone on the non-coplanar loop. In the previous work [J. Phys. Soc. Jpn. 87, 113701 (2018)], the velocity of the cone was calculated at respective Dirac points on the nodal loop based on our first-principles band structure calculations, which was a new method to derive an effective Hamiltonian with a 2 x 2 matrix. However, the Dirac cones on the nodal line are fully reproduced only at symmetric points. In the present paper, we show that our improved method well reproduces reasonable …
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 spectrosc…
A honeycomb lattice system has four types of Dirac electrons corresponding to the spin and valley degrees of freedom. We consider a state that contains only one type of massless electrons and three types of massive ones, which we call the single Dirac-cone state. We analyze quantum Hall (QH) effects in this state. We make a detailed investigation of the Chern and spin-Chern numbers. We make clear the origin of unconventional QH effects discovered in graphene. We also show that the single Dirac-cone state may have arbitrary large spin-Chern numbers in magnetic field. Such a state will be genera…
The unoccupied states in topological insulators Bi_2Se_3, PbSb_2Te_4, and Pb_2Bi_2Te_2S_3 are studied by the density functional theory methods. It is shown that a surface state with linear dispersion emerges in the inverted conduction band energy gap at the center of the surface Brillouin zone on the (0001) surface of these insulators. The alternative expression of Z_2 invariant allowed us to show that a necessary condition for the existence of the second Gamma Dirac cone is the presence of local gaps at the time reversal invariant momentum points of the bulk spectrum and change of parity in o…
The magnitude of electron spin polarization in topologically protected surface states is an important parameter with respect to spintronics applications. In order to analyze the warped spin texture in Bi$_2$Te$_3$ thin films, we combine angle- and spin-resolved photoemission experiments with theoretical \textit{ab initio} calculations. We find an \textit{in-plane} spin polarization of up to $\sim$~45\% in the topologically protected Dirac cone states near the Fermi level. The Fermi surface of the Dirac cone state is warped and shows an \textit{out-of-plane} spin polarization of $\sim$~15\%. Th…
Two-dimensional Dirac physics has aroused great interests in condensed matter physics ever since the discovery of graphene and topological insulators due to its importance in both fundamental physics and device applications. The ability to control the properties of Dirac cones, such as bandgap and Fermi velocity, is essential for the occurrence of various new phenomena and the development of next-generation electronic devices. Based on first-principles calculations and an analytical effective model, we propose a new Dirac system with eight Dirac cones in thin films of the (LaO)2(SbSe2)2 family…
We present first principles calculations of the nontrivial surface states and their spin-textures in the topological crystalline insulator SnTe. The surface state dispersion on the [001] surface exhibits four Dirac-cones centered along the intersection of the mirror plane and the surface plane. We propose a simple model of two interacting coaxial Dirac cones to describe both the surface state dispersion and the associated spin-texture. While the out-of-the-plane spin polarization is zero due to the crystalline and time-reversal symmetries, the in-plane spin texture shows helicity with some dis…
Recently a paper by Lin and Ku \cite{lin} was posted, where the authors propose a very interesting idea to engineer the Dirac points in material which originally did not have such points by inducing a CDW state through introduction of impurities like vacancy, substitution, or intercalation. In this comment we would like to explain the appearance of the Dirac points in such engineered structures by symmetry arguments.
We have performed angle-resolved photoemission spectroscopy (ARPES) on CeBi which undergoes a two-step antiferromagnetic (AF) transition with temperature. Soft-x-ray ARPES has revealed the inverted band structure at the X point of bulk Brillouin zone for CeBi (and also for LaBi) as opposed to LaSb with non-inverted band structure. Low-energy ARPES on CeBi has revealed the Dirac-cone band at the Gamma point in the paramagnetic phase associated with the bulk band inversion. On the other hand, a double Dirac-cone band appears on entering the first AF phase at T = 25 K, whereas a single Dirac-cone…
We propose that Dirac cones can be engineered in phosphorene with fourfold-coordinated phosphorus atom. The key is to separate in energy the in-plane ($s$, $p_x$ and $p_y$) and out-of-plane ($p_z$) oribtals through the $sp^2$ configuration, yielding respective $σ$- and $π$-character Dirac cones, and then quench the latter. As a proof-of-principle study, we realize $σ$-character Dirac cone in hydrogenated/fluorinated phosphorene with the honeycomb lattice. The obtained Dirac cones are at $K$-points, slightly anisotropic, with Fermi velocities of 0.91/1.23 times that of graphene along $Γ$K/KM di…
We study alpha, beta, and gamma graphyne, a class of graphene allotropes with carbon triple bonds, using a first-principles density-functional method and tight-binding calculation. We find that graphyne has versatile Dirac cones and it is due to remarkable roles of the carbon triple bonds in electronic and atomic structures. The carbon triple bonds modulate effective hopping matrix elements and reverse their signs, resulting in Dirac cones with reversed chirality in alpha graphyne, momentum shift of the Dirac point in beta graphyne, and switch of the energy gap in gamma graphyne. Furthermore, …
The low-energy theory of the surface of the topological crystalline insulator (TCI) is characterized by four Dirac cones anisotropic into the $x$ and $y$ directions. Recent experiments have shown that the band gap can be introduced in these Dirac cones by crystal distortion by applying strain to the crystal structure. The TCI surface provides us with a new way to valleytronics when gaps are given to Dirac cones. Indeed the system has the Chern number and three valley-Chern numbers. We investigate the optical absorption on the TCI surface. It shows a strong elliptic dichroism though the four Di…
Confining two dimensional Dirac fermions on the surface of topological insulators has remained an outstanding conceptual challenge. Here we show that Dirac fermion confinement is achievable in topological crystalline insulators (TCI), which host multiple surface Dirac cones depending on the surface termination and the symmetries it preserves. This confinement is most dramatically reflected in the flux dependence of these Dirac states in the nanowire geometry, where different facets connect to form a closed surface. Using SnTe as a case study, we show how wires with all four facets of the <100>…
Two-dimensional (2D) Dirac cone materials exhibit linear energy dispersion at the Fermi level, where the effective masses of carriers are very close to zero and the Fermi velocity is ultrahigh, only 2 ~ 3 orders of magnitude lower than the light velocity. Such the Dirac cone materials have great promise in high-performance electronic devices. Herein, we have employed the genetic algorithms methods combining with first-principles calculations to propose a new 2D anisotropic Dirac cone material, that is, orthorhombic boron phosphide (BP) monolayer named as borophosphene. Molecular dynamics simul…
Band splittings, chiral spin polarization and topological surface states generated by spin-orbit interactions at crystal surfaces are receiving a lot of attention for their potential device applications as well as fascinating physical properties. Most studies have focused on sp states near the Fermi energy, which are relevant for transport and have long lifetimes. Far less explored, though in principle stronger, are spin-orbit interaction effecs within d states, including those deep below the Fermi energy. Here, we report a joint photoemission/ab initio study of spin-orbit effects in the deep …
Topological insulators (TIs) and graphene present two unique classes of materials which are characterized by spin polarized (helical) and non-polarized Dirac-cone band structures, respectively. The importance of many-body interactions that renormalize the linear bands near Dirac point in graphene has been well recognized and attracted much recent attention. However, renormalization of the helical Dirac point has not been observed in TIs. Here, we report the experimental observation of the renormalized quasi-particle spectrum with a skewed Dirac cone in a single Bi bilayer grown on Bi2Te3 subst…
Recently, Valenti et al. pointed out the significance of the spin-orbit interaction (SOI) in organic materials, and explained the anomalous insulating behavior of a Dirac semimetal alpha-(BEDT-TTF)2I3 at low temperatures in terms of the small SOI gap. We propose a lattice model with plausible SOI coupling, and indicate that the gapped state is a topological insulator. This model is an organic analogue of the Kane-Mele model for graphene.
The Dirac electrons of graphene, an intrinsic zero gap semiconductor, uniquely carry spin and pseudospin that give rise to many fascinating electronic and transport properties. While isolated zigzag graphene nanoribbons are antiferromagnetic semiconductors, we show by means of first-principles and tight-binding calculations that zigzag graphene nanoribbons supported on graphene are half-metallic as a result of spin- and pseudospin-symmetry breaking. In particular, half-metallic Dirac cones are formed at K (K') near the Fermi level. The present results demonstrate that the unique combination of…
The massless Dirac electrons found at topological insulator surfaces are thought to be influenced very little by weak, non-magnetic disorder. However, a resonance effect of strongly perturbing non-magnetic impurities has been theoretically predicted to change the dispersion and physical nature of low-energy quasiparticles, resulting in unique particle-like states that lack microscopic translational symmetry. Here we report the direct observation of impurities reshaping the surface Dirac cone of the model 3D topological insulator Bi2Se3. For the first time, a pronounced kink-like dispersion fea…
Powered by effective parquet nesting a commensurate chiral honeycomb superstructure in a trigonally packed transition metal dichalcogenide TaSe$_2$ results in a Dirac cone anomaly in one-particle excitation spectrum. However, the formation of the well defined Dirac point seems to be hindered by effective scattering on 2D plasmons.
The Dirac materials, such as graphene and three-dimensional topological insulators, have attracted much attention because they exhibit novel quantum phenomena with their low energy electrons governed by the relativistic Dirac equations. One particular interest is to generate Dirac cone anisotropy so that the electrons can propagate differently from one direction to the other, creating an additional tunability for new properties and applications. While various theoretical approaches have been proposed to make the isotropic Dirac cones of graphene into anisotropic ones, it has not yet been met w…
Using density functional theory combined with orbital-selective band unfolding techniques, we study the effective band structure of silicene($3\times3$)/Ag(111)($4\times4$) structure. Consistent with the ARPES spectra recently obtained by Feng et al. [Proc. Natl. Acad. Sci. 113, 14656 (2016)], we observe six pairs of Dirac cones near the boundary of the Brillouin zone (BZ) of Ag($1\times1$), while no Dirac cone is observed inside the BZ. Furthermore, we find that these Dirac cones are induced by the interfacial Si-Ag hybridization, mainly composed of Si p$_z$ orbitals and Ag sp bands, which is…
The notion of chiral symmetry for the conventional Dirac cone is generalized to include the tilted Dirac cones, where the generalized chiral operator turns out to be non-hermitian. It is shown that the generalized chiral symmetry generically protects the zero modes (n=0 Landau level) of the Dirac cone even when tilted. The present generalized symmetry is equivalent to the condition that the Dirac Hamiltonian is elliptic as a differential operator, which provides an explicit relevance to the index theorem.
The symmetries that protect massless Dirac fermions from a gap opening may become ineffective if the Dirac equation is discretized in space and time, either because of scattering between multiple Dirac cones in the Brillouin zone (fermion doubling) or because of singularities at zone boundaries. Here we introduce an implementation of Dirac fermions on a space-time lattice that removes both obstructions. The quasi-energy band structure has a tangent dispersion with a single Dirac cone that cannot be gapped without breaking both time-reversal and chiral symmetries. We show that this topological …
Using the k.p theory and first-principles simulations, we report that applying a moderate pressure (> 0.6 GPa) on black phosphorus can diminish its band gap and produce one-dimensional and even two-dimensional (2D) Dirac cones, distinguishing this material for use in novel non-compound topological insulators. Similar to topological insulators, these 2D Dirac cones result from two competing mechanisms: the unique linear band dispersion tends to open a gap via a "pseudo spin-orbit" coupling, while the band symmetry requirements preserve the material's gapless spectrum. Moreover, these unique Dir…
In monolayer transition metal dichalcogenides, tightly bound excitons have been discovered with a valley pseudospin that can be optically addressed through polarization selection rules. Here, we show that this valley pseudospin is strongly coupled to the exciton center-of-mass motion through electron-hole exchange. This coupling realizes a massless Dirac cone with chirality index I=2 for excitons inside the light cone, i.e. bright excitons. Under moderate strain, the I=2 Dirac cone splits into two degenerate I=1 Dirac cones, and saddle points with a linear Dirac spectrum emerge in the bright e…
Transverse electric (TE) modes can not propagate through the conducting solids. This is because the continuum of particle-hole excitations of conductors contaminates with the TE mode and dampes it out. But in solids hosting tilted Dirac cone (TDC) that admit a description in terms of a modified Minkowski spacetime, the new spacetime structure remedies this issue and therefore a tilted Dirac cone material (TDM) supports the propagation of an undamped TE mode which is sustained by density fluctuations. The resulting TE mode propagates at fermionic velocities which strongly confines the mode to t…
The recently discovered topological Dirac semimetal represents a new exotic quantum state of matter. Topological Dirac semimetals can be viewed as three dimensional analogues of graphene, in which the Dirac nodes are protected by crystalline symmetry. It has been found that quantum confinement effect can gap out Dirac nodes and convert Dirac semimetal to a band insulator. The band insulator is either normal insulator or quantum spin Hall insulator depending on the thin film thickness. We present the study of disorder effects in thin film of Dirac semimetals. It is found that moderate Anderson …
Inspired by the great development of graphene, more and more works have been conducted to seek new two-dimensional (2D) materials with Dirac cones. Although 2D Dirac materials possess many novel properties and physics, they are rare compared with the numerous 2D materials. To provide explanation for the rarity of 2D Dirac materials as well as clues in searching for new Dirac systems, here we review the recent theoretical aspects of various 2D Dirac materials, including graphene, silicene, germanene, graphynes, several boron and carbon sheets, transition metal oxides (VO2)n/(TiO2)m and (CrO2)n/…
We have investigated several classes of strong spin-orbit chalcogenides related to the (Pb,Sn)Te series studied in connection with the Dirac fermion physics in the 1980s. Our first-principle theoretical calculations suggest that ternary chalcogenides TlBiX$_2$ and TlSbX$_2$ (X=Te, Se, S) series harbor small bandgap topological insulators with single Dirac cone on some selective surfaces whereas the isostructural and isoelectronic silver-based AgBiX$_2$ and AgSbX$_2$ (X=Te, Se, S) series do not. We find that several Tl-compounds are in the vicinity of a topological critical point. We identify t…
The quantum Hall effect in graphene is regarded to be involving half-integer topological numbers associated with the massless Dirac particle, this is usually not apparent due to the doubling of the Dirac cones. Here we theoretically consider two classes of lattice models in which we manipulate the Dirac cones with either (a) two Dirac points that have mutually different energies, or (b) multiple Dirac cones having different Fermi velocities. We have shown, with an explicit calculation of the topological (Chern) number for case (a) and with an adiabatic argument for case (b) that the results ar…
The interband optical absorption of linearly polarised light by two-dimensional (2D) semimetals hosting tilted and anisotropic Dirac cones in the bandstructure is analysed theoretically. Super-critically tilted (type-II) Dirac cones are characterised by an absorption that is highly dependent on the incident photon polarisation and frequency, and is tunable by changing the Fermi level with a back-gate voltage. Type-II Dirac cones exhibit open Fermi surfaces and large regions of the Brillouin zone where the valence and conduction bands sit either above or below the Fermi level. As a consequence,…
Based on first-principles method we predict a new low-energy Stone-Wales graphene SW40, which has an orthorhombic lattice with Pbam symmetry and 40 carbon atoms in its crystalline cell forming well-arranged Stone-Wales patterns. The calculated total energy of SW40 is just about 133 meV higher than that of graphene, indicating its excellent stability exceeds all the previously proposed graphene allotropes. We find that SW40 processes intrinsic Type-III Dirac-cone (Phys. Rev. Lett., 120, 237403, 2018) formed by band-crossing of a local linear-band and a local flat-band, which can result in highl…
While the quantum Hall effect in graphene has been regarded as a realization of the anomaly associated with the massless Dirac particle carrying half the usual topological integer, this is hidden due to the doubling of the Dirac cones. In order to confirm the half-integer contribution from each Dirac cone, here we theoretically consider a lattice model in which the relative energy between the two Dirac points is systematically shifted. With an explicit calculation of the topological (Chern) number, we have demonstrated that each Dirac cone does indeed contribute to the Hall conductivity as the…
We have investigated the nature of surface states in the Bi2Te3 family of three-dimensional topological insulators using first-principles calculations as well as model Hamiltonians. When the surface Dirac cone is warped due to Dresselhaus spin-orbit coupling in rhombohedral structures, the spin acquires a finite out-of-plane component. We predict a novel in-plane spin-texture of the warped surface Dirac cone with spins not perpendicular to the electron momentum. Our k.p model calculation reveals that this novel in-plane spin-texture requires high order Dresselhaus spin-orbit coupling terms.
We compute the dynamical polarizability of graphene beyond the usual Dirac cone approximation, integrating over the full Brillouin zone. We find deviations at $\hbarω=2t$ ($t$ the hopping parameter) which amount to a logarithmic singularity due to the van Hove singularity and derive an approximate analytical expression. Also at low energies, we find deviations from the results obtained from the Dirac cone approximation which manifest themselves in a peak spitting at arbitrary direction of the incoming wave vector $\q$. Consequences for the plasmon spectrum are discussed.
We use the Dirac cone model to explore the high Chern number (C) phases that are realized in the magnetic-doped topological insulator (TI) multilayer structures by Zhao et al. [Nature 588, 419 (2020)]. The Chern number is calculated by capturing the evolution of the phase boundaries with the parameters and then the Chern number phase diagrams of the TI multilayer structures are obtained. The high-C behavior is attributed to the band inversion of the renormalized Dirac cones, along with which the spin polarization at the Γpoint will get increased. Moreover, another two TI multilayer structures …
We have designed three-dimensional models of topological insulator thin films, showing a tunability of the odd number of Dirac cones on opposite surfaces driven by the atomic-scale geometry at the boundaries. This enables creation of a single Dirac cone at the $Γ$-point as well as possible suppression of quantum tunneling between Dirac states at opposite surfaces (and gap formation), when opposite surfaces are geometrically differentiated. The spin texture of surface states was found to change from a spin-momentum-locking symmetry to a progressive loss in surface spin polarization upon the int…
We performed low temperature scanning tunneling microscopy (STM) and spectroscopy (STS) studies on the electronic properties of (R3xR3)R30° phase of silicene on Ag(111) surface. We found the existence of Dirac Fermion chirality through the observation of -1.5 and -1.0 power law decay of quasiparticle interference (QPI) patterns. Moreover, in contrast to the trigonal warping of Dirac cone in graphene, we found that the Dirac cone of silicene is hexagonally warped, which is further confirmed by density functional calculations and explained by the unique superstructure of silicene. Our results de…
We theoretically investigate the indirect signatures of the tilted anisotropic Dirac cones on Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange interaction in a two dimensional polymorph of boron atoms. Unlike the case of isotropic non-tilted Dirac material-graphene, here we observe that the tilting of the Dirac cones exhibits a significant impact on the RKKY exchange interaction in terms of the suppression of oscillation frequency. The reason can be attributed to the behavior of the Fermi level and the corresponding density of states with respect to the tilting parameter. The direct measurement o…
We calculate conductance and noise for quantum transport at the nodal point for arbitrarily tilted and anisotropic Dirac or Weyl cones. Tilted and anisotropic dispersions are generic in absence of certain discrete symmetries, such as particle-hole and lattice point group symmetries. Whereas anisotropy affects the conductance g, but leaves the Fano factor F (the ratio of shot noise power and current) unchanged, a tilt affects both g and F. Since F is a universal number in many other situations, this finding is remarkable. We apply our general considerations to specific lattice models of straine…
We theoretically study the effect of the motion and the merging of Dirac cone on the interlayer magnetoresistance in multilayer graphene like systems. This merging, which could be induced by a uniaxial strain, gives rise in monolayer Dirac electron system to a topological transition from a semi-metallic phase to an insulating phase where Dirac points disappear. Based on a universal Hamiltonian proposed to describe the motion and the merging of Dirac points in two dimensional Dirac electron crystals, we calculate the interlayer conductivity of a stack of deformed graphene like layers using Kubo…
We propose magnonic analogs of topological crystalline insulators which possess Dirac surface states protected by the combined symmetry of time-reversal and half translation. Constructing models of the topological magnon systems, we demonstrate that the energy current flows through the systems in response to an electric field, owing to the Dirac surface states with the spin-momentum locking. We also propose a realization of the magnonic analogs of topological crystalline insulators in a magnetic compound CrI$_{3}$ with a monoclinic structure.
We show that a class of weak three-dimensional topological insulators feature one-dimensional Dirac electrons on their surfaces. Their hallmark is a line-like energy dispersion along certain directions of the surface Brillouin zone. These one-dimensional Dirac line degeneracies are topologically protected by a symmetry that we refer to as in-plane time-reversal invariance. We show how this invariance leads to Dirac lines in the surface spectrum of stacked Kane-Mele systems and more general models for weak three-dimensional topological insulators.
We study the quantum Hall effect of Dirac fermions on the surface of a Wilson-Dirac type topological insulator thin film in the strong topological insulating phase. Although a magnetic field breaks time reversal symmetry of the bulk, the surface states can survive even in a strong field regime. We examine how the Landau levels of the surface states are affected by symmetry breaking perturbations.
Using first principles pseudopotential density functional theory calculations, we find that terminating zigzag graphene nanoribbons (ZGNR) with monovalent alkali atoms at a reduced concentration has a dramatic impact on their properties. In particular, using sodium atoms for the saturation of ZGNR edges at half the concentration of edge-carbon atoms make it a one dimensional, perfect semimetal, where the valance and conduction bands meet at only a single, Dirac-like point. Unlike pristine graphene, the Dirac-"cones" of Na-ZGNR is not symmetric with respect to wave vector, but rather it is tilt…
