Electronic states on the surface of graphite

Graphite consists of graphene layers in an AB (Bernal) stacking arrangement. The introduction of defects can reduce the coupling between the top graphene layers and the bulk crystal producing new electronic states that reflect the degree of coupling. We employ low temperature high magnetic field scanning tunneling microscopy (STM) and spectroscopy (STS) to access these states and study their evolution with the degree of coupling. STS in magnetic field directly probes the dimensionality of electronic states. Thus two-dimensional states produce a discrete series of Landau levels while three-dimensional states form Landau bands providing a clear distinction between completely decoupled top layers and ones that are coupled to the substrate. We show that the completely decoupled layers are characterized by a single sequence of Landau levels with square-root dependence on field and level index indicative of massless Dirac fermions. In contrast weakly coupled bilayers produce special sequences reflecting the degree of coupling, and multilayers produce sequences reflecting the coexistence of massless and massive Dirac fermions. In addition we show that the graphite surface is soft and that an STM tip can be quite invasive when brought too close to the surface and that there is a characteristic tip-sample distance beyond which the effect of sample-tip interaction is negligible.     

Broken-symmetry states of Dirac fermions in graphene with a partially filled high Landau level

We report on numerical study of the Dirac fermions in partially filled N=3 Landau level (LL) in graphene. At half-filling, the equal-time density-density correlation function displays sharp peaks at nonzero wave vectors +/-q*. Finite-size scaling shows that the peak value grows with electron number and diverges in the thermodynamic limit, which suggests an instability toward a charge density wave. A symmetry broken stripe phase is formed at large system size limit, which is robust against perturbation from disorder scattering. Such a quantum phase is experimentally observable through transport measurements. Associated with the special wave functions of the Dirac LL, both stripe and bubble phases become possible candidates for the ground state of the Dirac fermions in graphene with lower filling factors in the N=3 LL.     

Landau level spectroscopy of ultrathin graphite layers

Far infrared transmission experiments are performed on ultrathin epitaxial graphite samples in a magnetic field. The observed cyclotron resonance-like and electron-positron-like transitions are in excellent agreement with the expectations of a single-particle model of Dirac fermions in graphene, with an effective velocity of c=1.03 x 10(6) m/s.     

Electric field effect tuning of electron-phonon coupling in graphene

Gate-modulated low-temperature Raman spectra reveal that the electric field effect (EFE), pervasive in contemporary electronics, has marked impacts on long-wavelength optical phonons of graphene. The EFE in this two-dimensional honeycomb lattice of carbon atoms creates large density modulations of carriers with linear dispersion (known as Dirac fermions). Our EFE Raman spectra display the interactions of lattice vibrations with these unusual carriers. The changes of phonon frequency and linewidth demonstrate optically the particle-hole symmetry about the charge-neutral Dirac point. The linear dependence of the phonon frequency on the EFE-modulated Fermi energy is explained as the electron-phonon coupling of massless Dirac fermions.     

Low energy excitations in graphite: The role of dimensionality and lattice defects

In this paper, we present a high resolution angle resolved photoemission spectroscopy (ARPES) study of the electronic properties of graphite. We found that the nature of the low energy excitations in graphite is particularly sensitive to interlayer coupling as well as lattice disorder. As a consequence of the interlayer coupling, we observed for the first time the splitting of the π bands by ≈0.7 eV near the Brillouin zone corner K. At low binding energy, we observed signatures of massless Dirac fermions with linear dispersion (as in the case of graphene), coexisting with quasiparticles characterized by parabolic dispersion and finite effective mass. We also report the first ARPES signatures of electron-phonon interaction in graphite: a kink in the dispersion and a sudden increase in the scattering rate. Moreover, the lattice disorder strongly affects the low energy excitations, giving rise to new localized states near the Fermi level. These results provide new insights on the unusual nature of the electronic and transport properties of graphite.     

Temperature relaxation and energy loss of hot carriers in graphene

The temperature relaxation and energy loss of hot Dirac fermions are investigated theoretically in graphene with carrier–optical phonon scattering. The time evolutions of temperature and energy loss for hot Dirac fermions in graphene are calculated self-consistently. It shows that the carrier–optical phonon coupling results in the energy relaxation of hot carriers excited by an electric field, and the relaxation time for temperature is about 0.5–1 ps and the corresponding energy loss is about 10–25 nW per carrier for typically doped graphene samples with a carrier density range of 1–5×10¹² cm^?2. Moreover, we analyze the dependence of temperature and energy relaxation on initial hot carrier temperature, lattice temperature and carrier density in detail.     

Tunneling of Dirac fermions through magnetic barriers in graphene

We have studied the tunneling of Dirac fermions through magnetic barriers in graphene. Magnetic barriers are produced via delta function-like inhomogeneous magnetic fields in which Dirac fermions in graphene experience the tunneling barrier in the real sense in contrast to Klein paradox caused by electrostatic barriers. The transmission through the magnetic barriers as functions of incident energy and angle of incoming fermions shows characteristic oscillations associated with tunneling resonances. We have also found the confined states in the magnetic barrier region which turn out to correspond to the total internal reflection in the usual optics.     

Reversal of Klein reflection by magnetic barriers in bilayer graphene

Massless Dirac fermions in monolayer graphene exhibit total transmission when normally incident on a scalar potential barrier, a consequence of the Klein paradox originally predicted by O Klein for relativistic electrons obeying the 3 + 1 dimensional Dirac equation. For bilayer graphene, charge carriers are massive Dirac fermions and, due to different chiralities, electron and hole states are not coupled to each other. Therefore, the wavefunction of an incident particle decays inside a barrier as for the non-relativistic Schr?dinger equation. This leads to exponentially small transmission upon normal incidence. We show that, in the presence of magnetic barriers, such massive Dirac fermions can have transmission even at normal incidence. The general consequences of this behavior for multilayer graphene consisting of massless and massive modes are mentioned. We also briefly discuss the effect of a bias voltage on such magnetotransport.     

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.     

New generation of massless Dirac fermions in graphene under external periodic potentials

We show that new massless Dirac fermions are generated when a slowly varying periodic potential is applied to graphene. These quasiparticles, generated near the supercell Brillouin zone boundaries with anisotropic group velocity, are different from the original massless Dirac fermions. The quasiparticle wave vector (measured from the new Dirac point), the generalized pseudospin vector, and the group velocity are not collinear. We further show that with an appropriate periodic potential of triangular symmetry, there exists an energy window over which the only available states are these quasiparticles, thus providing a good system to probe experimentally the new massless Dirac fermions. The required parameters of external potentials are within the realm of laboratory conditions.     

Two-dimensional quantum ring in a graphene layer in the presence of a Aharonov–Bohm flux

In this paper we study the relativistic quantum dynamics of a massless fermion confined in a quantum ring. We use a model of confining potential and introduce the interaction via Dirac oscillator coupling, which provides ring confinement for massless Dirac fermions. The energy levels and corresponding eigenfunctions for this model in graphene layer in the presence of Aharonov–Bohm flux in the centre of the ring and the expression for persistent current in this model are derived. We also investigate the model for quantum ring in graphene layer in the presence of a disclination and a magnetic flux. The energy spectrum and wave function are obtained exactly for this case. We see that the persistent current depends on parameters characterizing the topological defect.     

Angle-resolved photoemission spectroscopy studies of electron-electron interactions in graphene

Graphene is an emergent research topic that has attracted a huge amount of research interest ever since its experimental demonstration as a two-dimensional realization of Dirac fermions in 2005. In subsequent years, the research on graphene has rapidly expanded its field not only due to the new paradigm to study relativistic high energy physics in a condensed matter, but also due to its potential in the application for next generation devices. Most of the novel phenomena observed so far in graphene are attributed to its low-energy excitations, which is described by those of relativistic Dirac fermions. This article reviews recent progress in angle-resolved photoemission spectroscopy studies of electron-electron interactions in 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.     

Sub-Poissonian shot noise in graphene

We calculate the mode-dependent transmission probability of massless Dirac fermions through an ideal strip of graphene (length L, width W, no impurities or defects) to obtain the conductance and shot noise as a function of Fermi energy. We find that the minimum conductivity of order e2/h at the Dirac point (when the electron and hole excitations are degenerate) is associated with a maximum of the Fano factor (the ratio of noise power and mean current). For short and wide graphene strips the Fano factor at the Dirac point equals 1/3, 3 times smaller than for a Poisson process. This is the same value as for a disordered metal, which is remarkable since the classical dynamics of the Dirac fermions is ballistic.     

Scanning tunneling microscopy and spectroscopy of graphene layers on graphite

We report low temperature scanning tunneling microscopy and spectroscopy on graphene flakes supported on a graphite substrate. The experiments demonstrate that graphite is exceptionally well suited as a substrate for graphene because it offers support without disturbing the intrinsic properties of the charge carriers. The degree of coupling of a graphene flake to the substrate was recognized and characterized from the appearance of an anomalous Landau level sequence in the presence of a perpendicular magnetic field. By following the evolution of the Landau level spectra along the surface, we identified graphene flakes that are decoupled or very weakly coupled to the substrate. From the Landau level sequence in this flake, we extract the local Fermi velocity and energy of the Dirac point and find extremely weak spatial variation of these quantities confirming the high quality and non invasive nature of the graphite substrate.     

Band structures of symmetrical graphene superlattice with cells of three regions

We study the electronic band structures of massless Dirac fermions in symmetrical graphene superlattice with cells of three regions. opening gaps and additional Dirac points. Finally, we inspect the potential effect on minibands, the anisotropy of group velocity and the energy bands contours near Dirac points. We also discuss the evolution of gap edges and cutoff region near the vertical Dirac points.     

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.     

Single-layer behavior and its breakdown in twisted graphene layers

We report high magnetic field scanning tunneling microscopy and Landau level spectroscopy of twisted graphene layers grown by chemical vapor deposition. For twist angles exceeding ~3° the low energy carriers exhibit Landau level spectra characteristic of massless Dirac fermions. Above 20° the layers effectively decouple and the electronic properties are indistinguishable from those in single-layer graphene, while for smaller angles we observe a slowdown of the carrier velocity which is strongly angle dependent. At the smallest angles the spectra are dominated by twist-induced van Hove singularities and the Dirac fermions eventually become localized. An unexpected electron-hole asymmetry is observed which is substantially larger than the asymmetry in either single or untwisted bilayer graphene.     

Dynamical mean field study of the Dirac liquid

Renormalization is one of the basic notions of condensed matter physics. Based on the concept of renormalization, the Landau’s Fermi liquid theory has been able to explain, why despite the presence of Coulomb interactions, the free electron theory works so well for simple metals with extended Fermi surface (FS). The recent synthesis of graphene has provided the condensed matter physicists with a low energy laboratory of Dirac fermions where instead of a FS, one has two Fermi points. Many exciting phenomena in graphene can be successfully interpreted in terms of free Dirac electrons. In this paper, employing dynamical mean field theory (DMFT), we show that an interacting Dirac sea is essentially an effective free Dirac theory. This observation suggests the notion of Dirac liquid as a fixed point of interacting 2 + 1 dimensional Dirac fermions. We find one more fixed point at strong interactions describing a Mott insulating state, and address the nature of semi-metal to insulator (SMIT) transition in this system.     

Tunneling of Dirac fermions in graphene through a velocity barrier with modulated by magnetic fields

We study magnetic field modulated transport properties of Dirac fermions in graphene, where Dirac fermions penetrate through a velocity barrier. We find strong wave vector filtering and resonant effect. The angular-dependent region of resonant tunneling is suppressed by tuning velocity barriers. We can also found that the confined states in this velocity barrier can be changed by the magnetic field. Various novel devices, such as wavevector filter and magnetic switches, may be constructed based on our observed phenomena.