Self-energy Approach Research Articles

Spin-polarized tunneling current through a ferromagnetic insulator between two metallic or superconducting leads

Using the Keldysh formalism (Zh. Eksp. Teor. Fiz. 47, 1515 (1964) [Sov. Phys. JETP 20, 1018 (1965)]), the tunneling current through a hybrid structure where a confined magnetic insulator (I) is sandwiched between two nonmagnetic leads is calculated. The leads can be either normal metals (M) or superconductors (S). Each region is modeled as a single band in tight-binding approximation in order to understand the formation of the tunneling current as clearly as possible. The tunneling process itself is simulated by a hybridization between the lead and insulator conduction bands. The insulator is assumed to have localized moments which can interact with the tunneling electrons. This is described by the Kondo lattice model and treated within an interpolating self-energy approach. For the superconductor, the mean-field BCS theory is used. The spin polarization of the current shows a strong dependence both on the applied voltage and on the properties of the materials. Even for this idealized three band model, there is a qualitative agreement with experiment.

Influence of scattering processes on electron quantum states in nanowires

In the framework of quantum perturbation theory the self-consistent method of calculation of electron scattering rates in nanowires with the one-dimensional electron gas in the quantum limit is worked out. The developed method allows both the collisional broadening and the quantum correlations between scattering events to be taken into account. It is an alternativeper seto the Fock approximation for the self-energy approach based on Green’s function formalism. However this approach is free of mathematical difficulties typical to the Fock approximation. Moreover, the developed method is simpler than the Fock approximation from the computational point of view. Using the approximation of stable one-particle quantum states it is proved that the electron scattering processes determine the dependence of electron energy versus its wave vector.

Phase separation in the particle-hole asymmetric Hubbard model

The paramagnetic phase diagram of the Hubbard model with nearest-neighbor (NN) and next-nearest-neighbor (NNN) hopping on the Bethe lattice is computed at half-filling and in the weakly doped regime using the self-energy functional approach for dynamical mean-field theory. NNN hopping breaks the particle-hole symmetry and leads to a strong asymmetry of the electron-doped and hole-doped regimes. Phase separation occurs at and near half-filling, and the critical temperature of the Mott transition is strongly suppressed.

Negative Differential Resistance in Transport through Organic Molecules on Silicon

Recent scanning tunneling microscopy studies of individual organic molecules on Si(001) reported negative differential resistance (NDR) above a critical applied field, observations explained by a resonant tunneling model proposed prior to the experiments. Here we use both density functional theory and a many-electron GW self-energy approach to quantitatively assess the viability of this mechanism in hybrid junctions with organic molecules on Si. For cyclopentene on p-type Si(001), the frontier energy levels are calculated to be independent of applied electric fields, ruling out the proposed mechanism for NDR. Guidelines for achieving NDR are developed and illustrated with two related molecules, aminocyclopentene and pyrroline.

Carrier-induced ferromagnetism in diluted local-moment systems

The electronic and magnetic properties of concentrated and diluted ferromagnetic semiconductors are investigated by using the Kondo lattice model, which describes an interband exchange coupling between itinerant conduction electrons and localized magnetic moments. In our calculations, the electronic problem and the local magnetic problem are solved separately. For the electronic part an interpolating self-energy approach together with a coherent potential approximation (CPA) treatment of a dynamical alloy analogy is used to calculate temperature-dependent quasiparticle densities of states and the electronic self-energy of the diluted local-moment system. For constructing the magnetic phase diagram we use a modified RKKY theory by mapping the interband exchange to an effective Heisenberg model. The exchange integrals appear as functionals of the diluted electronic self-energy being therefore temperature- and carrier-concentration-dependent and covering RKKY as well as double exchange behavior. The disorder of the localized moments in the effective Heisenberg model is solved by a generalized locator CPA approach. The main results are: 1) extremely low carrier concentrations are sufficient to induce ferromagnetism; 2) the Curie temperature exhibits a strikingly non-monotonic behavior as a function of carrier concentration with a distinct maximum; 3) $T_C$ curves break down at critical $n/x$ due to antiferromagnetic correlations and 4) the dilution always lowers $T_C$ but broadens the ferromagnetic region with respect to carrier concentration.

Thermodynamic properties of the two-orbital Hubbard model

We investigate an infinite-dimensional two-orbital Hubbard model with different bandwidths by means of the self-energy functional approach. By calculating the quasi-particle weight and the entropy at finite temperatures, we discuss how thermal fluctuations affect the stability of an intermediate phase, called the orbital-selective Mott phase, which has localized as well as itinerant bands.

Local Self-Energy Approach for Electronic Structure Calculations

Using a novel self-consistent implementation of Hedin's perturbation theory, we calculate space- and energy-dependent self-energy for a number of materials. We find it to be local in real space and rapidly convergent on second- to third-nearest neighbors. Corrections beyond are evaluated and shown to be completely localized within a single unit cell. This can be viewed as a fully self-consistent implementation of the dynamical mean field theory for electronic structure calculations of real solids using a perturbative impurity solver.

Finite-temperature Mott transitions in the multiorbital Hubbard model

We investigate the Mott transitions in the multi-orbital Hubbard model at half-filling by means of the self-energy functional approach. The phase diagrams are obtained at finite temperatures for the Hubbard model with up to four-fold degenerate bands. We discuss how the first-order Mott transition points $U_{c1}$ and $U_{c2}$ as well as the critical temperature $T_c$ depend on the orbital degeneracy. It is elucidated that enhanced orbital fluctuations play a key role to control the Mott transitions in the multi-orbital Hubbard model.

Phase Diagram of Orbital-Selective Mott Transitions at Finite Temperatures

Mott transitions in the two-orbital Hubbard model with different bandwidths are investigated at finite temperatures. By means of the self-energy functional approach, we discuss the stability of the intermediate phase that has one orbital localized and the other itinerant; this phase is caused by the orbital-selective Mott transition (OSMT). It is shown that the OSMT realizes two different coexistence regions at finite temperatures in accordance with the recent results of Liebsch. We further find that a particularly interesting behavior emerges around the special conditions U = U ' and J =0, which includes a new type of coexistence region that has three distinct states. By systematically changing the Hund coupling, we establish the global phase diagram to elucidate the key role played by the Hund coupling on the Mott transitions.

Mott Transitions in Two-Orbital Hubbard Systems

We investigate the Mott transitions in two-orbital Hubbard systems. Applying the dynamical mean field theory and the self-energy functional approach, we discuss the stability of itinerant quasi-particle states in each band. It is shown that separate Mott transitions occur at different Coulomb interaction strengths in general. On the other hand, if some special conditions are satisfied for the interactions, spin and orbital fluctuations are equally enhanced at low temperatures, resulting in a single Mott transition. The phase diagrams are obtained at zero and finite temperatures. We also address the effect of the hybridization between two orbitals, which induces the Kondo-like heavy fermion states in the intermediate orbital-selective Mott phase.

Surface state quasiparticle dynamics at metal surfaces

Theoretical investigations on the dynamics of noble metal surface state quasiparticles are presented in this article. Decay processes of electrons and holes are mainly determined by the electron–electron (e–e) and electron–phonon (e–ph) interaction. The latter predominates at energies close to the Fermi level. The e–e interaction is treated within a many-body GW self-energy approach. The phonon-induced decay rate is studied by taking into account, in principle, all electron and phonon states, including surface states, and a linearly screened pseudopotential. These formalisms have been applied to the case of Au(111) surface state holes. The total linewidth has been calculated as a function of binding energy. Our results indicate that, for electron–electron interactions, the main decay channel for surface state holes is the decay into the surface band itself (intraband transitions). Interband transitions predominate in the case of electron–phonon interaction.

Self-energy approach to the correlated Kondo lattice model

We develop an interpolating self-energy approach to the correlated Kondo-lattice model. The correlation of the band electrons is taken into account by a Hubbard interaction. The method is based on a self-energy ansatz, the structure of which allows to fulfill a maximum number of exactly solvable limiting cases. The parameters of the ansatz are fitted to spectral moments via high-energy expansion of the self-energy. The band electron correlations are taken into account by an effective medium approach being correct in the strong coupling (U) regime. The theory is considered reliable for all temperatures, band occupations, and exchange couplings. Results are presented for the respective dependencies of spectral densities, quasiparticle densities of states, and characteristic correlation functions, and interpreted in terms of elementary spin exchange processes between itinerant conduction electrons and localized magnetic moments. The appearance of magnetic polarons, the typical quasiparticle of Kondo-lattices, in the energy spectrum is worked out. Spin exchange processes prevent a total spin polarization of the band electrons even for arbitrarily strong exchange couplings as long as the local moments are represented by quantum mechanical spins.

Ferromagnetism in the Kondo-lattice model

We propose a modified Rudermann, Kittel, Kasuya, Yosida (RKKY) technique to evaluate the magnetic properties of the ferromagnetic Kondo-lattice model. Together with a previously developed self-energy approach to the conduction-electron part of the model, we obtain a closed system of equations which can be solved self-consistently. The results allow us to study the conditions for ferromagnetism with respect to the band occupation n, the interband exchange coupling J, and the temperature T. Ferromagnetism appears for relatively low electron (hole) densities, while it is excluded around half-filling $(n=1).$ For small J the conventional RKKY theory $(\ensuremath{\sim}{J}^{2})$ is reproduced, but with strong deviations for very moderate exchange couplings. For not-too-small n a critical ${J}_{c}$ is needed to produce ferromagnetism with a finite Curie temperature ${T}_{C},$ which increases with J, then running into a kind of saturation, in order to fall off again and disappear above an upper critical exchange J. Spin waves show a uniform softening with rising temperature, and a nonuniform behavior as functions of n and J. The disappearance of ferromagnetism when varying T, J, and n is uniquely connected to the stiffness constant D becoming negative.

Vibrational characterization and electronic properties of long range-ordered, ideally hydrogen-terminated Si(111)

The use of a well defined, long range ordered surface is of fundamental interest for the determination of surface-specific intrinsic physical parameters. Ideally hydrogen terminated Si(111) surfaces are prepared by wet chemical treatment in basic HF solutions. The mechanism of formation is based on preferential etching of defects, leading to an ideal hydrogen terminaison of the (111) plane, without any reconstruction and with a high degree of perfection. Infrared spectroscopy is used to probe the quality of the surfaces by quantifying the extent of the perfect domains. High resolution photoemission spectroscopy of such highly homogeneous surfaces shows exceptional narrow features in both the valence band and the core level regions. The valence band levels and their dispersion are well described by first-principles calculations using a quasi particle self-energy approach within the Heidin's GW approximation. Two surfaces core level states are evidenced, arising from the silicon surface atoms and the backbonds. A crystal field effect splits the surface Si 2 p 3 2 component. Their position and relative intensity find a satisfactory agreement with recent calculations using first principles perturbation theory.

Cherenkov radiation: Electron self-energy approach

A short review is given of a previous paper on Cherenkov radiation (CR) by Fulop and Biro (1992), together with some aspects of the collective dipole oscillations of atomic microclusters (atomic analog of the nuclear giant resonance). Finally, the CR energy loss of a relativistic charged particle in matter is obtained by evaluating the self-energy of the particle in the medium.

Surface-plasmon dispersion and size dependence of Mie resonance: Silver versus simple metals.

The recently observed blueshift of the surface plasmon of Ag with increasing parallel momentum and of the Mie resonance of small Ag particles with decreasing radius are discussed in terms of a model for the dynamical response of a two-component s-d electron system. In the case of flat Ag surfaces, the 5s conduction electrons are treated as a semi-infinite homogeneous electron gas while the influence of the fully occupied 4d bands is described via a polarizable medium which extends up to a certain distance from the surface. Using the time-dependent density-functional approach it is shown that the absence of the s-d screening interaction in the surface region leads to a positive dispersion of the surface plasmon in agreement with the data. A self-energy approach is introduced which allows us to establish a qualitative relation between the scattering processes at a flat metal surface and those at the surface of a spherical particle. Using this approach it is argued that the blueshift of the Mie resonance of Ag particles can also be understood in terms of a reduced s-d interaction in the region where the s electrons spill out into the vacuum. Finally, it is shown that the polarizability of simple metal particles exhibits above the Mie resonance a collective excitation which is the analogue of the dipolar surface plasmon observed on the flat surfaces of various simple metals. This feature seems to have been observed in recent absorption spectra on large K clusters.

A self-energy approach to the energy loss in STEM

From a self-energy approach, a general expression for the energy loss probability in scanning transmission electron microscopy is derived. As an application, the coupling between a small particle and the supporting surface is studied.

Self-energy approach to the t-J model.

An approach to the problem of single-occupancy constraint in the t-J model is presented. In order to project out the states of double occupied sites, the electronic self-energy is introduced in an effective Hamiltonian. The self-energy is derived by applying the self-consistent moment method to the Hubbard model with infinite on-site Coulomb repulsion.

Electronic structure and its dependence on local order for H/Si(111)-(1 x 1) surfaces.

The valence and core level spectra of chemically prepared, ideally H-terminated Si(111) surfaces are characterized by remarkably sharp features. The valence band levels and their dispersion are well described by first-principles calculations using a quasiparticle self-energy approach within the GW approximation. From the ${\mathrm{Si}}_{2\mathit{p}}$ spectra, an upper limit of 35\ifmmode\pm\else\textpm\fi{}10 meV is derived from the core hole lifetime broadening, a value substantially lower than previously measured.

First-principles investigation of visible light emission from silicon-based materials.

The atomic and electronic structure of various Si-based layered structures is calculated using pseudopotential density-functional theory and a self-energy approach. A silicon-hydrogen compound, consisting of a stacking in the [111] direction of double layers of Si terminated with H, is found to have an almost direct band gap of 2.75 eV. Substituting OH groups for H atoms leads to the compound siloxene, which is found to have a direct band gap of ∼1.7 eV. Investigations of the band-edge states and calculations of matrix elements show that these direct transitions are very strong