Phonon-mediated electron pairing in graphene

The possibility of superconducting pairing of electrons in doped graphene due to in-plane and out-of-plane phonons is studied. Quadratic coupling of electrons with out-of-plane phonons is considered in details, taking into account both deformation potential and bond-stretch contributions. The order parameter of electron-electron pairing can have different structures due to four-component spinor character of electrons wave function. We consider s-wave pairing, diagonal on conduction and valence bands, but having arbitrary structure with respect to valley degree of freedom. The sign and magnitude of contribution of each phonon mode to effective electron-electron interaction turns out to depend on both the symmetry of phonon mode and the structure of the order parameter. Unconventional orbital-spin symmetry of the order parameter is found.     

The effect of multiple electron-electron scattering on the energy distribution of electrons in a correlated pair

A unit event of electron-electron scattering in LiF layers is studied by correlation spectroscopy of scattered electrons. The energy distribution of electrons in a correlated pair when a 15-to 55-eV free electron is scattered by a valence electron of LiF is studied. It is shown that single electron-electron scattering prevails and the distribution is uniform when the energy of the primary electron is below 25 eV. As the energy of the primary electron increases, the formation of correlated pairs of electrons with equal energies becomes the most probable. With the energy of the primary electron above 40 eV, the pairs with substantially different electron energies dominate. Such evolution of the energy distribution of the electrons in the pair stems from the fact that first one and then the other electron of the pair successively takes part in electron-electron scattering. A phenomenological model for the single scattering and double scattering of primary electrons in LiF films is considered. Results obtained indicate that the strengths of single scattering and double scattering channels become comparable at electron energies above 25 eV.     

Dynamical electron transport through a nanoelectromechanical wire in a magnetic field

We investigate dynamical transport properties of interacting electrons moving in a vibrating nanoelectromechanical wire in a magnetic field. We have built an exactly solvable model in which the electron-electron interaction is considered nonperturbatively and the electric current and mechanical vibration are treated fully quantum mechanically on an equal footing. We demonstrate our theory by calculating the admittance of a finite-size wire, which is influenced by the magnetic field strength, the electron-electron interaction, and the complex interplay between the mechanical and the electrical energy scales. Nontrivial features including sharp resonance peaks appear in the admittance, which may be experimentally observable.     

Persistent currents in one dimension: the counterpart of Leggett's theorem

We discuss the sign of the persistent current of N electrons in one dimensional rings. Using a topology argument, we establish lower bounds for the free energy in the presence of arbitrary electron-electron interactions and external potentials. Those bounds are the counterparts of upper bounds derived by Leggett. Rings with odd (even) numbers of polarized electrons are always diamagnetic (paramagnetic). We show that unpolarized electrons with N being a multiple of four exhibit either paramagnetic behavior or a superconductorlike current-phase relation.     

Hydrodynamic effects in interacting Fermi electron jets

We theoretically study hydrodynamic phenomena originating from electron-electron collisions in a two-dimensional Fermi system. We demonstrate that an electron beam sweeping past an aperture creates a pumping effect, attracting carriers from this aperture. This pumping effect originates from the specific electric potential distribution induced by the injected electrons. In the regions near the main stream of injected electrons, a positive potential is induced by the injected electrons. Thus, the normally repulsive Coulomb interaction leads to an attractive force in the Fermi system. This quantum pumping mechanism in a Fermi system differs qualitatively from the Bernoulli pumping effect in classical liquids. We also discuss possible experimental realizations.     

Effect of frequency dependent electron-electron interaction on resonant tunneling

In electron resonant tunneling through a double barrier structure, we show that dynamical electron-electron interactions in the resonant well can give rise to additional tunneling satellites due to collective electronic excitations. We present a first principle treatment for frequency-dependent electron-electron interactions in the resonant tunneling problem. The result confirms the previously proposed plasmon assisted resonant tunneling mechanism. We also find that the particle-hole excitation has very little effect on resonant tunneling. Our result can be applied to study the effects of various electronic excitations on the resonant tunneling of electrons.     

Momentum space distribution of electrons in an atom using hydrogenic wave functions

A formulation is developed to derive exact analytic expressions for electron-electron correlation and density of electrons in momentum space using hydrogenic wave functions. It is shown that for large atoms the expression for density of electrons has a simple form.     

Mechanisms of photo double ionization of helium by 530 eV photons

We have measured fully differential cross sections for photo double ionization of helium 450 eV above the threshold. We have found an extremely asymmetric energy sharing between the photoelectrons and an angular asymmetry parameter beta approximately 2 and beta approximately 0 for the fast and slow electrons, respectively. The electron angular distributions show a dominance of the shakeoff for 2 eV electrons and clear evidence of an inelastic electron-electron scattering at an electron energy of 30 eV. The data are in excellent agreement with convergent close-coupling calculations.     

Electronic structure and excitations on clean and nanostructured metal surfaces

We present a brief overview of recent studies and new theoretical results for electron-phonon interaction in the $\overline{Y}$ surface states on FCC(110) noble metal surfaces as well as in surface and quantum-well states of thin films. We discuss the oscillations of electron-phonon coupling parameter λ and the respective contribution to the lifetime broadening of these states. We analyse the effect of spin-orbit splitting of surface states on an electron-electron contribution to lifetimes of excited electrons (holes). Oscillations of the electron-electron contribution and quadratic dependence of the linewidth on energy is discussed for ultrathin Pb(111) films.     

Resonant two-photon single ionization of two identical atoms

Resonant two-photon single ionization in a system consisting of two spatially well-separated identical atoms is studied. Because of two-center electron-electron correlations, the ionization may also proceed through photoexcitation of both atoms with subsequent interatomic Coulombic decay. We show that this channel may qualitatively change the dependence of the photoionization on the field intensity as well as the spectra of emitted electrons.     

Die Energieverteilung von 1 MeV-Elektronen bei Elektron-Elektron-Streuung

The energy distribution of 1 MeV electrons scattered at 30° by Al, Cu and Ag is measured in the region of electron-electron scattering. The broadening of the distribution by the internal motion of the atomic electrons and by multiple scattering is investigated, especially in comparison with the energy loss by bremsstrahlung.     

Horizontal rolls in convective flow above a partially heated surface

Considering the nonlinearity arising from the interaction between electrons and lattice vibrations, an effective electronic model with a self-interaction cubic term is employed to study the interplay between electron-electron and electron-phonon interactions. Based on numerical solutions of the time-dependent nonlinear Schroedinger equation for an initially localized two-electron singlet state, we show that the magnitude of the electron-phonon coupling χ necessary to promote the self-trapping of the electronic wave packet decreases as a function of the electron-electron interaction U. We show that such dependence is directly linked to the narrowing of the band of bounded two-electron states as U increases. We obtain the transition line in the χ × U parameter space separating the phases of self-trapped and delocalized electronic wave packets. The present results indicates that nonlinear contributions plays a relevant role in the electronic wave packet dynamics, particularly in the regime of strongly correlated electrons.     

Self-trapping of interacting electrons in crystalline nonlinear chains

Considering the nonlinearity arising from the interaction between electrons and latticevibrations, an effective electronic model with a self-interaction cubic term is employedto study the interplay between electron-electron and electron-phonon interactions. Basedon numerical solutions of the time-dependent nonlinear Schroedinger equation for aninitially localized two-electron singlet state, we show that the magnitude of theelectron-phonon coupling χ necessary to promote the self-trapping of theelectronic wave packet decreases as a function of the electron-electron interactionU. We show that such dependence is directly linked to the narrowing ofthe band of bounded two-electron states as U increases. We obtain thetransition line in the χ × U parameter space separatingthe phases of self-trapped and delocalized electronic wave packets. The present resultsindicates that nonlinear contributions plays a relevant role in the electronic wave packetdynamics, particularly in the regime of strongly correlated electrons.     

Theory of the one-dimensional Peierls-Hubbard-model

We consider the properties of a one-dimensional Hamiltonian for electrons and phonons including the Fröhlich electron-phonon interaction as well as the Hubbard term for electron-electron interaction. The unperturbed band structure is of tight-binding form and half-filled.We derive the gap equation and the ground-state energy of the system in mean field approximation.We find antiferromagnetic ordering and lattice distortion and calculate the displacive and magnetic phase limits.D82 (Diss. TH Aachen)     

Eine quantitative Deutung der Elektronengruppen im elektronenstrahlerzeugten He-Niederdruckplasma mit Hilfe der Boltzmannschen Stoßgleichung

Neglecting electron-electron collisions the velocity distribution of plasma electrons in a beam generated He-low pressure plasma is evaluated with help of Boltzmann equation. The energy distribution of secondary electrons generated by the electron beam is considered applying the atom collision theory ofGryzinski. The resulting velocity distribution of plasma electrons shows group character. The “temperatures” of the ultimate and secondary electrons and their density ratio are in satisfying agreement with experiment.     

Numerical finite size scaling approach to many-body localization

We develop a numerical technique to study Anderson localization in interacting electronic systems. The ground state of the disordered system is calculated with quantum Monte Carlo simulations while the localization properties are extracted from the "Thouless conductance" g, i.e., the curvature of the energy with respect to an Aharonov-Bohm flux. We apply our method to polarized electrons in a two-dimensional system of size L. We recover the well-known universal beta(g)=dlogg/dlogL one parameter scaling function without interaction. Upon switching on the interaction, we find that beta(g) is unchanged while the system flows toward the insulating limit. We conclude that polarized electrons in two dimensions stay in an insulating state in the presence of weak to moderate electron-electron correlations.     

Nonequilibrium Luttinger liquid: zero-bias anomaly and dephasing

A one-dimensional system of interacting electrons out of equilibrium is studied in the framework of the Luttinger liquid model. We analyze several setups and develop a theory of tunneling into such systems. A remarkable property of the problem is the absence of relaxation in energy distribution functions of left and right movers yet the presence of the finite dephasing rate due to electron-electron scattering, which smears zero-bias-anomaly singularities in the tunneling density of states.     

Role of interactions in the far-infrared spectrum of a lateral quantum-dot molecule

We study the effects of electron-electron correlations and confinement potential on the far-infrared spectrum of a lateral two-electron quantum-dot molecule by exact diagonalization. The calculated spectra directly reflect the lowered symmetry of the external confinement potential. Surprisingly, we find interactions to drive the spectrum towards that of a high-symmetry parabolic quantum-dot. We conclude that far-infrared spectroscopy is suitable for probing effective confinement of the electrons in a quantum-dot system, even if interaction effects cannot be resolved in a direct fashion.     

Resistivity of inhomogeneous quantum wires

We study the effect of electron-electron interactions on the transport in an inhomogeneous quantum wire. We show that contrary to the well-known Luttinger liquid result, nonuniform interactions contribute substantially to the resistance of the wire. In the regime of weakly interacting electrons and moderately low temperatures we find a linear in T resistivity induced by the interactions. We then use the bosonization technique to generalize this result to the case of arbitrarily strong interactions.