Statistical measures and the Klein tunneling in single-layer graphene

Statistical complexity and Fisher–Shannon information are calculated in a problem of quantum scattering, namely the Klein tunneling across a potential barrier in graphene. The treatment of electron wave functions as masless Dirac fermions allows us to compute these statistical measures. The comparison of these magnitudes with the transmission coefficient through the barrier is performed. We show that these statistical measures take their minimum values in the situations of total transparency through the barrier, a phenomenon highly anisotropic for the Klein tunneling in graphene.     

Scanning tunneling microscopy with spin-polarized electrons

We present a short outline of the first STM experiments with spin-polarized electrons performed in ultrahigh vacuum by using ferromagnetic CrO₂ tips and a Cr(001) single crystal surface. A clear distinction can be made between topographic STM line scans obtained with a non-magnetic tungsten tip and those obtained with a ferromagnetic CrO₂ tip, which are modified due to an additional contribution from spin-dependent vacuum tunneling. STM therefore has the potential to measure the local electron spin polarization of the free surface as well as the spatial distribution of spins on the atomic scale.     

Resonant tunneling of electrons interacting with phonons

The effect of the electron-phonon interaction on resonant tunneling of electrons through a two-barrier nanostructure is investigated in the framework of a consistent quantum-mechanical model. The wave function is determined by solving the Schrödinger equation with correct boundary conditions in the semiclassical approximation in the electron-phonon interaction. The current calculated with the help of the wave function is averaged over the phonon subsystem with the help of the Bloch theorem. The analytic expressions derived for static and varying currents in a resonance tunnel diode taking into account the electron-phonon interaction formally coincide with the Mössbauer effect probability. In the adiabatic limit and for a strong electron-phonon interaction, the static current decreases in proportion to η, while the varying low-frequency current is proportional to η². The shape of the resonance curve becomes Gaussian with a width of τ _ph ^?1 . The fundamental result is that the properties inherent in coherent tunneling are preserved even in the limit η?1 (which is often regarded as incoherent). The most striking effect (analogous to the Mössbauer effect) is the conservation of a narrow Lorentzian resonance curve in the limit η?1, ω_ph?Γ. This means that even for η?1, the resonance current is due to coherent electrons (experiencing interference), but their fraction decreases in view of the electron-phonon interaction. It is concluded that the application of the rate equations and other approximate methods disregarding interference may lead to incorrect results. The expressions for the high-frequency and nonlinear responses are also derived. The quantum-mechanical regime is found to be less sensitive to the effect of phonons than the classical regime.     

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.     

The tunneling density-of-states of interacting massless Dirac fermions

We calculate the tunneling density-of-states (DOS) of a disorder-free two-dimensional interacting electron system with a massless-Dirac band Hamiltonian. The DOS exhibits two main features: (i) linear growth at large energies with a slope that is suppressed by quasiparticle velocity enhancement, and (ii) a rich structure of plasmaron peaks which appear at negative bias voltages in an n-doped sample and at positive bias voltages in a p-doped sample. We predict that the DOS at the Dirac point is non-zero even in the absence of disorder because of electron–electron interactions, and that it is then accurately proportional to the Fermi energy. The finite background DOS observed at the Dirac point of graphene sheets and topological insulator surfaces can therefore be an interaction effect rather than a disorder effect.     

Anomalous photon-assisted tunneling in graphene

We investigated the transmission of Dirac electrons through a potential barrier in the presence of circularly polarized light. An anomalous photon-assisted enhanced transmission is predicted and explained. It is demonstrated that the perfect transmission for nearly head-on collision in infinite graphene is suppressed in gapped dressed states of electrons, which is further accompanied by a shift of peaks as a function of the incident angle away from head-on collision. In addition, the perfect transmission is partially suppressed by a photon-induced gap in illuminated graphene. After the effect of rough edges of the potential barrier or impurity scattering is included, the perfect transmission with no potential barrier becomes completely suppressed and the energy range for the photon-assisted transmission is reduced at the same time.     

Plasma oscillations of massless Dirac electrons in a planar superlattice

The spectrum of plasma oscillations in a lateral superlattice of massless Dirac electrons has been calculated in the weak coupling approximation. The intensity of absorption of electromagnetic waves by plasmons of the superlattice at frequencies near the edges of band gaps has been found.     

Energy-exchange processes by tunneling electrons

Resistive heating, emission heating or cooling (e.g., the Nottingham effect), and thermal fluctuation radiation are examples of energy exchange processes which are fundamental in electron field emission and in tunneling junctions of scanning tunneling microscopy. These exchange processes are analyzed for both electronic tunneling processes. We first discuss the energy delivered by a monoatomic tip in the field emission process. Strong phonon excitation is expected for field emission currents exceeding 1 nA. Secondly we present a theoretical calculation of the thermal deposition associated with the Nottingham effect in a tunneling junction. The calculation is based on the free electron model for the electrode materials and the tunneling process across a planar vacuum gap. Our results show that the thermal power is deposited not only at the electron receiving electrode but also at the emitting electrode. This originates from a finite probability for electrons below the Fermi level to tunnel through the tunneling barrier replaced by electrons starting from the Fermi level. The comparison between the calculations and the recent STM measurements is given. Finally we discuss the other energy exchange processes in the tunneling junction, and conclude that the thermal coupling between the tip and the sample of STM is extremely small under UHV conditions. This is important for high temperature STM.     

Collisionless intraband absorption in a system of one-dimensional massless Dirac electrons

It has been shown that the Landau-damping-induced absorption of a modulated high-frequency electric field in a two-dimensional system of particles with a linear spectrum is absent up to the momentum of the field equal to the Fermi momentum of particles. This property qualitatively distinguishes such a system from the system of particles with a parabolic dispersion law, where the mentioned damping exists at any modulation period of an incident wave.     

Electron tunneling in single layer graphene with an energy gap

When a single layer graphene is epitaxially grown on silicon carbide,it will exhibit a finite energy gap like a conventional semiconductor,and its energy dispersion is no longer linear in momentum in the low energy regime.In this paper,we have investigated the tunneling characteristics through a two-dimensional barrier in a single layer graphene with an energy gap.It is found that when the electron is at a zero angle of incidence,the transmission probability as a function of incidence energy has a gap.Away from the gap the transmission coefficient oscillates with incidence energy which is analogous to that of a conventional semiconductor.The conductance under zero temperature has a gap.The properties of electron transmission may be useful for developing graphene-based nano-electronics.     

Light-modulated electron retroreflection and Klein tunneling in a graphene-based n-p-n junction

We investigate the electron retroreflection and the Klein tunneling across a graphene-based n-p-n junction irradiated by linearly polarized off-resonant light with the polarization along the x direction. The linearly polarized off-resonant light modifies the band structure of graphene, which leads to the anisotropy of band structure. By adjusting the linearly polarized light and the direction of n-p-n junction simultaneously, the electron retroreflection appears and the anomalous Klein tunneling, the perfect transmission at a nonzero incident angle regardless of the width and height of potential barrier, happens, which arises from the fact that the light-induced anisotropic band structure changes the relation of wavevector and velocity of electron. Our finding provides an alternative and flexible method to modulate electron retroreflection and Klein tunneling.     

Thermodynamics of electrons in the graphene bilayer

Some problems of the thermodynamics of electrons in a doped graphene bilayer are considered. Analytical expressions are derived for chemical potential and specific heat in the limiting cases of low and high temperatures. The Seebeck and Thomson coefficients are estimated. Landau levels are studied using a semi-classical approach. An expression for thermodynamic potential is obtained and the de Haas-van Alphen oscillations are studied. The oscillations of magnetic entropy and electron temperature in a magnetic field, i.e., the oscillating magnetocaloric effect, are investigated. For all parameters, the cases of graphene bilayer and monolayer are compared.     

Interaction of tunneling electrons with collective modes of the electrodes

The alteration of the tunneling current due to bulk electron-phonon coupling in one of the electrodes is calculated using the tunneling-Hamiltonian method. Lineshapes are presented for deformation-potential coupling to optical phonons in p-type silicon. The predicted lineshape of d²I/dV² in a metal-oxide-semiconductor junction shows deviations from the one-electron background which are symmetrical about zero bias in contrast to antisymmetrical structure predicted due to inelastic phonon creation by the tunneling electron.     

Practical aspects of counting electrons with a single-electron tunneling pump

This review covers various aspects of the single-electron tunneling pumps based on Al junctions studied at NIST over the past 15 years. The operation of a pump is described, and some important error mechanisms are summarized, which allows for a sketch of the basic pump parameters required for metrological accuracy. Fabrication of pumps, filtering of leads in the cryostat, and the electronics used to drive the pump are described next. The shuttle error technique that allows measurement of very rare errors is then described, and some outstanding questions about limitations of pumps based on Al junctions are mentioned. A detailed algorithm for cancelling the cross capacitance in a pump is described in an appendix. Official contribution of the National Institute of Standards and Technology; not subject to copyright in the United States.     

Resonance Raman scattering in graphene: Probing phonons and electrons

In this work, by using different laser excitation energies, we obtain important electronic and vibrational properties of mono- and bi-layer graphene. For monolayer graphene, we determine the phonon dispersion near the Dirac point for the in-plane transverse optical (iTO) mode. This result is compared with recent calculations that take into account electron–electron correlations for the phonon dispersion around the K point. For bilayer graphene we extract the Slonczewski–Weiss–McClure band parameters and compare them with recent infrared measurements. We also analyze the second-order feature in the Raman spectrum for trilayer graphene.     

Weak antilocalization in epitaxial graphene: evidence for chiral electrons

Transport in ultrathin graphite grown on silicon carbide is dominated by the electron-doped epitaxial layer at the interface. Weak antilocalization in 2D samples manifests itself as a broad cusplike depression in the longitudinal resistance for magnetic fields 10 mT相似文献