We study theoretically the dispersion of plasmonic honeycomb lattices and find Dirac spectra for both dipole and quadrupole modes. Zigzag edge states derived from Dirac points are found in ribbons of these honeycomb plasmonic lattices. The zigzag edge states for out-of-plane dipole modes are closely analogous to the electronic ones in graphene nanoribbons. The edge states for in-plane dipole modes and quadrupole modes, however, have rather unique characters due to the vector nature of the plasmonic excitations. The conditions for the existence of plasmonic edge states are derived analytically.
Pseudorelativistic Dirac quasiparticles have emerged in a plethora of artificial graphene systems that mimic the underlying honeycomb symmetry of graphene. However, it is notoriously difficult to manipulate their properties without modifying the lattice structure. Here we theoretically investigate polaritons supported by honeycomb metasurfaces and, despite the trivial nature of the resonant elements, we unveil rich Dirac physics stemming from a non-trivial winding in the light-matter interaction. The metasurfaces simultaneously exhibit two distinct species of massless Dirac polaritons, namely …
We demonstrate unexpected occurrence of linear bands resembling Dirac cone at the zone-center of Au$_2$Sn surface alloy with $\left( \begin{smallmatrix} 2&1\\ 1&3 \end{smallmatrix} \right)$ surface structure formed by deposition of about 0.9 ML Sn on Au(111) at elevated temperature. The surface exhibits an oblique symmetry with unequal lattice constants making it the first two dimensional surface alloy to exhibit Dirac cone with a non-honeycomb lattice.
The honeycomb lattice possesses a novel energy band structure, which is characterized by two distinct Dirac points in the Brillouin zone, dominating most of the physical properties of the honeycomb structure materials. However, up till now, the origin of the Dirac points is unclear yet. Here, we discover a hidden symmetry on the honeycomb lattice and prove that the existence of Dirac points is exactly protected by such hidden symmetry. Furthermore, the moving and merging of the Dirac points and a quantum phase transition, which have been theoretically predicted and experimentally observed on t…
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.
Recently, several new materials exhibiting massless Dirac fermions have been proposed. However, many of these do not have the typical graphene honeycomb lattice, which is often associated with Dirac cones. Here, we present a classification of these different two-dimensional Dirac systems based on the space groups, and discuss our findings within the context of a minimal two-band model. In particular, we show that the emergence of massless Dirac fermions can be attributed to the mirror symmetries of the materials. Moreover, we uncover several novel Dirac systems that have up to twelve inequival…
We give a rigorous deduction of the eigenvalue problem of the nonlinear Schrödinger equation (NLS) at Dirac Points for potential of honeycomb lattice symmetry. Based on a bootstrap method, we observe the bifurcation of the eigenfunctions into eight distinct modes from the two-dimensional degenerated eigenspace of the regressive linear Schrödinger equation. We give the existence, the way of construction, uniqueness in $H^2$ space and the $C^\infty$ continuity of these eigenfunctions.
We prove that the two-dimensional Schroedinger operator with a potential having the symmetry of a honeycomb structure has dispersion surfaces with conical singularities (Dirac points) at the vertices of its Brillouin zone. No assumptions are made on the size of the potential. We then prove the robustness of such conical singularities to a restrictive class of perturbations, which break the honeycomb lattice symmetry. General small perturbations of potentials with Dirac points do not have Dirac points; their dispersion surfaces are smooth. The presence of Dirac points in honeycomb structures is…
The discovery of the Dirac electron dispersion in graphene led to the question of the Dirac cone stability with respect to interactions. Coulomb interactions between electrons were shown to induce a logarithmic renormalization of the Dirac dispersion. With a rapid expansion of the list of compounds and quasiparticle bands with linear band touching, the concept of bosonic Dirac materials has emerged. We consider a specific case of ferromagnets consisting of the Van der Waals-bonded stacks of honeycomb layers, e.g chromium trihalides CrX3 (X = F, Cl, Br and I), that display two spin wave modes w…
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…
We examine the presence and evolution of magnetic Dirac nodes in the Heisenberg honeycomb lattice. Using linear spin theory, we evaluate the collinear phase diagram as well as the change in the spin dynamics with various exchange interactions. We show that the ferromagnetic structure produces bosonic Dirac and Weyl points due to the competition between superexchange interactions. Furthermore, it is shown that the criteria for magnetic Dirac nodes are coupled to the magnetic structure and not the overall crystal symmetry, where the breaking of inversion symmetry greatly affects the antiferromag…
We consider spin Hall effect in a system of massless Dirac fermions in a graphene lattice. Two types of spin-orbit interaction, pertinent to the graphene lattice, are taken into account - the intrinsic and Rashba terms. Assuming perfect crystal lattice, we calculate the topological contribution to spin Hall conductivity. When both interactions are present, their interplay is shown to lead to some peculiarities in the dependence of spin Hall conductivity on the Fermi level.
Motivated by recent experimental observations in $α$-RuCl$_3$, we study the $K$-$Γ$ model on the honeycomb lattice in an external magnetic field. By a slave-particle representation and Variational Monte Carlo calculations, we reproduce the phase transition from zigzag magnetic order to a field-induced disordered phase. The nature of this state depends crucially on the field orientation. For particular field directions in the honeycomb plane, we find a gapless Dirac spin liquid, in agreement with recent experiments on $α$-RuCl$_3$. For a range of out-of-plane fields, we predict the existence of…
We propose a family of free fermion lattice models that have "Dirac loops", closed lines of Dirac nodes in momentum space, on which the density of states vanishes linearly with energy. Those lattices all possess the planar trigonal connectivity present in graphene, but are three dimensional. We show that their highly anisotropic and multiply-connected Fermi surface leads to quantized Hall conductivities in three dimensions for magnetic fields with toroidal geometry. In the presence of spin-orbit coupling, we show that those structures have topological surface states. We discuss the feasibility…
The discovery of monolayer graphene has initiated two fertile fields in modern condensed matter physics, Dirac semimetals and atomically-thin layered materials. When these trends meet again in transition metal compounds, which possess spin and orbital degrees of freedom and strong electron correlations, more exotic phenomena are expected to emerge in the cross section of topological states of matter and Mott physics. Here, we show by using ab initio calculations that a monolayer form of transition metal trichalcogenides (TMTs), which has a honeycomb network of transition metal cations, may exh…
The past decade has witnessed numerous discoveries of two-dimensional (2D) semimetals and insulators, whereas 2D metals are rarely identified. Borophene, a monolayer boron sheet, has recently emerged as a perfect 2D metal with unique structure and electronic properties. Here we study collective excitations in borophene, which exhibit two major plasmon modes with low damping rates extending from infrared to ultraviolet regime. The anisotropic 1D plasmon originates from electronic excitations of tilted Dirac cones in borophene, analogous to that in heavily doped Dirac semimetals. These features …
Intriguing physical property of materials stems from their chemical constituent whereas the connection between them is often not clear. Here, we uncover a general chemical classification for the two quantum phases in the honeycomb ABX structure--topological insulator (TI) and topological Dirac semimetal (TDSM). First, we find among the 816 (existing as well as hypothetical) calculated compounds, 160 TI's (none were noted before), 96 TDSM's, 282 normal insulators (NI's), and 278 metals. Second, based on this classification, we have distilled a simple chemical regularity based on compound formul…
We discuss plasmons of biased twisted bilayer graphene when the Fermi level lies inside the gap. The collective excitations are a network of chiral edge plasmons (CEP) entirely composed of excitations in the topological electronic edge states (EES) that appear at the AB-BA interfaces. The CEP form an hexagonal network with an unique energy scale $ε_p=\frac{e^2}{ε_0εt_0}$ with $t_0$ the moiré lattice constant and $ε$ the dielectric constant. From the dielectric matrix we obtain the plasmon spectra that has two main characteristics: (i) a diverging density of states at zero energy, and (ii) the …
The electronic band topology of monolayer $β$-Sb (antimonene) is studied from the flat honeycomb to the equilibrium buckled structure using first-principles calculations and analyzed using a tight-binding model and low energy Hamiltonians. In flat monolayer Sb, the Fermi level occurs near the intersection of two warped Dirac cones, one associated with the $p_z$-orbitals, and one with the $\{p_x,p_y\}$-orbitals. The differently oriented threefold warping of these two cones leads to an unusually shaped nodal line, which leads to anisotropic in-plane transport properties and goniopolarity. A slig…
Phase transitions in the Hubbard model and ionic Hubbard model at half-filling on the honeycomb lattice are investigated in the strong coupling perturbation theory which corresponds to an expansion in powers of the hopping $t$ around the atomic limit. Within this formulation we find analytic expressions for the single-particle spectrum, whereby the calculation of the insulating gap is reduced to a simple root finding problem. This enables high precision determination of the insulating gap that does not require any extrapolation procedure. The critical value of Mott transition on the honeycomb …
Nonreciprocal plasmonic response of drift-biased two-dimensional metals
Istituto Italiano di Tecnologia（意大利理工大学）；University of Southern Denmark（南丹麦大学）；Danish Institute for Advanced Study, University of Southern Denmark（南丹麦大学丹麦高等研究院）
The search for materials with novel and unusual electronic properties is at the heart of condensed matter physics as well as the basis to develop conceptual new technologies. In this context, the correlated honeycomb transition metal oxides attract large attention for both, being a possible experimental realization of the theoretically predicted magnetic Kitaev exchange and the theoretical prospect of topological nontriviality. The Mott insulating sodium iridate is prototypical among these materials with the promising prospect to bridge the field of strongly correlated systems with topology, f…
Recently, the concept of topological insulators has been generalized to topological semimetals, including three-dimensional (3D) Weyl semimetals, 3D Dirac semimetals, and 3D node-line semimetals. In particular, several compounds (e.g., certain three-dimensional graphene networks, Cu3PdN, Ca3P2) were discovered to be 3D node-line semimetals, in which the conduction and the valence bands cross at closed lines in the Brillouin zone. Except for the two-dimensional (2D) Dirac semimetal (e.g., in graphene), 2D topological semimetals are much less investigated. Here, we propose the new concept of a 2…
One of the most exciting subjects in solid state physics is a single layer of graphite which exhibits a variety of unconventional novel properties. The key feature of its electronic structure are linear dispersive bands which cross in a single point at the Fermi energy. This so-called Dirac cone is closely related to the surface states of the recently discovered topological insulators. The ternary compounds, such as LiAuSe and KHgSb with a honeycomb structure of their Au-Se and Hg-Sb layers feature band inversion very similar to HgTe which is a strong precondition for existence of the topologi…
Muffin-tin methods have been instrumental in the design of honeycomb lattices that show, in contrast to graphene, separated s and in-plane p bands, a p orbital Dirac cone, and a p orbital flat band. Recently, such lattices have been experimentally realized using the 2D electron gas on Cu(111). A possible next avenue is the introduction of spin-orbit coupling to these systems. Intrinsic spin-orbit coupling is believed to open topological gaps, and create a topological flat band. Although Rashba coupling is straightforwardly incorporated in the muffin-tin approximation, intrinsic spin-orbit coup…
The intriguing properties, especially Dirac physics in graphene, have inspired the pursuit of two-dimensional materials in honeycomb structure. Here we achieved a monolayer transition metal monochalcogenide AgTe on Ag(111) by tellurization of the substrate. High-resolution scanning tunneling microscopy, combined with low-energy electron diffraction, angle-resolved photoemission spectroscopy, and density functional theory calculations, demonstrates the planar honeycomb structure of AgTe. The first principle calculations further reveal that, protected by the in-plane mirror reflection symmetry, …
Artificial lattices have served as a platform to study the physics of unconventional superconductivity. We study semiconductor artificial graphene -- a honeycomb superlattice imposed on a semiconductor heterostructure -- which hosts the Dirac physics of graphene but with a tunable periodic potential strength and lattice spacing, allowing control of the strength of the electron-electron interactions. We demonstrate a new mechanism for superconductivity due to repulsive interactions which requires a strong lattice potential and a minimum doping away from the Dirac points. The mechanism relies on…
Isospectral transformations of exactly solvable models constitute a fruitful method for obtaining new structures with prescribed properties. In this paper we study the stability group of the Dirac algebra in honeycomb lattices representing graphene or boron nitride. New crystalline arrays with conical (Dirac) points are obtained; in particular, a model for dichalcogenide monolayers is proposed and analyzed. In our studies we encounter unitary and non-unitary transformations. We show that the latter give rise to $\mbox{$\cal P\,$}\mbox{$\cal T\,$}$-symmetric Hamiltonians, in compliance with kno…
Dirac points and Weyl phase in a honeycomb altermagnet
Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices, State Key Laboratory of Optoelectronic Materials and Technologies, Center for Neutron Science and Technology, School of Physics, Sun Yat-Sen University（中山大学物理学院）
Honeycomb structures of group IV elements can host massless Dirac fermions with non-trivial Berry phases. Their potential for electronic applications has attracted great interest and spurred a broad search for new Dirac materials especially in monolayer structures. We present a detailed investigation of the β12 boron sheet, which is a borophene structure that can form spontaneously on a Ag(111) surface. Our tight-binding analysis revealed that the lattice of the β12-sheet could be decomposed into two triangular sublattices in a way similar to that for a honeycomb lattice, thereby hosting Dirac…
