Spin currents in graphene under tension

Based on the Tight-Binding model, we have asymmetric massless Dirac fermions as the carriers in graphene under tension. Because of uniaxial strain, the velocities of Dirac fermions depend on their directions. This work studies the effect of the uniaxial strain on the spin transport through a single magnetic barrier of the strained graphene system. The result shows that graphene has a great potential for applications in nano-mechanical spintronic devices. This is because of strain in graphene can induce the spin-dependent pseudo-potentials at the barrier to control the spin currents of the junction.     

Survival of the Dirac points in rippled graphene

We study the effects of the rippling of a graphene sheet on quasiparticle dispersion. This is achieved using a generalization to the honeycomb lattice of the momentum average approximation, which is accurate for all coupling strengths and at all energies. We show that even though the position of the Dirac points may move and the Fermi speed can be renormalized significantly, quasiparticles with very long lifetimes survive near the Dirac points even for very strong couplings.     

Strain-dependent splitting of the double-resonance Raman scattering band in graphene

Under homogeneous uniaxial strains, the Raman 2D band of graphene involving two-phonon double-resonance scattering processes splits into two peaks and they altogether redshift strongly depending on the direction and magnitude of the strain. Through polarized micro-Raman measurements and first-principles calculations, the effects are shown to originate from significant changes in resonant conditions owing to both the distorted Dirac cones and anisotropic modifications of phonon dispersion under uniaxial strains. Quantitative agreements between the calculation and experiment enable us to determine the dominant double-resonance Raman scattering path, thereby answering a fundamental question concerning this key experimental analyzing tool for graphitic systems.     

Tunable multiple layered Dirac cones in optical lattices

We show that multiple layered Dirac cones can emerge in the band structure of properly addressed multicomponent cold fermionic gases in optical lattices. The layered Dirac cones contain multiple copies of massless spin-1/2 Dirac fermions at the same location in momentum space, whose different Fermi velocity can be tuned at will. On-site microwave Raman transitions can further be used to mix the different Dirac species, resulting in either splitting of or preserving the Dirac point (depending on the symmetry of the on-site term). The tunability of the multiple layered Dirac cones allows us to simulate a number of fundamental phenomena in modern physics, such as neutrino oscillations and exotic particle dispersions with E~p(N) for arbitrary integer N.     

Transmission through biased graphene strip

We solve the 2D Dirac equation describing graphene in the presence of a linear vector potential. The discretization of the transverse momentum due to the infinite mass boundary condition reduced our 2D Dirac equation to an effective massive 1D Dirac equation with an effective mass equal to the quantized transverse momentum. We use both a numerical Poincaré map approach, based on space discretization of the original Dirac equation, and a direct analytical method. These two approaches have been used to study tunneling phenomena through a biased graphene strip. The numerical results generated by the Poincaré map are in complete agreement with the analytical results.     

Electronic structure,Dirac points and Fermi arc surface states in three-dimensional Dirac semimetal Na_3Bi from angle-resolved photoemission spectroscopy

The three-dimensional(3D) Dirac semimetals have linearly dispersive 3D Dirac nodes where the conduction band and valence band are connected. They have isolated 3D Dirac nodes in the whole Brillouin zone and can be viewed as a 3D counterpart of graphene. Recent theoretical calculations and experimental results indicate that the 3D Dirac semimetal state can be realized in a simple stoichiometric compound A_3Bi(A = Na, K, Rb). Here we report comprehensive high-resolution angle-resolved photoemission(ARPES) measurements on the two cleaved surfaces,(001) and(100), of Na_3Bi. On the(001) surface, by comparison with theoretical calculations, we provide a proper assignment of the observed bands, and in particular, pinpoint the band that is responsible for the formation of the three-dimensional Dirac cones. We observe clear evidence of 3D Dirac cones in the three-dimensional momentum space by directly measuring on the k_x–k_y plane and by varying the photon energy to get access to different out-of-plane k_zs. In addition, we reveal new features around the Brillouin zone corners that may be related with surface reconstruction. On the(100) surface, our ARPES measurements over a large momentum space raise an issue on the selection of the basic Brillouin zone in the(100) plane. We directly observe two isolated 3D Dirac nodes on the(100) surface. We observe the signature of the Fermi-arc surface states connecting the two 3D Dirac nodes that extend to a binding energy of ~150 me V before merging into the bulk band. Our observations constitute strong evidence on the existence of the Dirac semimetal state in Na_3Bi that are consistent with previous theoretical and experimental work. In addition, our results provide new information to clarify on the nature of the band that forms the3 D Dirac cones, on the possible formation of surface reconstruction of the(001) surface, and on the issue of basic Brillouin zone selection for the(100) surface.     

Magnetic Kronig-Penney-type graphene superlattices: finite energy Dirac points with anisotropic velocity renormalization

We study the energy band structure of magnetic graphene superlattices with delta-function magnetic barriers and zero average magnetic field. The dispersion relation obtained using the T-matrix approach shows the emergence of an infinite number of Dirac-like points at finite energies, while the original Dirac point is still located at the same place as that for pristine graphene. The carrier group velocity at the original Dirac point is isotropically renormalized, but at finite energy Dirac points it is generally anisotropic. An asymmetry in the width between the wells and the barriers of the periodic potential induces a shift of the original Dirac point in the zero-energy plane, keeping the velocity renormalization isotropic.     

Highly anisotropic Dirac cones in epitaxial graphene modulated by an island superlattice

We present a new method to engineer the charge carrier mobility and its directional asymmetry in epitaxial graphene by using metal cluster superlattices self-assembled onto the moiré pattern formed by graphene on Ir(111). Angle-resolved photoemission spectroscopy reveals threefold symmetry in the band structure associated with strong renormalization of the electron group velocity close to the Dirac point giving rise to highly anisotropic Dirac cones. We further find that the cluster superlattice also affects the spectral-weight distribution of the carbon bands as well as the electronic gaps between graphene states.     

Enhanced Seebeck effect in graphene devices by strain and doping engineering

In this work, we investigate the possibility of enhancing the thermoelectric power (Seebeck coefficient) in graphene devices by strain and doping engineering. While a local strain can result in the misalignment of Dirac cones of different graphene sections in the k-space, doping engineering leads to their displacement in energy. By combining these two effects, we demonstrate that a conduction gap as large as a few hundred meV can be achieved and hence the enhanced Seebeck coefficient can reach a value higher than 1.4 mV/K in graphene doped heterojunctions with a locally strained area. Such hetero-channels appear to be very promising for enlarging the applications of graphene devices as in strain and thermal sensors.     

Probing interlayer coupling in twisted single‐crystal bilayer graphene by Raman spectroscopy

Twisted bilayer graphene, in which interlayer interaction plays a critical role in this coupled system, is characterized for its angle‐dependent electronic and optical properties. Here, we present a systematic Raman study of single‐crystal twisted bilayer graphene grains, with the spectra of each bilayer graphene precisely correlated to its twist angle using combined transmission electron microscopic technique. Van Hove singularities develop as a result of band rehybridization at the crossing Dirac cones of the two layers, giving rise to a critical twist angle that determines the energy separation between the saddle points in the band structure and the resonance Raman spectra accordingly. The 2D mode becomes sensitive to the twist angle, showing the angle‐dependent position, peak width, and intensity. Our results interpreted in the framework of angle‐dependent double resonance scattering provide an important experimental perspective in understanding the coupled bilayer graphene system. Copyright © 2014 John Wiley & Sons, Ltd.     

Competition for graphene: graphynes with direction-dependent Dirac cones

The existence of Dirac cones in the band structure of two-dimensional materials accompanied by unprecedented electronic properties is considered to be a unique feature of graphene related to its hexagonal symmetry. Here, we present other two-dimensional carbon materials, graphynes, that also possess Dirac cones according to first-principles electronic structure calculations. One of these materials, 6,6,12-graphyne, does not have hexagonal symmetry and features two self-doped nonequivalent distorted Dirac cones suggesting electronic properties even more amazing than that of graphene.     

Velocity renormalization and carrier lifetime in graphene from the electron-phonon interaction

We present a first-principles investigation of the phonon-induced electron self-energy in graphene. The energy dependence of the self-energy reflects the peculiar linear band structure of graphene and deviates substantially from the usual metallic behavior. The effective band velocity of the Dirac fermions is found to be reduced by 4%-8%, depending on doping, by the interaction with lattice vibrations. Our results are consistent with the observed linear dependence of the electronic linewidth on the binding energy in photoemission spectra.     

Layer stacking dependence on thermoelectric properties of massive Dirac fermions in bilayer graphene

We numerically study the thermoelectric transport in AB- and AA-stacked bilayer graphene in the presence of a strong magnetic field and disorder. In the AB-stacked case, we find that the thermoelectric conductivities display different asymptotic behaviors, depending on the ratio between the temperature and the width of the disorder-broadened Landau levels (LLs), similar to those of monolayer graphene. In the high temperature regime, the transverse thermoelectric conductivity α _xy saturates to a universal value 5.54k _B e/h at the center of each LL, and displays a linear temperature dependence at low temperatures. The calculated Nernst signal has a peak with a height of the order of k _B /e, and the thermopower changes sign at the central LL. We attribute this unique behavior to the coexistence of particle and hole LLs. In the AA-stacked bilayer case, it is found that the thermoelectric transport properties are consistent with the behavior of a band insulator. The obtained results demonstrate the sensitivity of the thermoelectric conductivity to the band gap near the Dirac point.     

Acoustic analogue of graphene: observation of Dirac cones in acoustic surface waves

We demonstrate the presence of Dirac cones in the dispersion relation of acoustic waves propagating on the surface of a plate of methyl methacrylate containing a honeycomb lattice of cylindrical boreholes. This structure represents the acoustic analogue of graphene, the cylindrical cavities playing the role of carbon atoms while acoustic surface waves are the equivalent of electronic waves in graphene. Analytical expressions for the Dirac frequency and Dirac velocity in acoustics are given as a function of the radius and depth of boreholes. These parameters have been experimentally determined for a constructed structure and the data are in fairly good agreement with the predicted values.     

Anisotropic Dirac cones in monoatomic hexagonal lattices: a DFT study

In the last few years, the fascinating properties of graphene have been thoroughly investigated. The existence of Dirac cones is the most important characteristic of the electronic band-structure of graphene. In this theoretical paper, hexagonal monolayers of silicon (h-Si) and germanium (h-Ge) are examined using density functional theory, within the generalized gradient approximation. Our numerical results indicate that both h-Si and h-Ge are chemically stable. The lattice parameters, electronic dispersion relations and densities of states for these systems are reported. The electronic dispersion relations display Dirac cones with the symmetry of an equilateral triangle (the group D₃) in the vicinity of the K-points. Hence, the Fermi velocity depends on the wave vector direction around K-points. Fermi velocities for holes and electrons are significantly different. The maximum and minimum Fermi velocities are also reported.     

Magneto-electronic properties of rhombohedral trilayer graphene: Peierls tight-binding model

Magneto-electronic properties of rhombohedral (ABC-stacked) trilayer graphene are investigated by the tight-binding (TB) model with all important interlayer interactions taken into account. A numerical strategy, band-like matrix, is applied to solve the huge Hamiltonian matrix and thus the eigenvalues and eigenvectors of Landau levels (LLs) are well defined. Based on the characteristics of the wave functions, the LLs are divided into three groups. These LLs are strongly affected by the stacking configuration and interlayer interactions. The LL spectra do reflect the main features of the zero-field subbands, i.e., the existence of three LL groups, specified onset energies of the three groups, and asymmetric electronic structure. In an ABC-stacked structure, the LL wave functions are each composed of six magnetic TB Bloch functions for six sublattices. Each magnetic TB Bloch function exhibits the spatial symmetry, localization feature, and oscillation modes. Three sets of effective quantum numbers are defined to index the LLs of the three groups based on the oscillation modes in specific sublattices. These effective quantum numbers are useful for defining the optical selection rules of the optical absorption spectra.     

Optimizing long-range order, band gap, and group velocities for graphene on close-packed metal surfaces

We compare different growth methods with the aim of optimizing the long-range order of a graphene layer grown on Ru(0001). Combining chemical vapor deposition with carbon loading and segregation of the surface layer leads to autocorrelation lengths of 240 ?. We present several routes to band gap and charge carrier mobility engineering for the example of graphene on Ir(111). Ir cluster superlattices self-assembled onto the graphene moiré pattern produce a strong renormalization of the electron group velocity close to the Dirac point, leading to highly anisotropic Dirac cones and the enlargement of the gap from 140 to 340 meV. This gap can further be enhanced to 740 meV by Na co-adsorption onto the Ir cluster superlattice at room temperature. This value is close to that of Ge, and the high group velocity of the charge carriers is fully preserved. We also present data for Na adsorbed without the Ir clusters. In both cases we find that the Na is on top of the graphene layer.     

High Chern number phase in topological insulator multilayer structures: A Dirac cone model study

We employ 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, 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 $\varGamma$ point will get increased. Moreover, another two TI multilayer structures as well as the TI superlattice structures are studied.     

Electric field manipulation of multiple nonequivalent Dirac cones in the electronic structures of hexagonal CrB_4 sheet

Two-dimensional materials with Dirac cones have significant applications in photoelectric technology. The origin and manipulation of multiple Dirac cones need to be better understood. By first-principle calculations, we study the influence of external fields on the electronic structure of the hexagonal CrB_4 sheet with double nonequivalent Dirac cones. Our results show that the two cones are not sensitive to tensile strain and out-of-plane electric field, but present obviously different behaviors under the in-plane external electric field(along the B-B direction), i.e., one cone holds while the other vanishes with a gap opening. More interestingly, a new nonequivalent cone emerges under a proper in-plane electric field. We also discuss the origin of the cones in CrB_4 sheet. Our study provides a new method on how to obtain Dirac cones by the external field manipulation, which may motivate potential applications in nanoelectronics.     

Fano Factor in Strained Graphene Nanoribbon Nanodevices

We investigate the Fano factor in a strained armchair and zigzag graphene nanoribbon nanodevice under the effect of ac fheld in a wide range of frequencies at different temperatures(10 K-70 K). This nanodevice is modeled as follows: a graphene nanoribbon is connected to two metallic leads. These two metallic leads operate as a source and a drain. The conducting substance is the gate electrode in this three-terminal nanodevice. Another metallic gate is used to govern the electrostatics and the switching of the graphene nanoribbon channel. The substances at the graphene nanoribbon/metal contact are controlled by the back gate. The photon-assisted tunneling probability is deduced by solving the Dirac eigenvalue differential equation in which the Fano factor is expressed in terms of this tunneling probability. The results show that for the investigated nanodevice, the Fano factor decreases as the frequency of the induced ac fheld increases, while it increases as the temperature increases.In general, the Fano factors for both strained armchair and zigzag graphene nanoribbons are different. This is due to the effect of the uniaxial strain. It is shown that the band structure parameters of graphene nanoribbons at the energy gap, the C-C bond length, the hopping integral, the Fermi energy and the width are modulated by uniaxial strain. This research gives us a promise of the present nanodevice being used for digital nanoelectronics and sensors.