Shot noise in ballistic graphene

We have investigated shot noise in graphene field effect devices in the temperature range of 4.2-30 K at low frequency (f=600-850 MHz). We find that for our graphene samples with a large width over length ratio W/L, the Fano factor F reaches a maximum F ~ 1/3 at the Dirac point and that it decreases strongly with increasing charge density. For smaller W/L, the Fano factor at Dirac point is significantly lower. Our results are in good agreement with the theory describing that transport at the Dirac point in clean graphene arises from evanescent electronic states.     

Electronic transport for armchair graphene nanoribbons with a potential barrier

We theoretically investigate the electronic transport properties through a rectangular potential barrier embedded in armchair-edge graphene nanoribbons (AGNRs) of various widths. Using the Landauer formula and Dirac equation with the continuity conditions for all segments of wave functions at the interfaces between regions inside and outside the barrier, we calculate analytically the conductance and Fano factor for the both metallic and semiconducting AGNRs, respectively. It is shown that, by some numerical examples, at Dirac point the both types of AGNRs own a minimum conductance associated with the maximum Fano factor. The results are discussed and compared with the previous relevant works.     

Shot noise in magnetic field modulated graphene superlattice

We investigate the shot noise properties in a monolayer graphene superlattice modulated by N parallel ferromagnets deposited on a dielectric layer. It is found that for the antiparallel magnetization configuration or when magnetic field is zero the new Dirac-like point appears in graphene superlattice. The transport is almost forbidden at this new Dirac-like point, and the Fano factor reaches its maximum value 1/3. In the parallel magnetization configuration as the number of magnetic barriers increases, the shot noise increases. In this case, the transmission can be blocked by the magnetic–electric barrier and the Fano factor approaches 1, which is dramatically distinguishable from that in antiparallel alignment. The results may be helpful to control the electron transport in graphene-based electronic devices.     

Fano resonance in electronic transport induced by the magnetic confinement in a graphene nanoribbon

Based on the Floquet scattering theory, a model of graphene-based electronic device is presented, in which electrical transport is controlled by adjusting Dirac fermions energy near resonance conditions. The presence of an oscillating field leads to the Fano resonance in transport through a magnetic structure in an armchair graphene nanoribbon (AGNR). The Fano resonance originates from bound states of the magnetic confinement, according to subband indices in the AGNR. The ballistic conductance is markedly affected by the Fano resonance due to the quasi-one-dimensional nature of AGNRs. The results may help realizing graphene electronics with the resonant characteristics in the conductance.     

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.     

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.     

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.     

Shot noise in graphene

We report measurements of current noise in single-layer and multilayer graphene devices. In four single-layer devices, including a p-n junction, the Fano factor remains constant to within +/-10% upon varying carrier type and density, and averages between 0.35 and 0.38. The Fano factor in a multilayer device is found to decrease from a maximal value of 0.33 at the charge-neutrality point to 0.25 at high carrier density. These results are compared to theories for shot noise in ballistic and disordered graphene.     

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.     

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.     

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.     

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.     

Effects of strain on shot noise properties in graphene superlattices

In this paper the transmission and the shot noise properties through the strain-inducedgraphene superlattices are studied. It is found that for the zigzag direction strain theFano factor shows a peak at new Dirac-like point and the position of the new Dirac pointvaries against the strain. Also, Fano factor has an oscillatory behavior with respect tostrain strength and the oscillation period decreases by increasing the number of barriers.However, for the armchair direction strain the transmission can be blocked by the electricbarrier and the Fano factor approaches 1, this is different from the zigzag directionstrain.     

Manipulation of resonant tunneling by substrate-induced inhomogeneous energy band gaps in graphene with square superlattice potentials

We investigate the resonant transmission of Dirac electrons through inhomogeneous band gap graphene with square superlattice potentials by transfer matrix method. The effects of the incident angle of the electrons, Fermi energy and substrate-induced Dirac gaps on the transmission are considered. It is found that the Dirac gap of graphene adds another degree of freedom with respect to the incident angle, the Fermi energy and the parameters of periodic superlattice potentials (i.e., the number, width and height of the barriers) for the transmission. In particular, the inhomogeneous Dirac gap induced by staggered substrates can be used to manipulate the transmission. The properties of the conductance and Fano factor at the resonant peaks are found to be affected by the gaps significantly. The results may be helpful for the practical application of graphene-based electronic devices.     

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.     

Charge transport and shot noise on the surface of a topological insulator with a magnetic modulation

In this paper, we investigate the transport features and the Fano factor of Dirac electrons on the surface of a three-dimensional topological insulator with a magnetic modulation. We consider a hard wall bounding condition on the edge of the topological insulator, which implies that a surface state of the topological insulator is insulating. We find that a valley of conductivity at the Dirac point is associated with a Fano factor peak, and more interestingly, this topological metal changes from insulating to metallic by controlling the effective exchange field.     

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.     

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.     

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.     

Electronic shot noise in fractal conductors

By solving a master equation in the Sierpiński lattice and in a planar random-resistor network, we determine the scaling with size L of the shot noise power P due to elastic scattering in a fractal conductor. We find a power-law scaling P proportional, variantL;{d_{f}-2-alpha}, with an exponent depending on the fractal dimension d_{f} and the anomalous diffusion exponent alpha. This is the same scaling as the time-averaged current I[over ], which implies that the Fano factor F=P/2eI[over ] is scale-independent. We obtain a value of F=1/3 for anomalous diffusion that is the same as for normal diffusion, even if there is no smallest length scale below which the normal diffusion equation holds. The fact that F remains fixed at 1/3 as one crosses the percolation threshold in a random-resistor network may explain recent measurements of a doping-independent Fano factor in a graphene flake.