Dirac Electrons with Molecular Relaxation Time at Electrochemical Interface between Graphene and Water.

The time dynamics of charge accumulation at the electrochemical interface between graphene and water is important for supercapacitors, batteries, and chemical and biological sensors. By using impedance spectroscopy, we have found that measured capacitance (Cm) at this interface with the gate voltage Vgate ≈ 0.1 V follows approximate laws Cm~T1.2 and Cm~T0.11 (T is Vgate period) in frequency ranges (1000-50,000) Hz and (0.02-300) Hz, respectively. In the first range, this dependence demonstrates that the interfacial capacitance (Cint) is only partially charged during the charging period. The observed weaker frequency dependence of the measured capacitance (Cm) at frequencies below 300 Hz is primarily determined by the molecular relaxation of the double-layer capacitance (Cdl) and by the graphene quantum capacitance (Cq), and it also implies that Cint is mostly charged. We have also found a voltage dependence of Cm below 10 Hz, which is likely related to the voltage dependence of Cq. The observation of this effect only at low frequencies indicates that Cq relaxation time is much longer than is typical for electron processes, probably due to Dirac cone reconstruction from graphene electrons with increased effective mass as a result of their quasichemical bonding with interfacial molecular charges.

Dirac cones and chiral selection of elastic waves in a soft strip.

We study the propagation of in-plane elastic waves in a soft thin strip, a specific geometrical and mechanical hybrid framework which we expect to exhibit a Dirac-like cone. We separate the low frequencies guided modes (typically 100 Hz for a 1-cm-wide strip) and obtain experimentally the full dispersion diagram. Dirac cones are evidenced together with other remarkable wave phenomena such as negative wave velocity or pseudo-zero group velocity (ZGV). Our measurements are convincingly supported by a model (and numerical simulation) for both Neumann and Dirichlet boundary conditions. Finally, we perform one-way chiral selection by carefully setting the source position and polarization. Therefore, we show that soft materials support atypical wave-based phenomena, which is all of the more interesting as they make most of the biological tissues.

Direct Observation of Global Elastic Intervalley Scattering Induced by Impurities on Graphene.

The scattering process induced by impurities in graphene plays a key role in transport properties. Especially, the disorder impurities can drive the ordered state with a hexagonal superlattice on graphene by electron-mediated interaction at a transition temperature. Using angle-resolved photoemission spectroscopy (ARPES), we reveal that the epitaxial monolayer and bilayer graphene with various impurities display global elastic intervalley scattering and quantum interference below the critical temperature (34 K), which leads to a set of new folded Dirac cones at the Brillouin-zone center by mixing two inequivalent Dirac cones. The Dirac electrons generated from intervalley scattering without chirality can be due to the breaking of the sublattice symmetry. In addition, the temperature-dependent ARPES measurements indicate the thermal damping of quantum interference patterns from Dirac electron scattering on impurities. Our results demonstrate that the electron scattering and interference induced by impurities can completely modulate the Dirac bands of graphene.

On the Quantization of AB Phase in Nonlinear Systems.

Self-intersecting energy band structures in momentum space can be induced by nonlinearity at the mean-field level, with the so-called nonlinear Dirac cones as one intriguing consequence. Using the Qi-Wu-Zhang model plus power law nonlinearity, we systematically study in this paper the Aharonov-Bohm (AB) phase associated with an adiabatic process in the momentum space, with two adiabatic paths circling around one nonlinear Dirac cone. Interestingly, for and only for Kerr nonlinearity, the AB phase experiences a jump of π at the critical nonlinearity at which the Dirac cone appears and disappears (thus yielding π-quantization of the AB phase so long as the nonlinear Dirac cone exists), whereas for all other powers of nonlinearity, the AB phase always changes continuously with the nonlinear strength. Our results may be useful for experimental measurement of power-law nonlinearity and shall motivate further fundamental interest in aspects of geometric phase and adiabatic following in nonlinear systems.

Reconfiguring graphene to achieve intrinsic negative Poisson's ratio and strain-tunable bandgap.

A new two-dimensional carbon-based material consisting of pentagonal and hexagonal elements is identified by numerical experiments, which is called phgraphene and possesses not only a tunable semimetallic feature but also a direction-dependent even sign-changed Poisson's ratio. The structural stability of such a new material is first checked systematically. It is found that phgraphene has a similar energy as theγ-graphyne, a thermally stable structure from the room temperature to 1500 K, and elastic constants satisfying the Born-Huang criterion. Both the band structure and density of states are further verified with different techniques, which demonstrate a Dirac semimetallic characteristic of phgraphene. A more interesting finding is that the band structure can be easily tuned by an external loading, resulting in the transition from semimetal to semiconductor or from type I to type III. As a new material that may be applied in the future, the mechanical property of phgraphene is further evaluated. It shows that phgraphene is a typically anisotropic material, which has not only direction-dependent Young's moduli but also direction-dependent even sign-changed Poisson's ratios. The microscopic mechanisms of both the electrical and mechanical properties are revealed. Such a versatile material with tunable band structure and auxetic effect should have promising applications in the advanced nano-electronic field in the future.

Electronic and optical properties of boron-based hybrid monolayers.

Anisotropic 2D Dirac cone materials are important for the fabrication of nanodevices having direction-dependent characteristics since the anisotropic Dirac cones lead to different values of Fermi velocities yielding variable carrier concentrations. In this work, the feasibility of the B-based hybrid monolayers BX (X = As, Sb, and Bi), as anisotropic Dirac cone materials is investigated. Calculations based on density functional theory and molecular dynamics method find the stability of these monolayers exhibiting unique electronic properties. For example, the BAs monolayer possesses a robust self-doping feature, whereas the BSb monolayer carries the intrinsic charge carrier concentration of the order of 1012cm-2which is comparable to that of graphene. Moreover, the direction-dependent optical response is predicted in these B-based monolayers; a high IR response in thex-direction is accompanied with that in the visible region along they-direction. The results are, therefore, expected to help in realizing the B-based devices for nanoscale applications.

Direct evidence of interaction-induced Dirac cones in a monolayer silicene/Ag(111) system.

Silicene, analogous to graphene, is a one-atom-thick 2D crystal of silicon, which is expected to share many of the remarkable properties of graphene. The buckled honeycomb structure of silicene, along with enhanced spin-orbit coupling, endows silicene with considerable advantages over graphene in that the spin-split states in silicene are tunable with external fields. Although the low-energy Dirac cone states lie at the heart of all novel quantum phenomena in a pristine sheet of silicene, a hotly debated question is whether these key states can survive when silicene is grown or supported on a substrate. Here we report our direct observation of Dirac cones in monolayer silicene grown on a Ag(111) substrate. By performing angle-resolved photoemission measurements on silicene(3 × 3)/Ag(111), we reveal the presence of six pairs of Dirac cones located on the edges of the first Brillouin zone of Ag(111), which is in sharp contrast to the expected six Dirac cones centered at the K points of the primary silicene(1 × 1) Brillouin zone. Our analysis shows clearly that the unusual Dirac cone structure we have observed is not tied to pristine silicene alone but originates from the combined effects of silicene(3 × 3) and the Ag(111) substrate. Our study thus identifies the case of a unique type of Dirac cone generated through the interaction of two different constituents. The observation of Dirac cones in silicene/Ag(111) opens a unique materials platform for investigating unusual quantum phenomena and for applications based on 2D silicon systems.

Large-Gap Magnetic Topological Heterostructure Formed by Subsurface Incorporation of a Ferromagnetic Layer.

Inducing magnetism into topological insulators is intriguing for utilizing exotic phenomena such as the quantum anomalous Hall effect (QAHE) for technological applications. While most studies have focused on doping magnetic impurities to open a gap at the surface-state Dirac point, many undesirable effects have been reported to appear in some cases that makes it difficult to determine whether the gap opening is due to the time-reversal symmetry breaking or not. Furthermore, the realization of the QAHE has been limited to low temperatures. Here we have succeeded in generating a massive Dirac cone in a MnBi2Se4/Bi2Se3 heterostructure, which was fabricated by self-assembling a MnBi2Se4 layer on top of the Bi2Se3 surface as a result of the codeposition of Mn and Se. Our experimental results, supported by relativistic ab initio calculations, demonstrate that the fabricated MnBi2Se4/Bi2Se3 heterostructure shows ferromagnetism up to room temperature and a clear Dirac cone gap opening of ∼100 meV without any other significant changes in the rest of the band structure. It can be considered as a result of the direct interaction of the surface Dirac cone and the magnetic layer rather than a magnetic proximity effect. This spontaneously formed self-assembled heterostructure with a massive Dirac spectrum, characterized by a nontrivial Chern number C = -1, has a potential to realize the QAHE at significantly higher temperatures than reported up to now and can serve as a platform for developing future "topotronics" devices.

Manipulating the Topological Interface by Molecular Adsorbates: Adsorption of Co-Phthalocyanine on Bi2Se3.

Topological insulators are a promising class of materials for applications in the field of spintronics. New perspectives in this field can arise from interfacing metal-organic molecules with the topological insulator spin-momentum locked surface states, which can be perturbed enhancing or suppressing spintronics-relevant properties such as spin coherence. Here we show results from an angle-resolved photemission spectroscopy (ARPES) and scanning tunnelling microscopy (STM) study of the prototypical cobalt phthalocyanine (CoPc)/Bi2Se3 interface. We demonstrate that that the hybrid interface can act on the topological protection of the surface and bury the Dirac cone below the first quintuple layer.

Engineering Topological Surface States of Cr-Doped Bi2Se3 Films by Spin Reorientation and Electric Field.

The tailoring of topological surface states in topological insulators is essential for device applications and for exploring new topological phase. Here, we propose a practical way to induce the quantum anomalous Hall phase and unusual metal-insulator transitions in Cr-doped Bi2Se3 films based on the model Hamiltonian and first-principles calculations. Using the combination of in-plane and plane-normal components of the spin along with external electric fields, we demonstrate that the topological state and band structures of topological insulating films exhibit rich features such as the shift of Dirac cones and the opening of nontrivial band gaps. We also show that the in-plane magnetization leads to significant suppression of inter-TSS scattering in Cr-doped Bi2Se3. Our work provides new strategies to obtain the desired electronic structures for the device, complementary to the efforts of an extensive material search.

Two-Dimensional Phosphorus Carbide: Competition between sp(2) and sp(3) Bonding.

We propose previously unknown allotropes of phosphorus carbide (PC) in the stable shape of an atomically thin layer. Different stable geometries, which result from the competition between sp(2) bonding found in graphitic C and sp(3) bonding found in black P, may be mapped onto 2D tiling patterns that simplify categorizing of the structures. Depending on the category, we identify 2D-PC structures that can be metallic, semimetallic with an anisotropic Dirac cone, or direct-gap semiconductors with their gap tunable by in-layer strain.

Observation of single-spin Dirac fermions at the graphene/ferromagnet interface.

With the discovery and first characterization of graphene, its potential for spintronic applications was recognized immediately. Since then, an active field of research has developed trying to overcome the practical hurdles. One of the most severe challenges is to find appropriate interfaces between graphene and ferromagnetic layers, which are granting efficient injection of spin-polarized electrons. Here, we show that graphene grown under appropriate conditions on Co(0001) demonstrates perfect structural properties and simultaneously exhibits highly spin-polarized charge carriers. The latter was conclusively proven by observation of a single-spin Dirac cone near the Fermi level. This was accomplished experimentally using spin- and angle-resolved photoelectron spectroscopy, and theoretically with density functional calculations. Our results demonstrate that the graphene/Co(0001) system represents an interesting candidate for applications in devices using the spin degree of freedom.

Two-Dimensional Boron Hydride Sheets: High Stability, Massless Dirac Fermions, and Excellent Mechanical Properties.

Two-dimensional (2D) boron sheets have been successfully synthesized in recent experiments, however, some important issues remain, including the dynamical instability, high energy, and the active surface of the sheets. In an attempt to stabilize 2D boron layers, we have used density functional theory and global minimum search with the particle-swarm optimization method to predict four stable 2D boron hydride layers, namely the C2/m, Pbcm, Cmmm, and Pmmn sheets. The vibrational normal mode calculations reveal all these structures are dynamically stable, indicating potential for successful experimental synthesis. The calculated Young's modulus indicates a high mechanical strength for the C2/m and Pbcm phases. Most importantly, the C2/m, Pbcm, and Pmmn structures exhibit Dirac cones with massless Dirac fermions and the Fermi velocities for the Pbcm and Cmmm structures are even higher than that of graphene. The Cmmm phase is reported as the first discovery of Dirac ring material among boron-based 2D structures. The unique electronic structure of the 2D boron hydride sheets makes them ideal for nanoelectronics applications.

Asymmetric Tilt-Induced Quantum Beating of Conductance Oscillation in Magnetically Modulated Dirac Matter Systems.

Herein, we investigate the effect of tilt mismatch on the quantum oscillations of spin transport properties in two-dimensional asymmetrically tilted Dirac cone systems. This study involves the examination of conductance oscillation in two distinct junction types: transverse- and longitudinal-tilted Dirac cones (TTDCs and LTDCs). Our findings reveal an unusual quantum oscillation of spin-polarized conductance within the TTDC system, characterized by two distinct anomaly patterns within a single period, labeled as the linear conductance phase and the oscillatory conductance phase. Interestingly, these phases emerge in association with tilt-induced orbital pseudo-magnetization and exchange interaction. Our study also demonstrates that the structure of the LTDC can modify the frequency of spin conductance oscillation, and the asymmetric effect within this structure results in a quantum beating pattern in oscillatory spin conductance. We note that an enhancement in the asymmetric longitudinal tilt velocity ratio within the structure correspondingly amplifies the beating frequency. Our research potentially contributes valuable insights for detecting the asymmetry of tilted Dirac fermions in type-I Dirac semimetal-based spintronics and quantum devices.

Electronic Band Engineering of Two-Dimensional Kagomé Polymers.

Two-dimensional conjugated polymers (2DCPs) are an emerging class of materials that exhibit properties similar to graphene yet do not have the limitation of zero bandgap. On-surface synthesis provides exceptional control on the polymerization reaction, allowing tailoring properties by choosing suitable monomers. Heteroatom-substituted triangulene 2DCPs constitute a playing ground for such a design and are predicted to exhibit graphene-like band structures with high charge mobility and characteristic Dirac cones in conduction or valence states. However, measuring these properties experimentally is challenging and requires long-range-ordered polymers, preferably with an epitaxial relationship with the substrate. Here, we investigate the electronic properties of a mesoscale-ordered carbonyl-bridged triphenylamine 2DCP (P2TANGO) and demonstrate the presence of a Dirac cone by combining angle-resolved photoemission spectroscopy (ARPES) with density functional theory (DFT) calculations. Moreover, we measure the absolute energy position of the Dirac cone with respect to the vacuum level. We show that the bridging functionality of the triangulene (ether vs carbonyl) does not significantly perturb the band structure but strongly affects the positioning of the bands with respect to the Au(111) states and allows control of the ionization energy of the polymer. Our results provide proof of the controllable electronic properties of 2DCPs and bring us closer to their use in practical applications.

Excitonic instability in transition metal dichalcogenides.

When transition-metal dichalcogenide monolayers lack inversion symmetry, their low-energy single particle spectrum near some high-symmetry points can, in some cases, be described by tilted massive Dirac Hamiltonians. The so-called Janus materials fall into that category. Inversion symmetry can also be broken by the application of out-of-plane electric fields, or by the mere presence of a substrate. Here we explore the properties of excitons in TMDC monolayers lacking inversion symmetry. We find that exciton binding energies can be larger than the electronic band gap, making such materials promising candidates to host the elusive exciton insulator phase. We also investigate the excitonic contribution to their optical conductivity and discuss the associated optical selection rules.

Dirac-cone-like electronic states on nematic antiferromagnetic FeSe and FeTe.

We investigate the Dirac-cone-like (DCL) topological electronic properties of nematic-like antiferromagnetic (AFM) states of monolayer FeSe and FeTe designed artificially through first-principles calculations and Wannier-function-based tight-binding (WFTB) method. Our calculations reveal most of them have a pair of DCL bands on the Γ-Xline in the Brillouin zone (BZ) near the Fermi level and open a gap of about 20 meV in the absence and presence of spin-orbit coupling (SOC), respectively, similar to the lowest-energy pair-checkerboard AFM FeSe. We further confirm that they are weak topological insulators based on nonzeroZ2and fragile surface states, which are calculated by the WFTB method. For FeSe and FeTe in pair-checkerboard AFM states, we find that the in-plane compression strain in a certain range can give rise to another pair of DCL bands located on the Γ-X' line in the BZ. In addition, the magnetic moments, energies, and Fe-Se/Te distances for various nematic-like AFM configurations are presented. These calculations the combining effect of magnetism and topology in a single material and the understanding of the superconducting phenomena in iron-based FeSe and FeTe.

Multiple Dirac cones and Lifshitz transition in a two-dimensional Cairo lattice as a Hawking evaporation analogue.

The linear energy-momentum dispersion of Dirac cones offers a unique platform for mimicking the fantastical phenomena in high energy physics, such as Dirac fermions and black hole (BH) horizons. Three types of Dirac cones (I, III, and II) with different tilts have been proposed individually in specific materials but lack of integral lattice model. Here, we demonstrated the three types of Dirac cones inherited in aπ-conjugated Cairo lattice of double-degeneratedπandpzorbitals by means of tight-binding (TB) approach, which paves a way for the design of two-dimensional (2D) Dirac materials. From first-principles calculations, we predicted a candidate material,penta-NiSb2monolayer, to achieve these multiple Dirac cones and the Lifshitz transition between different Dirac cones driven by external biaxial strain. The coexistence of the three types of Dirac cones renderspenta-NiSb2monolayer a promising 2D fermionic analogue to simulate the event-horizon evaporation with a high Hawking temperature.

Dielectric response of electron-hole systems. Nondegenerate case and quantum corrections.

Analytical results for the dielectric function in RPA are derived for three-, two-, and one-dimensional semiconductors in the weakly-degenerate limit. Based on this limit, quantum corrections are derived. Further attention is devoted to systems with linear carrier dispersion and the resulting Dirac-cone physics.

Quantum Size Effects, Multiple Dirac Cones, and Edge States in Ultrathin Bi(110) Films.

The presence of inherently strong spin-orbit coupling in bismuth, its unique layer-dependent band topology and high carrier mobility make it an interesting system for both fundamental studies and applications. Theoretically, it has been suggested that strong quantum size effects should be present in the Bi(110) films, with the possibility of Dirac Fermion states in the odd-bilayer (BL) films, originating from dangling pz orbitals and quantum-spin hall (QSH) states in the even-bilayer films. However, the experimental verification of these claims has been lacking. Here, we study the electronic structure of Bi(110) films grown on a high-Tc superconductor, Bi2Sr2CaCu2O8+δ (Bi2212) using angle-resolved photoemission spectroscopy (ARPES). We observe an oscillatory behavior of electronic structure with the film thickness and identify the Dirac-states in the odd-bilayer films, consistent with the theoretical predictions. In the even-bilayer films, we find another Dirac state that was predicted to play a crucial role in the QSH effect. In the low thickness limit, we observe several extremely one-dimensional states, probably originating from the edge-states of Bi(110) islands. Our results provide a much needed experimental insight into the electronic and structural properties of Bi(110) films.