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-induced pseudo-magnetic fields and charging effects on CVD-grown graphene

Atomically resolved imaging and spectroscopic characteristics of graphene grown by chemical vapor deposition (CVD) on copper are investigated by means of scanning tunneling microscopy and spectroscopy (STM/STS). For CVD-grown graphene remaining on the copper substrate, the monolayer carbon structures exhibit ripples and appear strongly strained, with different regions exhibiting different lattice structures and electronic density of states (DOS). In particular, ridges appear along the boundaries of different lattice structures, which exhibit excess charging effects. Additionally, the large and non-uniform strain induces pseudo-magnetic field up to ~ 50 T, as manifested by the DOS peaks at quantized energies that correspond to pseudo-magnetic field-induced integer and fractional Landau levels. In contrast, for graphene transferred from copper to SiO₂ substrates after the CVD growth, the average strain on the whole diminishes, so do the corresponding charging effects and pseudo-magnetic fields except for sample areas near topological defects. These findings suggest feasible nano-scale “strain engineering” of the electronic states of graphene by proper design of the substrates and growth conditions.     

Dynamics of Dirac quasi-particles in lattice vibration and anomalous phonon frequency shift of graphene

By exact solution of time-dependent Schrödinger equation of electron in graphene under interaction with E_2g phonons, we investigate the dynamical behavior of Dirac quasi-particle in the process of lattice vibration. Due to the global geometric phases acquired by electron during lattice vibration, an anomalous shift of the vibration frequency is obtained. We calculate the Fermi energy dependence of frequency shift which is in consistence with experiment in case of small doping density.     

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.     

Magnetic-like field inducing negative Dirac mass in graphene on hexagonal boron nitride

The tight-binding electrons in graphene grown on top of hexagonal boron nitride (h-BN) substrate are studied. The two types of surfaces on the h-BN substrate give rise to Dirac fermions having positive and negative masses. The positive and negative masses of the Dirac fermions lead to the gapped graphene to behave as a “pseudo” ferromagnet. A very large (pseudo) tunneling magnetoresistance is predicted when the Fermi level approaches the gap region. The energy gap due to the breaking of sublattice symmetry in graphene on h-BN substrate is analogous to magnetic-induced energy gap on surface of topological insulators. We point out that positive and negative masses may correspond to signs of magnetic-like field perpendicular to graphene sheet acting on pseudo magnetic dipole moment of electrons, leading to pseudo-Larmor precession and Stern–Gerlach magnetic force.     

Strain induced topological transitions in twisted double bilayer graphene

We theoretically study the band structures and the valley Chern numbers of the AB–AB and AB–BA stacked twisted double bilayer graphene under heterostrain effect. In the absence of heterostrain, due to the constrains by the spatial symmetries, the central two flat bands of the AB–AB are topological trivial bands, while in the AB–BA they have a finite Chern number. The heterostrain breaks all the point group symmetries and the constrains are lifted, hence the topological properties of the two arrangements can be tuned by different strain magnitudes ϵ and directions ϕ. The heterostrain has dissimilar impacts on the Chern numbers of the AB–AB and AB–BA, owing to their different band gaps, and these gaps can be modified by a vertical electric field. Our results show that the topological transitions for both arrangements occur in the ϵ range of 0.1%–0.4%, which can be realized in the graphene-based sample.     

Weak localization of Dirac fermions in graphene

In the presence of the charged impurities, we study the weak localization effect by evaluating the quantum interference correction to the conductivity of Dirac fermions in graphene. With the inelastic scattering rate due to electron-electron interactions obtained from our previous work, we investigate the dependence of the quantum interference correction on the carrier concentration, the temperature, the magnetic field, and the size of the sample. It is found that weak localization is present in large size samples at finite carrier doping. Its strength becomes weakened or quenched when the sample size is less than a few microns at low temperatures as studied in the experiments. In the region close to zero doping, the system may become delocalized. The minimum conductivity at low temperature for experimental sample sizes is found to be close to the data.     

Manipulation of Dirac points in graphene-like crystals

We review different scenarios for the motion and merging of Dirac points in 2D crystals. These different types of merging can be classified according to a winding number (a topological Berry phase) attached to each Dirac point. For each scenario, we calculate the Landau level spectrum and show that it can be quantitatively described by a semiclassical quantization rule for the constant energy areas. This quantization depends on how many Dirac points are enclosed by these areas. We also emphasize that different scenarios are characterized by different numbers of topologically protected zero energy Landau levels.     

电场诱导氧化石墨烯的极化动力学特性研究

本文通过外加电场改变氧化石墨烯团簇分子的共振能量,利用激光激发氧化石墨烯产生的共振荧光特性测量氧化石墨烯在电场作用下的极化动力学特性. 发现存在外加电场使得荧光共振峰的半高全宽趋于饱和的时间特性,而不同的氧化石墨烯团簇分子的荧光共振峰的暂态特性同时反映了电场对氧化石墨烯产生定向极化和变形极化的动力学特性. 关键词： 氧化石墨烯 团簇分子 电场 极化动力学     

Theory of superconductivity for Dirac electrons in graphene

Phonon-exchange-induced superconducting pairing of effectively ultrarelativistic electrons in graphene is investigated. The Eliashberg equation obtained for describing pairing in the Cooper channel with allowance for delayed interaction are matrix equations with indices corresponding to the valence and conduction bands. The equations are solved in the high doping limit, in which pairing is effectively a single-band process, and in the vicinity of a critical quantum point of underdoped graphene for a value of the coupling constant for which pairing is an essentially multiband process. For such cases, analytic estimates are obtained for the superconducting transition temperature of the system. It is shown that the inclusion of dynamic effects makes it possible to determine the superconducting transition temperature, as well as the critical coupling constant for underdoped graphene, more accurately than in the static approximation of the BCS type. Estimates of the constants of electron interaction with the scalar optical phonon mode in graphene indicate that an appreciable superconducting transition temperature can be attained under a high chemical doping level of graphene.     

Magnetic confinement of massless Dirac fermions in graphene

Because of Klein tunneling, electrostatic potentials are unable to confine Dirac electrons. We show that it is possible to confine massless Dirac fermions in a monolayer graphene sheet by inhomogeneous magnetic fields. This allows one to design mesoscopic structures in graphene by magnetic barriers, e.g., quantum dots or quantum point contacts.     

BCS Superconductivity of Dirac electrons in graphene layers

Possible superconductivity of electrons with the Dirac spectrum is analyzed using the BCS model. We calculate the critical temperature, the superconducting energy gap, and the supercurrent as functions of the doping level and of the pairing interaction strength. Zero doping is characterized by the existence of a quantum critical point such that the critical temperature vanishes below some finite value of the interaction strength. However, the critical temperature remains finite for any nonzero electron or hole doping level when the Fermi energy is shifted away from the Dirac point. As distinct from usual superconductors, the supercurrent density is not proportional to the number of electrons but is strongly decreased due to the presence of the Dirac point.     

Qualitative analysis of trapped Dirac fermions in graphene

We study the confinement of Dirac fermions in graphene and in carbon nanotubes by an external magnetic field, mechanical deformations or inhomogeneities in the substrate. By applying variational principles to the square of the Dirac operator, we obtain sufficient and necessary conditions for confinement of the quasi-particles. The rigorous theoretical results are illustrated on the realistic examples of the three classes of traps.     

Strain engineering in graphene

Graphene is a two dimensional metallic membrane. Deformations of the membrane, i.e. strains, and topological defects of the crystalline lattice, couple to the electrons in the same way as external gauge fields. The origin of these fields, and their effects on the electronic properties of graphene, are reviewed.     

直流电场下水中石墨烯定向行为研究

纳米颗粒在液体环境中的定向控制与系统物理性能的调控及新型纳米器件的制备等应用领域密切相关.本文使用分子动力学模拟方法,研究了水中单片不带电矩形石墨烯在直流电场下的定向行为.结果发现石墨烯平面趋向平行于电场方向且随着电场强度增大定向性增强,其主要原因在于极性水分子在电场下的响应以及水合作用;减小石墨烯长宽比,石墨烯法向矢量和长边矢量的定向性减弱,定量结果表明法向和长边定向度分别与绕长边和法向的转动扩散系数存在负相关关系.     

Control of the Dirac point in graphene by UV light

It is experimentally shown that the initially shifted Dirac point in grapheme-on-dielectric devices can be brought to zero by illuminating the samples with UV light. This is much easier to accomplish compared to the common procedure of annealing at high temperature. Internal photoemission is concluded to be responsible for the observed effect.     

Dissipative quantum hall effect in graphene near the Dirac point

We report on the unusual nature of the nu=0 state in the integer quantum Hall effect (QHE) in graphene and show that electron transport in this regime is dominated by counterpropagating edge states. Such states, intrinsic to massless Dirac quasiparticles, manifest themselves in a large longitudinal resistivity rho(xx) > or approximately h/e(2), in striking contrast to rho(xx) behavior in the standard QHE. The nu=0 state in graphene is also predicted to exhibit pronounced fluctuations in rho(xy) and rho(xx) and a smeared zero Hall plateau in sigma(xy), in agreement with experiment. The existence of gapless edge states puts stringent constraints on possible theoretical models of the nu=0 state.     

Carrier relaxation in epitaxial graphene photoexcited near the Dirac point

We study the carrier dynamics in epitaxially grown graphene in the range of photon energies from 10 to 250 meV. The experiments complemented by microscopic modeling reveal that the carrier relaxation is significantly slowed down as the photon energy is tuned to values below the optical-phonon frequency; however, owing to the presence of hot carriers, optical-phonon emission is still the predominant relaxation process. For photon energies about twice the value of the Fermi energy, a transition from pump-induced transmission to pump-induced absorption occurs due to the interplay of interband and intraband processes.