Part Of Self-energy Research Articles

Band-Edge Quasiparticles from Electron-Phonon Coupling and Resistivity Saturation.

We address the problem of resistivity saturation observed in materials such as the A-15 compounds. To do so, we calculate the resistivity for the Hubbard-Holstein model in infinite spatial dimensions to second order in on-site repulsion U≤D and to first order in (dimensionless) electron-phonon coupling strength λ≤0.5, where D is the half bandwidth. We identify a unique mechanism to obtain two parallel quantum conducting channels: low-energy and band-edge high-energy quasi-particles. We identify the source of the hitherto unremarked high-energy quasiparticles as a positive slope in the frequency dependence of the real part of the electron self-energy. In the presence of phonons, the self-energy grows linearly with the temperature at high T, causing the resistivity to saturate. As U is increased, the saturation temperature is pushed to higher values, offering a mechanism by which electron correlations destroy saturation.

States-conserving density of states for Altshuler-Aronov effect: Heuristic derivation

Altshuler and Aronov (AA) have shown that the electron-electron interaction in a weakly-disordered metal suppresses the single-particle density of states (DOS) in the vicinity of the Fermi level (EF). According to the AA theory the suppressed DOS exhibits the energy dependence ∝|E−EF| valid for |E − EF| smaller than a certain correlation energy Uco. Recent experiments have shown that at energies larger than Uco the DOS exhibits a states-conserving dependence on energy, namely, the states removed from near the Fermi level are found at energies above Uco in the energy range of about 3Uco. In this work the AA effect is studied beyond the low energy limit theoretically. We consider the AA model in which the electrons interact via the statically screened Coulomb interaction and the modification of the DOS is due to the exchange part of the electron self-energy. We derive the states-conserving DOS heuristically. Namely, we show that the self-energy consists of a diverging part (which we skip on physical grounds) and of the small part of the order of the pair Coulomb energy. This small part gives the states-conserving DOS which is in qualitative accord with experimental observations at energies above Uco and which reproduces the AA result at energies below Uco.

Erratum to: The β-function for Yukawa theory at large N f

There was an error in the computation of the n-loop part of the scalar self-energy in our paper [1].

Quantum Oscillation from In-Gap States and a Non-Hermitian Landau Level Problem.

Motivated by recent experiments on Kondo insulators, we theoretically study quantum oscillations from disorder-induced in-gap states in small-gap insulators. By solving a non-Hermitian Landau level problem that incorporates the imaginary part of electron's self-energy, we show that the oscillation period is determined by the Fermi surface area in the absence of the hybridization gap, and we derive an analytical formula for the oscillation amplitude as a function of the indirect band gap, scattering rates, and temperature. Over a wide parameter range, we find that the effective mass is controlled by scattering rates, while the Dingle factor is controlled by the indirect band gap. We also show the important effect of scattering rates in reshaping the quasiparticle dispersion in connection with angle-resolved photoemission measurements on heavy fermion materials.

The ultraviolet behavior of quantum gravity

A theory of quantum gravity has been recently proposed by means of a novel quantization prescription, which is able to turn the poles of the free propagators that are due to the higher derivatives into fakeons. The classical Lagrangian contains the cosmological term, the Hilbert term, sqrt{-g}{R}_{mu nu }{R}^{mu nu } and sqrt{-g}{R}^2 . In this paper, we compute the one-loop renormalization of the theory and the absorptive part of the graviton self energy. The results illustrate the mechanism that makes renormalizability compatible with unitarity. The fakeons disentangle the real part of the self energy from the imaginary part. The former obeys a renormalizable power counting, while the latter obeys the nonrenormalizable power counting of the low energy expansion and is consistent with unitarity in the limit of vanishing cosmological constant. The value of the absorptive part is related to the central charge c of the matter fields coupled to gravity.

On Higgs decays to hadrons and the R-ratio at N4LO

We present the first determination of Higgs-boson decay to hadrons at the next-to-next-to-next-to-next-to-leading order of perturbative QCD in the limit of a heavy top quark and massless light flavours. This result has been obtained by computing the absorptive parts of the relevant five-loop self-energy for a general gauge group and combining the outcome with the corresponding coefficient function already known to this order in QCD. Our new result reduces the uncertainty due to the truncation of the perturbation series to a fraction of the uncertainty due to the present error of the strong coupling constant. We have also performed the corresponding but technically simpler computations for direct Higgs decay to bottom quarks and for the electromagnetic R-ratio in e+e− → hadrons, thus verifying important fifth-order results obtained only by one group so far.

Accurate Determination of the Quasiparticle and Scaling Properties Surrounding the Quantum Critical Point of Disordered Three-Dimensional Dirac Semimetals.

Exploiting the enabling power of the Lanczos method in momentum space, we determine accurately the quasiparticle and scaling properties of disordered three-dimensional Dirac semimetals surrounding the quantum critical point separating the semimetal and diffusive metal regimes. We unveil that the imaginary part of the quasiparticle self-energy obeys a common power law before, at, and after the quantum phase transition, but the power law is nonuniversal, whose exponent is dependent on the disorder strength. More intriguingly, whereas a common power law is also found for the real part of the self-energy before and after the phase transition, a distinctly different behavior is identified at the critical point, characterized by the existence of a nonanalytic logarithmic singularity. This nonanalytical correction serves as the very basis for the unusual power-law behaviors of the quasiparticles and many other physical properties surrounding the quantum critical point. Our approach also allows the ready and reliable determination of the scaling properties of the correlation length and dynamical exponents. We further show that the central findings are valid for both uncorrelated and correlated disorder distributions and should be directly comparable with future experimental observations.

Reconstruction of bands in metallic hydrogen

The generalized theory of normal properties of a metal for the case of the properties of the electronic band of electron–phonon systems with a variable electron density of states is used to study the normal phase of metallic hydrogen at a pressure of 500 GPa and a temperature of 200 K. We calculated the frequency dependence of the real ReΣ(ω) and imaginary ImΣ(ω) parts of the self-energy part of the electron Green’s function Σ(ω), as well as the electron density of states N(e) of the stable phase of metallic hydrogen with the I41/amd symmetry at a pressure of 500 GPa, renormalized by the strong electron–phonon coupling. It is found that the electron conduction band of the I41/amd phase of metallic hydrogen undergoes insignificant reconstruction near the Fermi level because of the renormalization by the electron–phonon coupling.

GAUGE-INVARIANT RELATIVISTIC PERTURBATION THEORY APPROACH TO DETERMINATION OF ENERGY and SPECTRAL CHARACTERISTICS FOR HEAVY AND SUPERHEAVY ATOMS AND IONS: REVIEW

We reviewed an effective consistent ab initio approach to relativistic calculation of the spectra for multi-electron heavy and superheavy ions with an account of relativistic, correlation, nuclear, radiative effects is presented. The method is based on the relativistic gauge-invariant (approximation to QED) perturbation theory (PT) and generalized effective field nuclear model with using the optimized one-quasiparticle representation firstly in theory of the hyperfine structure for relativistic atom. The wave function zeroth basis is found from the Dirac equation with potential, which includes the core ab initio potential, the electric and polarization potentials of a nucleus. The correlation corrections of the high orders are taken into account within the Green functions method (with the use of the Feynman diagram’s technique). There have taken into account all correlation corrections of the second order and dominated classes of the higher orders diagrams (electrons screening, particle-hole interaction, mass operator iterations). The magnetic inter-electron interaction is accounted in the lowest on α parameter (α is the fine structure constant), approximation, the self-energy part of the Lamb shift is taken effectively into consideration within the Ivanov-Ivanova non-perturbative procedure, the Lamb shift polarization part - in the generalized Uehling-Serber approximation with accounting for the Källen-Sabry α2 (αZ) and Wichmann-Kroll α(αZ)n corrections.

Normal state of metallic hydrogen sulfide

Generalized theory of the normal properties of the metal in the case of the electron-phonon (EP) systems with not constant density of electronic states is used to examine the normal state of the SH3 and SH2 phase of the hydrogen sulfide at different pressures. The frequency dependence of the real and imaginary part of the self-energy part (SP) of the electron Green's function, the real and imaginary part of the complex renormalization of the electron mass, the real and imaginary part of the complex renormalization of the chemical potential, as well as the renormalized with the strong electron-phonon interaction the electron density of states are calculated. The calculations are performed for the stable orthorhombic IM-3M hydrogen sulfide SH3 structure at three pressures P = 170 GPa, P = 180 GPa, P = 225 GPa and SH2 structure with the symmetry I4/MMM (D4H-17) for the three values of pressure P = 150 GPa , P = 180 GPa, P = 225 GPa at the temperature of T = 200K. Key words: hydrogen sulfide, electron-phonon system, the pressure, the electronic properties.

THE HYPERFINE STRUCTURE AND OSCILLATOR STRENGTHS PARAMETERS FOR SOME HEAVY ELEMENTS ATOMS AND IONS: REVIEW OF DATA BY RELATIVISTIC MANY-BODY PERTURBATION THEORY CALCULATION

The energies and hyperfine structure constants for some heavy Li-like multicharged ions are calculated within the relativistic many-body perturbation theory formalism with a correct and effective taking into account the exchange-correlation, relativistic, nuclear and radiative corrections. The magnetic inter-electron interaction is accounted for in the lowest order on a2 (a is the fine structure constant) parameter. The Lamb shift polarization part is taken into account in the modified Uehling-Serber approximation, the Lamb shift self-energy part - within the generalized Ivanov-Ivanova procedure. The combined relativistic energy approach and many-body perturbation theory with the zeroth order optimized one-particle approximation are used for computing the Li-like ions (Z=11-42,69,70) and Cs energies and oscillator strengths, in particular, of radiative transitions from the ground state to the lowexcited and Rydberg states 2s1/2 – np1/2,3/2, np1/2,3/2-nd3/2,5/2 (n=2-12) in the Li-like ions. A comparison of the calculated oscillator strengths with available theoretical and experimental data is performed.

Quark self-energy in an ellipsoidally anisotropic quark-gluon plasma

We calculate the quark self-energy in a quark-gluon plasma that possesses an ellipsoidal momentum-space anisotropy in the local rest frame. By introducing additional transverse momentum anisotropy parameters into the parton distribution functions, we generalize previous results which were obtained for the case of a spheroidal anisotropy. Our results demonstrate that the presence of anisotropies in the transverse directions affects the real and imaginary parts of quark self-energy and, consequently, the self-energy depends on both the polar and azimuthal angles in the local rest frame of the matter. Our results for the quark self-energy set the stage for the calculation of the effects of ellipsoidal momentum-space anisotropy on quark-gluon plasma photon spectra and collective flow.

Reconstruction of the conduction band in metallic hydrogen sulfide

The theory of the normal properties of a metal generalized to the case of particular properties of an electron band with a finite width for electron–phonon systems with a varying electron density of states has been used to study the normal state of the SH3 phase of hydrogen sulfide at a pressure of 225 GPa and a temperature of 200 K. The frequency dependences of the real, ReΣ(ω), and imaginary, ImΣ(ω), parts of the selfenergy part of the Green’s function of the electron Σ(ω), as well as the electron density of states N(e) of the Im–3m stable orthorhombic structure of SH3 hydrogen sulfide at a pressure of P = 225 GPa, which is renormalized by the strong electron–phonon coupling, have been calculated. It has been established that a part of the electron conduction band of the SH3 phase of hydrogen sulfide adjacent to the Fermi level undergoes renormalization-induced reconstruction in the form of a number of energy pockets with the widths equal to fractions of the characteristic phonon energies of the system.

Characterizing featureless Mott insulating state by quasiparticle interference: A dynamical mean field theory view

The quasiparticle interferences (QPIs) of a Mott insulator are investigated using the $T$-matrix formalism implemented with the dynamical mean-field theory ($T$-DMFT). In Mott insulating state, because DMFT predicts a singularity in the real part of the electron self energy $\Re \Sigma(\omega) \sim \eta/\omega$ at low frequency, where $\eta$ can be considered as the 'order parameter' for Mott insulating state, QPIs are completely washed out at the small bias voltage. However, a further analysis shows that $\Re \Sigma(\omega)$ in fact serves as an energy-dependent chemical potential shift. As a result, the effective bias voltage seen by the system is $eV' = eV - \Re \Sigma(eV)$. Due to the singular behavior of $\Re \Sigma(\omega)$, a critical bias voltage $eV_c = \sqrt{\eta}$ satisfying $eV'=0$ exists if and only if in Mott insulating state. Consequently, the same QPI patterns produced by the non-interacting Fermi surfaces appears at this critical bias voltage $eV_c$ in Mott insulating state. We propose that this reentry of non-interacting QPI patterns at $eV_c$ could serve as an experimental signature of Mott insulating state, and the 'order parameter' can be experimentally measured as $\eta \sim (eV_c)^2$.

Electron elastic scattering offA@C60: The role of atomic polarization under confinement

The present paper explores possible features of electron elastic scattering off endohedral fullerenes $A$@C$_{60}$. It focuses on how dynamical polarization of the encapsulated atom $A$ by an incident electron might alter scattering off $A$@C$_{60}$ compared to the static-atom-$A$ case, as well as how the C$_{60}$ confinement modifies the impact of atomic polarization on electron scattering compared to the free-atom case. The aim is to provide researchers with a "relative frame of reference" for understanding which part of the scattering processes could be due to electron scattering off the encapsulated atom and which due to scattering off the C$_{60}$ cage. To meet the goal, the C$_{60}$ cage is modeled by an attractive spherical potential of a certain inner radius, thickness, and depth which is a model used frequently in a great variety of fullerene studies to date. Then, the Dyson equation for the self-energy part of the Green's function of an incident electron moving in the combined field of an encapsulated atom $A$ and C$_{60}$ is solved in order to account for the impact of dynamical polarization of the encaged atom upon $e + A@{\rm C_{60}}$ scattering. The Ba@C$_{60}$ endohedral is chosen as the case study. The impact is found to be significant, and its utterly different role compared to that in $e + Ba$ scattering is unraveled.

Electron-phonon interaction and scattering in Si and Ge: Implications for phonon engineering

We report ab-initio results for electron-phonon (e-ph) coupling and display the existence of a large variation in the coupling parameter as a function of electron and phonon dispersion. This variation is observed for all phonon modes in Si and Ge, and we show this for representative cases where the initial electron states are at the band gap edges. Using these e-ph matrix elements, which include all possible phonon modes and electron bands within a relevant energy range, we evaluate the imaginary part of the electron self-energy in order to obtain the associated scattering rates. The temperature dependence is seen through calculations of the scattering rates at 0 K and 300 K. The results provide a basis for understanding the impacts of phonon scattering vs. orientation and geometry in the design of devices, and in analysis of transport phenomena. This provides an additional tool for engineering the transfer of energy from carriers to the lattice.

Thermal conductivity of hot pionic medium due to pion self-energy for πσ and πρ loops

The thermal conductivity of pionic medium has been evaluated with the help of its standard expression from the relaxation time approximation, where inverse of pion relaxation time or pion thermal width has been obtained from the imaginary part of pion self-energy. In the real-time formalism of thermal field theory, the finite temperature calculations of pion self-energy for πσ and πρ loops have been done. The numerical value of our thermal conductivity increases with temperature very softly, though at particular temperature, our estimation has to consider a large band of phenomenological uncertainty.

Single-particle spectral density of the unitary Fermi gas: Novel approach based on the operator product expansion, sum rules and the maximum entropy method

Making use of the operator product expansion, we derive a general class of sum rules for the imaginary part of the single-particle self-energy of the unitary Fermi gas. The sum rules are analyzed numerically with the help of the maximum entropy method, which allows us to extract the single-particle spectral density as a function of both energy and momentum. These spectral densities contain basic information on the properties of the unitary Fermi gas, such as the dispersion relation and the superfluid pairing gap, for which we obtain reasonable agreement with the available results based on quantum Monte-Carlo simulations.

Quasiparticle properties of the superconducting state of the two-dimensional Hubbard model

Cluster dynamical mean field methods are used to calculate the normal and anomalous components of the electron self energy of the two dimensional Hubbard model. From these the evolution of the superconducting gap and the momentum dependent photoemission and inverse photoemission spectra across the phase diagram are determined. In the pseudogap regime, decreasing the temperature into the superconducting state leads to a decrease in the energy gap and the formation of a `peak-dip-hump' structure in the electronic density of states. The peak feature disperses very weakly. The calculated spectral functions are in good qualitative agreement with published data. The mathematical origin of the behavior is found to be the effect of the superconductivity on the pole structure giving rise to the normal state pseudogap. In particular the "hump" feature is found to arise from a zero crossing of the real part of the electron self energy rather than from an onset of scattering. The effect of superconductivity on the zone diagonal spectra is presented.

Quantum transport of a nanowire field-effect transistor with complex phonon self–energy

In this work, the impact of the real part of the phonon self-energy on the transfer characteristics of a silicon nanowire transistor is investigated. The physical effects of the real part of the self-energy are to create a broadening and a shift on the density of states. This increases the drain current in the sub–threshold region and decreases it in the above–the–threshold region. In the first region, the current is increased as a result of an increase of charge in the middle of the channel. In the second one, the electrostatic self–consistency or the enforcement of charge neutrality in the channel reduces the current because a substantial amount of electrons are under the first subband and have imaginary wave vectors. The change in the phonon–limited mobility due to the real part of self–energy is evaluated for a nanowire transistor and a nanowire in which there is not source to drain barrier. We also assess the validity of Mathiessen's rule using the self–consistent NEGF simulations and the Kubo–Greenwood formalism.