Many-body Self-energy Research Articles

Dynamical mean-field theory for spin-dependent electron transport in spin-valve devices

We present a combination of density functional theory and dynamical mean-field theory (DMFT) for computing the electron transmission through two-terminal nanoscale devices. The method is then applied to metallic junctions presenting alternating Cu and Co layers, which exhibit spin-dependent charge transport and the giant magnetoresistance (GMR) effect. The calculations show that the coherent transmission through the $3d$ states is greatly suppressed by electron correlations. This is mainly due to the finite lifetime induced by the electron-electron interaction and is directly related to the imaginary part of the computed many-body DMFT self-energy. At the Fermi energy, where in accordance with the Fermi-liquid behavior the imaginary part of the self-energy vanishes, the suppression of the transmission is entirely due to the shifts of the energy spectrum induced by electron correlations. Based on our results, we finally suggest that the GMR measured in Cu/Co heterostructures for electrons with energies about 1 eV above the Fermi energy is a manifestation of dynamical correlation effects.

Numerically Precise Benchmark of Many-Body Self-Energies on Spherical Atoms.

We investigate the performance of beyond-GW approaches in many-body perturbation theory by addressing atoms described within the spherical approximation via a dedicated numerical treatment based on B-splines and spherical harmonics. We consider the GW, second Born (2B), and GW + second order screened exchange (GW+SOSEX) self-energies and use them to obtain ionization potentials from the quasi-particle equation (QPE) solved perturbatively on top of independent-particle calculations. We also solve the linearized Sham–Schlüter equation (LSSE) and compare the resulting xc potentials against exact data. We find that the LSSE provides consistent starting points for the QPE but does not present any practical advantage in the present context. Still, the features of the xc potentials obtained with it shed light on possible strategies for the inclusion of beyond-GW diagrams in the many-body self-energy. Our findings show that solving the QPE with the GW+SOSEX self-energy on top of a PBE or PBE0 solution is a viable scheme to go beyond GW in finite systems, even in the atomic limit. However, GW shows a comparable performance if one agrees to use a hybrid starting point. We also obtain promising results with the 2B self-energy on top of Hartree–Fock, suggesting that the full time-dependent Hartree–Fock vertex may be another viable beyond-GW scheme for finite systems.

Combining Eliashberg Theory with Density Functional Theory for the Accurate Prediction of Superconducting Transition Temperatures and Gap Functions.

We propose a practical alternative to Eliashberg equations for the abinitio calculation of superconducting transition temperatures and gap functions. Within the recent density functional theory for superconductors, we develop an exchange-correlation functional that retains the accuracy of Migdal's approximation to the many-body electron-phonon self-energy, while having a simple analytic form. Our functional is based on a parametrization of the Eliashberg self-energy for a superconductor with a single Einstein frequency, and enables density functional calculations of experimental excitation gaps. By merging electronic structure methods and Eliashberg theory, the present approach sets a new standard in quality and computational feasibility for the prediction of superconducting properties.

CHEERS: a tool for correlated hole-electron evolution from real-time simulations

We put forward a practical nonequilibrium Green’s function (NEGF) scheme to perform real-time evolutions of many-body interacting systems driven out of equilibrium by external fields. CHEERS is a computational tool to solve the NEGF equation of motion in the so called generalized Kadanoff–Baym ansatz and it can be used for model systems as well as first-principles Hamiltonians. Dynamical correlation (or memory) effects are added to the Hartree–Fock dynamics through a many-body self-energy. Applications to time-dependent quantum transport, time-resolved photoabsorption and other ultrafast phenomena are discussed.

Diagrammatic expansion for positive spectral functions beyondGW: Application to vertex corrections in the electron gas

We present a diagrammatic approach to construct self-energy approximations within many-body perturbation theory with positive spectral properties. The method cures the problem of negative spectral functions which arises from a straightforward inclusion of vertex diagrams beyond the GW approximation. Our approach consists of a two-steps procedure: we first express the approximate many-body self-energy as a product of half-diagrams and then identify the minimal number of half-diagrams to add in order to form a perfect square. The resulting self-energy is an unconventional sum of self-energy diagrams in which the internal lines of half a diagram are time-ordered Green's functions whereas those of the other half are anti-time-ordered Green's functions, and the lines joining the two halves are either lesser or greater Green's functions. The theory is developed using noninteracting Green's functions and subsequently extended to self-consistent Green's functions. Issues related to the conserving properties of diagrammatic approximations with positive spectral functions are also addressed. As a major application of the formalism we derive the minimal set of additional diagrams to make positive the spectral function of the GW approximation with lowest-order vertex corrections and screened interactions. The method is then applied to vertex corrections in the three-dimensional homogeneous electron gas by using a combination of analytical frequency integrations and numerical Monte-Carlo momentum integrations to evaluate the diagrams.

Bridging density-functional and many-body perturbation theory: Orbital-density dependence in electronic-structure functionals

Energy functionals which depend explicitly on orbital densities, rather than on the total charge density, appear when applying self-interaction corrections to density-functional theory; this is, e.g., the case for Perdew-Zunger and Koopmans-compliant functionals. In these formulations the total energy is not invariant under unitary rotations of the orbitals, and local, orbital-dependent potentials emerge. We argue that this is not a shortcoming, and that instead these potentials can provide, in a functional form, a simplified quasiparticle approximation to the spectral potential, i.e., the local, frequency-dependent contraction of the many-body self-energy that is sufficient to describe exactly the spectral function. As such, orbital-density-dependent functionals have the flexibility to accurately describe both total energies and quasiparticle excitations in the electronic-structure problem. In addition, and at variance with the Kohn-Sham case, orbital-dependent potentials do not require nonanalytic derivative discontinuities. We present numerical solutions based on the frequency-dependent Sham-Schl\"uter equation to support this view, and examine some of the existing functionals in this perspective, highlighting the very close agreement between exact and approximate orbital-dependent potentials.

Screening and nonlocal correlations in the extended Hubbard model from self-consistent combinedGWand dynamical mean field theory

We describe a recent implementation of the combined $GW$ and dynamical mean field method ($GW$+DMFT) for the two-dimensional Hubbard model with onsite and nearest-neighbor repulsion. We clarify the relation of the $GW$+DMFT scheme to alternative approaches in the literature, and discuss the corresponding approximations to the free-energy functional of the model. Furthermore, we describe a numerically exact technique for the solution of the $GW$+DMFT equations, namely, the hybridization expansion continuous-time algorithm for impurity models with retarded interactions. We compute the low-temperature phase diagram of the half-filled extended Hubbard model, addressing the metal-insulator transition at small intersite interactions and the transition to a charge-ordered state for stronger intersite repulsions. $GW$+DMFT introduces a nontrivial momentum dependence into the many-body self-energy and polarization. We find that the charge fluctuations included in the present approach have a larger impact on the latter than on the former. Finally, within the $GW$+DMFT framework, as in extended DMFT, the intersite repulsion translates into a frequency dependence of the local effective interaction. We analyze this dependence and show how it affects the local spectral function.

Spintronic properties of one-dimensional electron gas in graphene armchair ribbons

We have investigated, using effective mass approach (EMA), magnetic properties of a one-dimensional electron gas in graphene armchair ribbons when the electrons occupy only the lowest conduction subband. We find that magnetic properties of the one-dimensional electron gas may depend sensitively on the width of the ribbon. For ribbon widths Lx=3Ma0, a critical point separates ferromagnetic and paramagnetic states while for Lx=(3M+1)a0 paramagnetic state is stable (M is an integer and a0 is the length of the unit cell). These width-dependent properties are a consequence of eigenstates that have a subtle width-dependent mixture of K and K′ states, and can be understood by examining the wavefunction overlap that appears in the expression for the many-body exchange self-energy. Ferromagnetic and paramagnetic states may be used for spintronic purposes.

Ab initiomany-body effects in TiSe2: A possible excitonic insulator scenario from GW band-shape renormalization

We present both theoretical ab-initio results within the Hedin's GW approximation and experimental angle-resolved photoemission and scanning tunneling spectroscopy measurements on TiSe${}_{2}$. With respect to the density-functional Kohn-Sham metallic picture, the many-body GW self-energy leads to a $\ensuremath{\approx}$0.2-eV band-gap insulator consistent with our STS spectra at 5 K. The highest valence and the lowest conduction bands are strongly renormalized, with a loss of ${k}^{2}$ parabolic dispersion toward a ${k}^{4}$ shape. In particular, GW moves the top of valence moved toward a circle of points away from $\ensuremath{\Gamma}$, arising in a Mexican hat shape commonly associated with an excitonic insulator. Our calculations are in good agreement with experiment.

Correlation effects in bistability at the nanoscale: Steady state and beyond

The possibility of finding multistability in the density and current of an interacting nanoscale junction coupled to semi-infinite leads is studied at various levels of approximation. The system is driven out of equilibrium by an external bias and the nonequilibrium properties are determined by real-time propagation using both time-dependent density functional theory (TDDFT) and many-body perturbation theory (MBPT). In TDDFT the exchange-correlation effects are described within a recently proposed adiabatic local density approximation (ALDA). In MBPT the electron-electron interaction is incorporated in a many-body self-energy which is then approximated at the Hartree-Fock (HF), second-Born, and $GW$ level. Assuming the existence of a steady state and solving directly the steady-state equations we find multiple solutions in the HF approximation and within the ALDA. In these cases we investigate whether and how these solutions can be reached through time evolution and how to reversibly switch between them. We further show that for the same cases the inclusion of dynamical correlation effects suppresses bistability.

Materials specific electronic correlation effects and spectral weight ‘hot spots’ in intermetallic actinides

ABSTRACTMany metallic actinide systems host partially filled 5f electrons in the low-energy spectrum. Consequently, they exhibit diverse quantum mechanical phenomena such as magnetism, superconductivity, a mysterious hidden-order phase, or heavy-fermion behavior. Here we present results of a unified theoretical method based on the self-consistent GW formalism for the electronic many-body self-energy. We calculate the dynamic electronic correlation spectra starting from materials specific first-principles electronic band-structure. In particular, we present results for four isostructural intermetallic actinides PuCoIn5, PuCoGa5, PuRhGa5, and UCoGa5. A common underlying property of these materials is a strong spin–orbit coupling split band structure that enables substantial spin fluctuations. In a feedback effect on the electronic structure they create electronic ‘hot spots’, where the single-particle spectral weight is maximum, resulting in a universal peak-dip-hump feature. These results are in good agreement with experiments, suggesting that actinides are adequately described by the intermediate Coulomb interaction regime, where both itinerant (peak) and localized (hump) features coexist.

Electronic properties of zircon and hafnon from many-body perturbation theory

The electronic properties of zircon and hafnon, two wide-gap high-$\ensuremath{\kappa}$ materials, are investigated using many-body perturbation theory (MBPT) combined with the Wannier interpolation technique. For both materials, the calculated band structures differ from those obtained within density-functional theory and MBPT by (i) a slight displacement of the highest valence-band maximum from the $\ensuremath{\Gamma}$ point and (ii) an opening of the indirect band gap to 7.6 and 8.0 eV for zircon and hafnon, respectively. The introduction of vertex corrections in the many-body self-energy does not modify the results except for a global rigid shift of the many-body corrections.

Reflectance-anisotropy spectroscopy and surface differential reflectance spectra at the Si(100) surface: Combined experimental and theoretical study

We present reflectance-anisotropy spectroscopy (RAS) and surface differential reflectivity (SDR) experiments carried out on well-characterized single-domain nominal silicon (100) surface at room temperature. The results are compared with first-principles calculations which include many-body effects, namely, self-energy and excitonic effects. These strongly modify the line shape of the optical spectra. For a set of the five measurements, the RAS of clean, monohydride, and dyhidride surfaces, and the corresponding SDRs, good agreement between theory and experiment is obtained only when, in the calculation, the electron-hole interaction is accounted for.

Nucleon-nucleus optical potential in the particle-hole approach

Feshbach's projection formalism in the particle-hole model space leads to a microscopic description of scattering in terms of the many-body self-energy. To investigate the feasibility of this approach, an optical potential for O-16 is constructed starting from two previous calculations of the self-energy for this nucleus. The results reproduce the background phase shifts for positive parity waves and the resonances beyond the mean field. The latter can be computed microscopically for energies of astrophysical interest using Green's function theory.

Study of the 16O(p, γ) Reaction at Astrophysical Energies

The Feshbach theory of the optical potential naturally leads to a microscopic description of scattering in terms of the many-body self-energy. We consider a recent calculation of this quantity for 16 O and study the possibility of applying it at astrophysical energies. The results obtained for the phase shifts and the 16 O(p, γ ) capture suggest that such studies are feasible but the calculations require some improvement geared to this specific task.

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.

Relativistic Photoemission Theory for General Nonlocal Potentials

An improved formulation of the one-step model of photoemission from crystal surfaces is proposed which overcomes different limitations of the original theory. Considering the results of an electronic-structure calculation, the electronic (one-particle) potential and the (many-body) self-energy, as given quantities, we derive explicit expressions for the dipole transition-matrix elements. The theory is formulated within a spin-polarized, relativistic framework for general nonspherical and space-filling one-particle potentials and general nonlocal, complex and energy-dependent self-energies. It applies to semi-infinite lattices with perfect lateral translational invariance and arbitrary number of atoms per unit cell.

Power law scenario for hole excitations in Bi-2212

We present a continued fraction analysis of the many-body self-energy for holes in a cuprate above T c. The ansatz terminates in a phenomenological low energy power law. As shown by quantitative fits to ARPES lines in optimally doped Bi-2212, this is a possible answer to the question posed by P.W. Anderson: “How to have your Fermi surface without a Fermi liquid?” A connection of this scenario with the 1D Luttinger liquid is not evident.

QUANTUM DOTS OF LIGHT

Basic ingredients of a microscopic theory describing the degenerate four-wave mixing of the outgoing field from a mesoscopic source particle were established. Starting from many-body theory and selfenergy quantum electrodynamics it is argued that the best spatial confinement one might hope to obtain of the source field is given by the extension of the transverse part of the current density distribution induced in the mesoscopic particle. Taking into account the phaseconjugation of evanescent components of the source field, the existence of so-called quantum dots of light having a subwavelength extension is predicted. Using the outgoing field from the tip of an optical near-field microscope in combination with a phaseconjugating mirror exhibiting a sufficiently long memory time light dots can be made experimentally. A new nonlocal nonlinear response tensor enabling one to study the four-wave mixing process of the local field itself is presented.

Equation of state of 3He submonolayers in 4He films: Multiple-spectra Green's functions.

Utilizing a model effective interaction for [sup 3]He atoms in a [sup 4]He film that consists of two-body potentials, phonon exchange, and ripplon exchange, we calculate the [sup 3]He equation of state. The energy and pressure are determined in the Hartree-Fock approximation allowing for [sup 3]He population of multiple discrete transverse states. In this work we use a two-state approximation and self-consistently solve the matrix Dyson equation for the 2[times]2 self-energy matrix. We find that the many-body self-energy decreases the gap between the lowest and first excited transverse state from the noninteracting model but that no clear evidence exists for a self-bound state.