2D Dirac Materials Research Articles

Information measures and topological-band insulator transitions in 2D-Dirac materials under external circularly polarized lasers, and static electric and magnetic fields

The graphene family of 2D-Dirac materials shows different topological phases induced by the application of electric fields and the circularly polarized lasers. In this paper we present an informational analysis of these topological phases. Additionally, we determine the entropic uncertainty of these systems in the plane given by the electric and light fields, showing the different topological phases.

Electronic properties of silicene in BN/silicene van der Waals heterostructures**Project supported by the National Key Research and Development Program of China (Grant No. 2016YFA0202300), the National Natural Science Foundation of China (Grant Nos. 61390501 and 61471337), the National Basic Research Program of China (Grant No. 2013CBA01600), the CAS Pioneer Hundred Talents Program, and the Beijing Nova Program, China (Grant No.

Silicene is a promising 2D Dirac material as a building block for van der Waals heterostructures (vdWHs). Here we investigate the electronic properties of hexagonal boron nitride/silicene (BN/Si) vdWHs using first-principles calculations. We calculate the energy band structures of BN/Si/BN heterostructures with different rotation angles and find that the electronic properties of silicene are retained and protected robustly by the BN layers. In BN/Si/BN/Si/BN heterostructure, we find that the band structure near the Fermi energy is sensitive to the stacking configurations of the silicene layers due to interlayer coupling. The coupling is reduced by increasing the number of BN layers between the silicene layers and becomes negligible in BN/Si/(BN)3/Si/BN. In (BN)n/Si superlattices, the band structure undergoes a conversion from Dirac lines to Dirac points by increasing the number of BN layers between the silicene layers. Calculations of silicene sandwiched by other 2D materials reveal that silicene sandwiched by low-carbon-doped boron nitride or HfO2 is semiconducting.

Thermal Casimir and Casimir–Polder interactions in N parallel 2D Dirac materials

The Casimir and Casimir–Polder interactions are investigated in a stack of equally spaced graphene layers. The optical response of the individual graphene is taken into account using gauge invariant components of the polarization tensor extended to the whole complex frequency plane. The planar symmetry for the electromagnetic boundary conditions is further used to obtain explicit forms for the Casimir energy stored in the stack and the Casimir–Polder energy between an atom above the stack. Our calculations show that these fluctuation induced interactions experience strong thermal effects due to the graphene Dirac-like energy spectrum. The spatial dispersion and temperature dependence in the optical response are also found to be important for enhancing the interactions especially at smaller separations. Analytical expressions for low and high temperature limits and their comparison with corresponding expressions for an infinitely conducting planar stack are further used to expand our understanding of Casimir and Casimir–Polder energies in Dirac materials. Our results may be useful to experimentalists as new ways to probe thermal effects at the nanoscale in such universal interactions.

Dirac Signature in Germanene on Semiconducting Substrate.

2D Dirac materials supported by nonmetallic substrates are of particular interest due to their significance for the realization of the quantum spin Hall effect and their application in field‐effect transistors. Here, monolayer germanene is successfully fabricated on semiconducting germanium film with the support of a Ag(111) substrate. Its linear‐like energy–momentum dispersion and large Fermi velocity are derived from the pronounced quasiparticle interference patterns in a √3 × √3 superstructure. In addition to Dirac fermion characteristics, the theoretical simulations reveal that the energy gap opens at the Brillouin zone center of the √3 × √3 restructured germanene, which is evoked by the symmetry‐breaking perturbation potential. These results demonstrate that the germanium nanosheets with √3 × √3 germanene can be an ideal platform for fundamental research and for the realization of high‐speed and low‐energy‐consumption field‐effect transistors.

Phase Transitions of the Polariton Condensate in 2D Dirac Materials.

For the quantum well in an optical microcavity, the interplay of the Coulomb interaction and the electron-photon (e-ph) coupling can lead to the hybridizations of the exciton and the cavity photon known as polaritons, which can form the Bose-Einstein condensate above a threshold density. Additional physics due to the nontrivial Berry phase comes into play when the quantum well consists of the gapped two-dimensional Dirac material such as the transition metal dichalcogenide MoS_{2} or WSe_{2}. Specifically, in forming the polariton, the e-ph coupling from the optical selection rule due to the Berry phase can compete against the Coulomb electron-electron (e-e) interaction. We find that this competition gives rise to a rich phase diagram for the polariton condensate involving both topological and symmetry breaking phase transitions, with the former giving rise to the quantum anomalous Hall and the quantum spin Hall phases.

Excitonic instability in optically pumped three-dimensional Dirac materials

Recently it was suggested that transient excitonic instability can be realized in optically-pumped two-dimensional (2D) Dirac materials (DMs), such as graphene and topological insulator surface states. Here we discuss the possibility of achieving a transient excitonic condensate in optically-pumped three-dimensional (3D) DMs, such as Dirac and Weyl semimetals, described by non-equilibrium chemical potentials for photoexcited electrons and holes. Similar to the equilibrium case with long-range interactions, we find that for pumped 3D DMs with screened Coulomb potential two possible excitonic phases exist, an excitonic insulator phase and the charge density wave phase originating from intranodal and internodal interactions, respectively. In the pumped case, the critical coupling for excitonic instability vanishes; therefore, the two phases coexist for arbitrarily weak coupling strengths. The excitonic gap in the charge density wave phase is always the largest one. The competition between screening effects and the increase of the density of states with optical pumping results in a reach phase diagram for the transient excitonic condensate. Based on the static theory of screening, we find that under certain conditions for the value of the dimensionless coupling constant screening in 3D DMs can be weaker than in 2D DMs. Furthermore, we identify the signatures of the transient excitonic condensate that could be probed by scanning tunneling spectroscopy, photoemission and optical conductivity measurements. Finally, we provide estimates of critical temperatures and excitonic gaps for existing and hypothetical 3D DMs.

Dynamic conductivity modified by impurity resonant states in doping three-dimensional Dirac semimetals

The impurity effect is studied in three-dimensional Dirac semimetals in the framework of a T-matrix method to consider the multiple scattering events of Dirac electrons off impurities. It has been found that a strong impurity potential can significantly restructure the energy dispersion and the density of states of Dirac electrons. An impurity-induced resonant state emerges and significantly modifies the pristine optical response. It is shown that the impurity state disturbs the common longitudinal optical conductivity by creating either an optical conductivity peak or double absorption jumps, depending on the relative position of the impurity band and the Fermi level. More importantly, these conductivity features appear in the forbidden region between the Drude and interband transition, completely or partially filling the Pauli block region of optical response. The underlying physics is that the appearance of resonance states as well as the broadening of the bands leads to a more complicated selection rule for the optical transitions, making it possible to excite new electron-hole pairs in the forbidden region. These features in optical conductivity provide valuable information to understand the impurity behaviors in 3D Dirac materials.

High efficiency and non-Richardson thermionics in three dimensional Dirac materials

Three dimensional (3D) topological materials have a linear energy dispersion and exhibit many electronic properties superior to conventional materials such as fast response times, high mobility, and chiral transport. In this work, we demonstrate that 3D Dirac materials also have advantages over conventional semiconductors and graphene in thermionic applications. The low emission current suffered in graphene due to the vanishing density of states is enhanced by an increased group velocity in 3D Dirac materials. Furthermore, the thermal energy carried by electrons in 3D Dirac materials is twice of that in conventional materials with a parabolic electron energy dispersion. As a result, 3D Dirac materials have the best thermal efficiency or coefficient of performance when compared to conventional semiconductors and graphene. The generalized Richardson-Dushman law in 3D Dirac materials is derived. The law exhibits the interplay of the reduced density of states and enhanced emission velocity.

Design of Two-Dimensional Graphene-like Dirac Materials β12-XBeB5 (X = H, F, Cl) from Non-graphene-like β12-Borophene.

Two-dimensional (2D) Dirac materials and boron sheets have attracted intensive interest recently. However, 2D Dirac materials remain rare and difficult to be realized experimentally, and 2D boron sheets generally have high dynamical instability. Stimulated by the experimental observation of Dirac cones in nongraphene-like β12 boron sheets and based on the understanding of boron sheet electronic organization, we theoretically design new 2D Dirac materials β12-XBeB5 (X = H, F, Cl) with high stability. We confirm β12-HBeB5 as the global energy minimum among its 2D allotropes based on global structure search methods, a strong indication of its experimental feasibility. Our designed β12-HBeB5 has not only a high Fermi velocity, but also a Dirac state very robust against extraordinary large tensile strains, an advantage for flexible electronics applications. Our work opens a new avenue to designing feasible 2D Dirac materials and stabilizing borophene sheets.

Inhomogeneous screening of gate electric field by interface states in graphene FETs

The electronic states at graphene-SiO2 interface and their inhomogeneity is investigated using the back-gate-voltage dependence of local tunnel spectra acquired with a scanning tunneling microscope. The conductance spectra show two, or occasionally three, minima that evolve along the bias-voltage axis with the back gate voltage. This evolution is modeled using tip-gating and interface states. The energy dependent interface states’ density, , required to model the back-gate evolution of the minima, is found to have significant inhomogeneity in its energy-width. A broad leads to an effect similar to a reduction in the Fermi velocity while the narrow leads to the pinning of the Fermi energy close to the Dirac point, as observed in some places, due to enhanced screening of the gate electric field by the narrow . Finally, this also demonstrates STM as a tool to probe the density of interface states in various 2D Dirac materials.

First-Principles Study on the Mechanism of Hydrogen Decomposition and Spillover on Borophene

Borophane, a derivate of borophene, has been shown to eliminate the phonon imaginary frequency of borophene entirely with enhanced structural stability and be a 2D Dirac material with many appealing properties similar to its counterpart graphene. However, the mechanisms involved in borophene hydrogenation are still unclear, which are essential to borophane fabrication in experimental studies and which benefit our understanding of borophene functionalization. In this work, we investigate H2 adsorption and dissociation with (without) an external field and the subsequent spillover of H atoms on borophene based on density functional theory (DFT) to shed light on the procedure of borophene hydrogenation. We find that the incorporation of positive electric fields could facilitate the borophane formation with shallower energy barriers for H2 decomposition and H atoms present ultrahigh mobility on borophene under positive field. The origin of the field modulated energy barriers has been discussed. Our work provid...

Double Dirac point semimetal in 2D material: Ta2Se3

Here, we report by first-principles calculations one new stable 2D Dirac material, Ta2Se3 monolayer. For this system, stable layered bulk phase exists, and exfoliation should be possible. Ta2Se3 monolayer is demonstrated to support two Dirac points close to the Fermi level, achieving the exotic 2D double Dirac semimetal. And like 2D single Dirac and 2D node-line semimetals, spin–orbit coupling could introduce an insulating state in this new class of 2D Dirac semimetals. Moreover, the Dirac feature in this system is layer-dependent and a metal-to-insulator transition is identified in Ta2Se3 when reducing the layer-thickness from bilayer to monolayer. These findings are of fundamental interests and of great importance for nanoscale device applications.

Flatland plasmonics and nanophotonics based on graphene and beyond

AbstractIn this paper, we review and discuss how the recently discovered two-dimensional (2D) Dirac materials, particularly graphene, may be utilized as new efficient platforms for excitations of propagating and localized surface plasmon polaritons (SPPs) in the terahertz (THz) and mid-infrared (MIR) regions. The surface plasmon modes supported by the metallic 2D materials exhibit tunable plasmon resonances that are essential, yet missing, ingredients needed for THz and MIR photonic and optoelectronic devices. We describe how the atomically thin graphene monolayer and metamaterial structures based on it may tailor and control the spectral, spatial, and temporal properties of electromagnetic radiation. In the same frequency range, the newly unveiled nonlocal, nonlinear, and nonequilibrium electrodynamics in graphene show a variety of nonlinear and amplifying electromagnetic responses, whose potential applications are yet unexplored. With these 2D material platforms, virtually all plasmonic, optoelectronic, and nonlinear functions found in near-infrared (NIR) and visible devices can be analogously transferred to the long-wavelength regime, even with enhanced tunability and new functionalities. The spectral range from THz to MIR is particularly compelling because of the many spectral fingerprints of key chemical, gas, and biological agents, as well as a myriad of remote sensing, imaging, communication, and security applications.

Dirac Nodal Lines and Tilted Semi-Dirac Cones Coexisting in a Striped Boron Sheet.

The enchanting Dirac fermions in graphene stimulated us to seek other 2D Dirac materials, and boron monolayers may be a good candidate. So far, a number of monolayer boron sheets have been theoretically predicted, and three have been experimentally prepared. However, none of intrinsic sheets possess Dirac electrons near the Fermi level. Herein, by means of density functional theory computations, we identified a new boron monolayer, namely, hr-sB, with two types of Dirac fermions coexisting in the sheet: One type is related to Dirac nodal lines traversing Brillouin zone (BZ) with velocities approaching 106 m/s, and the other is related to tilted semi-Dirac cones with strong anisotropy. This newly predicted boron monolayer consists of hexagon and rhombus stripes. With an exceptional stability comparable to the experimentally achieved boron sheets, it is rather optimistic to grow hr-sB on some suitable substrates such as the Ag (111) surface.

Creating stable Floquet\u2013Weyl semimetals by laser-driving of 3D Dirac materials

Tuning and stabilizing topological states, such as Weyl semimetals, Dirac semimetals or topological insulators, is emerging as one of the major topics in materials science. Periodic driving of many-body systems offers a platform to design Floquet states of matter with tunable electronic properties on ultrafast timescales. Here we show by first principles calculations how femtosecond laser pulses with circularly polarized light can be used to switch between Weyl semimetal, Dirac semimetal and topological insulator states in a prototypical three-dimensional (3D) Dirac material, Na3Bi. Our findings are general and apply to any 3D Dirac semimetal. We discuss the concept of time-dependent bands and steering of Floquet–Weyl points and demonstrate how light can enhance topological protection against lattice perturbations. This work has potential practical implications for the ultrafast switching of materials properties, such as optical band gaps or anomalous magnetoresistance.

A new Dirac cone material: a graphene-like Be3C2 monolayer.

Two-dimensional (2D) materials with Dirac cones exhibit rich physics and many intriguing properties, but the search for new 2D Dirac materials is still a current hotspot. Using the global particle-swarm optimization method and density functional theory, we predict a new stable graphene-like 2D Dirac material: a Be3C2 monolayer with a hexagonal honeycomb structure. The Dirac point occurs exactly at the Fermi level and arises from the merging of the hybridized pz bands of Be and C atoms. Most interestingly, this monolayer exhibits a high Fermi velocity in the same order of graphene. Moreover, the Dirac cone is very robust and retains even included spin-orbit coupling or external strain. These outstanding properties render the Be3C2 monolayer a promising 2D material for special electronics applications.

High-Dimensional Disorder-Driven Phenomena in Weyl Semimetals, Semiconductors, and Related Systems

It is commonly believed that a noninteracting disordered electronic system can undergo only the Anderson metal-insulator transition. It has been suggested, however, that a broad class of systems can display disorder-driven transitions distinct from Anderson localization that have manifestations in the disorder-averaged density of states, conductivity, and other observables. Such transitions have received particular attention in the context of recently discovered 3D Weyl and Dirac materials but have also been predicted in cold-atom systems with long-range interactions, quantum kicked rotors, and all sufficiently high-dimensional systems. Moreover, such systems exhibit unconventional behavior of Lifshitz tails, energy-level statistics, and ballistic-transport properties. Here, we review recent progress and the status of results on non-Anderson disorder-driven transitions and related phenomena.

Revivals of electron currents and topological-band insulator transitions in 2D gapped Dirac materials

We have studied the time evolution of electron wave packets in silicene under perpendicular magnetic and electric fields to characterize topological-band insulator transitions. We have found that at the charge neutrality points, the periodicities exhibited by the wave packet dynamics (classical and revival times) reach maximum values, and that the electron currents reflect the transition from a topological insulator to a band insulator. This provides a signature of topological phase transition in silicene that can be extended to other 2D Dirac materials isostructural to graphene and with a buckled structure and a significant spin-orbit coupling.

Chiral plasmons without magnetic field

Plasmons, the collective oscillations of interacting electrons, possess emergent properties that dramatically alter the optical response of metals. We predict the existence of a new class of plasmons-chiral Berry plasmons (CBPs)-for a wide range of 2D metallic systems including gapped Dirac materials. As we show, in these materials the interplay between Berry curvature and electron-electron interactions yields chiral plasmonic modes at zero magnetic field. The CBP modes are confined to system boundaries, even in the absence of topological edge states, with chirality manifested in split energy dispersions for oppositely directed plasmon waves. We unveil a rich CBP phenomenology and propose setups for realizing them, including in anomalous Hall metals and optically pumped 2D Dirac materials. Realization of CBPs will offer a powerful paradigm for magnetic field-free, subwavelength optical nonreciprocity, in the mid-IR to terahertz range, with tunable splittings as large as tens of THz, as well as sensitive all-optical diagnostics of topological bands.

Temperature-dependent many-body effects in Dirac-Weyl materials: Interacting compressibility and quasiparticle velocity

We calculate, within the single-loop or equivalently the Hartree-Fock Approximation (HFA), the finite-temperature interacting compressibility for three-dimensional (3D) Dirac materials and renormalized quasiparticle velocities for 3D and two-dimensional (2D) Dirac materials. We find that in the extrinsic (i.e., doped) system, the inverse compressibility (incompressibility) and renormalized quasiparticle velocity at $k=0$ show nonmonotonic dependences on temperature. At low temperatures the incompressibility initially decreases to a shallow minimum with a $T^2 \ln T$ dependence. As the temperature increases further, the incompressibility rises to a maximum and beyond that it decreases with increasing temperature. On the other hand, the renormalized quasiparticle velocity at $k=0$ for both 2D and 3D Dirac materials first increases with $T^2$, rises to a maximum, and after reaching the maximum it decreases with increasing temperature. We also find that within the HFA, the leading-order temperature correction to the low-temperature renormalized extrinsic Fermi velocity for both 2D and 3D doped Dirac materials is $\ln (1/T)$.