Part Of Self-energy Research Articles

Efficient Full-Frequency GW Calculations Using a Lanczos Method.

The GW approximation is widely used for reliable and accurate modeling of single-particle excitations. It also serves as a starting point for many theoretical methods, such as its use in the Bethe-Salpeter equation (BSE) and dynamical mean-field theory. However, full-frequency GW calculations for large systems with hundreds of atoms remain computationally challenging, even after years of efforts to reduce the prefactor and improve scaling. We propose a method that reformulates the correlation part of the GW self-energy as a resolvent of a Hermitian matrix, which can be efficiently and accurately computed using the standard Lanczos method. This method enables full-frequency GW calculations of material systems with a few hundred atoms on a single computing workstation. We further demonstrate the efficiency of the method by calculating the defect-state energies of silicon quantum dots with diameters up to 4nm and nearly 2,000 silicon atoms using only 20 computational nodes.

Interactions of omega mesons in nuclear matter and with nuclei

In-medium interactions of omega -mesons in infinite nuclear matter and finite nuclei are investigated in a microscopic approach, focused on the particle-hole excitations of the medium involving nucleonic NN^{-1} and N^*N^{-1} modes, where N^* denotes a nucleon resonance. The nuclear polarization tensors include relativistic mean-field dynamics by self–consistent scalar and vector fields. The resulting self-energies are transmitted to finite nuclei in local density approximation. Real and imaginary parts of longitudinal and transversal self-energies are discussed. The relation of the present approach to meson cloud models is addressed and an ambiguity is pointed out. Applications to recent data on the in–medium width of omega mesons scattered on a Niobium target serve to determine unknown N^*Nomega in-medium coupling constants. The data are well described by N^*N^{-1} self–energies containing S–wave and P-wave N^* resonances. Exploratory investigations, however, show that the spectroscopic composition of self-energies depends crucially on the near-threshold properties of the width which at present is known only within large error bars. The calculations predict the prevalence of transversal self–energies, implying that vector current conservation is still maintained in the nuclear medium by slightly more than 90%. Schrödinger-equivalent potentials are derived and scattering lengths and effective range parameters are extracted for the longitudinal and transversal channel. Longitudinal and transversal spectral distributions are discussed and the dependencies on momentum and nuclear density are investigated. Schrödinger-type omega +{}^{93}Nb optical potentials are constructed. Low-energy parameters are determined, are used to study the pole structure of the S-matrix at threshold. The effective range expansion of the omega-nucleus K-matrix led to a omega +{}^{93}Nb bound states with binding energy Re(varepsilon _B)=-448 keV but of width Gamma _B=4445 keV.

Non-Fermi liquid behavior at flat hot spots from quantum critical fluctuations at the onset of charge- or spin-density wave order

We analyze quantum fluctuation effects at the onset of charge- or spin-density wave order with a $2{k}_{F}$ wave vector $\mathbf{Q}$ in two-dimensional metals, for the special case where $\mathbf{Q}$ connects a pair of hot spots situated at high symmetry points of the Fermi surface with a vanishing Fermi surface curvature. We compute the order parameter susceptibility and the fermion self-energy in one-loop approximation. The susceptibility has a pronounced peak at $\mathbf{Q}$, and the self-energy displays non-Fermi liquid behavior at the hot spots, with a linear frequency dependence of its imaginary part. The real part of the one-loop self-energy exhibits logarithmic divergencies with universal prefactors as a function of both frequency and momentum, which may be interpreted as perturbative signatures of power laws with universal anomalous dimensions. As a result, one obtains a non-Fermi liquid metal with a vanishing quasiparticle weight at the hot spots, and a renormalized dispersion relation with anomalous algebraic momentum dependencies near the hot spots.

Dynamics and lifetimes of resonant phonons in the quasiparticle and nonquasiparticle regimes

The dynamics and lifetimes of a phonon with model resonant interactions from the quasiparticle to nonquasiparticle regime were investigated employing Green's function and the Green-Kubo method. In the weak-coupling case, the dynamics of the resonant phonon are analogous to a damped harmonic oscillator and its lifetime $\ensuremath{\tau}$ is in accordance with the standard phonon transport theory $\ensuremath{\tau}=\frac{1}{2\mathrm{\ensuremath{\Gamma}}}$ ($\mathrm{\ensuremath{\Gamma}}$ being the imaginary part of phonon self-energy). In the strong-coupling nonquasiparticle regime, however, the resonant phonon ``propagates'' in a complex form of wave packets and the actual phonon lifetime ${\ensuremath{\tau}}_{\mathrm{GK}}$ as determined from the Green-Kubo formula significantly deviates from the standard $\ensuremath{\tau}=\frac{1}{2\mathrm{\ensuremath{\Gamma}}}$ relation. Taking the four-phonon resonant ${\mathrm{AgCrSe}}_{2}$ and three-phonon resonant PbSe model systems as examples, the phonon nonquasiparticle dynamics and their lifetimes in real materials are further investigated by first-principle calculations. Substantial discrepancies between ${\ensuremath{\tau}}_{\mathrm{GK}}$ and $\ensuremath{\tau}$ are found for the strongly resonant phonons at high-symmetrical points in both materials. Meanwhile, the lifetime ${\ensuremath{\tau}}_{\mathrm{GK}}$ of the phonons that are not subjected to resonant phonon interactions almost recovers to the conventional theoretical result $\ensuremath{\tau}$ despite the non-Lorentzian spectral feature of these phonons. It is suggested that $\ensuremath{\omega}{\ensuremath{\tau}}_{\mathrm{GK}}$, instead of the conventional $\ensuremath{\omega}\ensuremath{\tau}$, can be applied as a criterion to distinguish phonon quasiparticles and nonquasiparticles in addition to the phonon spectral functions.

T-channel singularities in cosmology and particle physics

The t-channel singularity of a cross section for a binary 2→2 scattering occurs when the particle exchanged in the t-channel is kinematically allowed to be on its mass shell, that is when the process can be viewed as a sequence of two physical subprocesses: a two-body decay 1→2 and an inverse decay 2→1. We derive conditions for the singularity to be present in a binary process. A class of divergent cross sections for Standard Model processes has been determined and illustrated by the weak analog of the Compton scattering Ze−→Ze−. After critically reviewing regularization methods proposed in literature, we discuss singular processes that occur in a medium composed of particles in thermal equilibrium. The medium is shown to regulate the singularities naturally as particles acquire a non-zero width. We demonstrate a possible cosmological application by calculating thermally averaged cross section for an elastic scattering within a simple scalar model. The transition probability, which is divergent in vacuum, becomes finite when the process occurs in a thermal bath due to the imaginary part of the t-channel mediator's self-energy computed within the Keldysh-Schwinger formalism.

Scaling of the Fock-space propagator and multifractality across the many-body localization transition

We implement a recursive Green function method to extract the Fock space (FS) propagator and associated self-energy across the many-body localization (MBL) transition, for one-dimensional interacting fermions in a random onsite potential. We show that the typical value of the imaginary part of the local FS self-energy, \Delta_t, related to the decay rate of an initially localized state, acts as a probabilistic order parameter for the thermal to MBL phase transition; and can be used to characterize critical properties of the transition as well as the multifractal nature of MBL states as a function of disorder strength W. In particular, we show that a fractal dimension D_s extracted from \Delta_t jumps discontinuously across the transition, from D_s<1 in the MBL phase to D_s= 1 in the thermal phase. Moreover, \Delta_t follows an asymmetrical finite-size scaling form across the thermal-MBL transition, where a non-ergodic volume in the thermal phase diverges with a Kosterlitz-Thouless like essential singularity at the critical point W_c, and controls the continuous vanishing of \Delta_t as W_c is approached. In contrast, a correlation length ({\xi}) extracted from \Delta_t exhibits a power-law divergence on approaching W_c from the MBL phase.

Model-QED operator for superheavy elements

The model-QED-operator approach [Phys. Rev. A 88, 012513 (2013)] to calculations of the radiative corrections to binding and transition energies in atomic systems is extended to the range of nuclear charges $110 \leqslant Z \leqslant 170$. The self-energy part of the model operator is represented by a nonlocal potential based on diagonal and off-diagonal matrix elements of the ab initio self-energy operator with the Dirac-Coulomb wave functions. The vacuum-polarization part consists of the Uehling contribution which is readily computed for an arbitrary nuclear-charge distribution and the Wichmann-Kroll contribution represented in terms of matrix elements similarly to the self-energy part. Performance of the method is studied by comparing the model-QED-operator predictions with the results of ab initio calculations. The model-QED operator can be conveniently incorporated in any numerical approach based on the Dirac-Coulomb-Breit Hamiltonian to account for the QED effects in a wide variety of superheavy elements.

The geometrical and temperature-dependent local field correction effects on the effective mass renormalization in a 2DEG

The paper aims at providing new theoretical insights into geometrical and local field correction effects on the effective mass renormalization of interacting electrons in a two-dimensional electron gas, at finite temperature. For this purpose, the temperature-dependent dynamic dielectric function is studied within random phase approximation. Then, the short-range effects of exchange-correlation holes around electrons are employed in calculations through local field correction using Hubbard, finite-temperature Hubbard, and Singwi-Tosi-Land-Sjolander approximations. Finally, the effective mass renormalization is calculated utilizing the real part of the electron self-energy. The outcomes indicate that the effective mass renormalization is decreased with increasing of the thickness at all dimensionless electron densities within all approximations. Likewise, utilizing a local field correction will lead to reductions in effective mass renormalization at any temperature and dimensionless electron density.

Exploring temperature dependent electron–electron interaction of rocksalt SnS and SnSe within Matsubara-time domain

Both experimental and theoretical studies show non-trivial topological behaviour in native rocksalt phase for SnS and SnSe and categorize these materials in topological crystalline insulators. Here, the detailed electronic structures studies of SnS and SnSe in the rocksalt phase are carried out using many-body GW based theory and density functional theory both for ground states and temperature dependent excited states. The estimated values of fundamental direct bandgaps around L-point using G 0 W 0 (mBJ) are ∼0.27 (∼0.13) eV and ∼0.37 (∼0.17) eV for SnS and SnSe, respectively. The strength of hybridization between Sn 5p and S 3p (Se 4p) orbitals for SnS (SnSe) shows strong k-dependence. The behaviour of (ω), which is the averaged value of diagonal matrix elements of fully screened Coulomb interaction, suggests to use full-GW method for exploring the excited states because the correlation effects within these two materials are relatively weak. The temperature dependent electronic structure calculations for SnS and SnSe provide linearly decreasing behaviour of bandgaps with rise in temperatures. The existence of collective excitation of quasiparticles in form of plasmon is predicted for these compounds, where the estimated values of plasmon frequency are ∼9.5 eV and ∼9.3 eV for SnS and SnSe, respectively. The imaginary part of self-energy and mass renormalization factor (Z k (ω)) due to electron–electron interaction (EEI) are also calculated along W–L–Γ direction for both the materials, where the estimated ranges of Z k (ω) are 0.70 to 0.79 and 0.71 to 0.78 for SnS and SnSe, respectively, along this k-direction. The present comparative study reveals that the behaviour of temperature dependent EEI for SnS and SnSe are the almost same and EEI is important for high temperature transport properties.

Electronic spectra with paramagnon fractionalization in the single-band Hubbard model

We examine spectral properties of a recently proposed theory of the intermediate temperature pseudogap metal phase of the cuprates. We show that this theory can be obtained from the familiar paramagnon theory of nearly antiferromagnetic metals by fractionalizing the paramagnon into two ``hidden'' layers of $S=1/2$ spins. The first hidden layer of spins hybridizes with the electrons as in a Kondo lattice heavy Fermi liquid, whereas the second hidden layer of spins forms a spin liquid with fractionalized spinon excitations. We compute the imaginary part of the electronic self-energy induced by the spinon excitations. The energy and momentum dependence of the photoemission spectrum across the Brillouin zone provides a good match to observations by He et al. [Science 331, 1579 (2011)] in $({\mathrm{Pb}}_{x},{\mathrm{Bi}}_{2\ensuremath{-}x})({\mathrm{La}}_{y}{\mathrm{Sr}}_{2\ensuremath{-}y}){\mathrm{CuO}}_{6+\ensuremath{\delta}}$ and by Chen et al. [Science 366, 1099 (2019)] in ${(\mathrm{Bi},\mathrm{Pb})}_{2}{\mathrm{Sr}}_{2}\mathrm{Ca}{\mathrm{Cu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$.

B_{1g}-Phonon Anomaly Driven by Fermi Surface Instability at Intermediate Temperature in YBa_{2}Cu_{3}O_{7-δ}.

We performed temperature- and doping-dependent high-resolution Raman spectroscopy experiments on YBa_{2}Cu_{3}O_{7-δ} to study B_{1g} phonons. The temperature dependence of the real part of the phonon self-energy shows a distinct kink at T=T_{B1g} above T_{c} due to softening, in addition to the one due to the onset of the superconductivity. T_{B1g} is clearly different from the pseudogap temperature with a maximum in the underdoped region and resembles charge density wave onset temperature, T_{CDW}. We attribute the B_{1g}-phonon softening to an energy gap on the Fermi surface induced by a charge density wave order, which is consistent with the results of a recent electronic Raman scattering study. Our work demonstrates a way to investigate Fermi surface instabilities above T_{c} via phonon Raman studies.

Positron elastic scattering by a semifilled-shell atom* *Prof. Dr. M Ya Amusia passed away on September 15, 2021.

We theoretically study the positron elastic scattering by an atom with a multielectron semifilled subshell in its structure. We focus on gaining the initial insight into the specifics of such a process. The positron scattering by the Mn(…3d54s2, 6S) atom with a 3d5 semifilled subshell (e+ + Mn scattering) is chosen as a case study. We account for both the electron correlation and the formation of a e+ + e− virtual positronium (Ps) in the intermediate states of the e+ + Mn system. Electron correlation is taken into account in the framework of the self-energy part of the scattering positron Green function generalized for the application to semifilled-shell atoms. The influence of the virtual Ps formation on the positron scattering is taken into account by the reduction of the energy of the virtual positron plus atomic-excited-configuration states by the Ps-binding energy, to a reasonable approximation. We unravel the importance and specificity of the influence of both the virtual Ps and electron correlation on e+ + Mn elastic scattering. We demonstrate spectacular differences between the electron and positron scattering processes.

Impact of Electron-Phonon Interaction on Thermal Transport: A Review

ABSTRACT A thorough understanding of the microscopic picture of heat conduction in solids is critical to a broad range of applications, from thermal management of microelectronics to more efficient thermoelectric materials. The transport properties of phonons, the major microscopic heat carriers in semiconductors and insulators, particularly their scattering mechanisms, have been a central theme in microscale heat conduction research. In the past two decades, significant advancements have been made in computational and experimental efforts to probe phonon-phonon, phonon-impurity, and phonon-boundary scattering channels in detail. In contrast, electron-phonon scatterings were long thought to have negligible effects on thermal transport in most materials under ambient conditions. This article reviews the recent progress in first-principles computations and experimental methods that show clear evidence for a strong impact of electron-phonon interaction on phonon transport in a wide variety of technologically relevant solid-state materials. Under thermal equilibrium conditions, electron-phonon interactions can modify the total phonon scattering rates and renormalize the phonon frequency, as determined by the imaginary part and the real part of the phonon self-energy, respectively. Under nonequilibrium transport conditions, electron-phonon interactions can affect the coupled transport of electrons and phonons in the bulk through the “phonon/electron drag” mechanism as well as the interfacial thermal transport. Based on these recent results, we evaluate the potential use of electron-phonon interactions to control thermal transport in solids. We also provide an outlook on future directions of computational and experimental developments.

Neutrino decoherence in an electron and nucleon background

We consider the decoherence effects in the propagation of active neutrinos due to the non-forward neutrino scattering processes in a matter background composed of electrons and nucleons. We calculate the contribution to the imaginary part of the neutrino self-energy arising from such processes. Since the initial neutrino state is depleted but does not actually disappear (the initial neutrino transitions into a neutrino of a different flavor but does not decay) those processes should be associated with decoherence effects that cannot be described in terms of the coherent evolution of the state vector. Based on the formalism developed in our previous work for treating the non-forward scattering processes using the notion of the stochastic evolution of the state, we identify the jump operators, as used in the context of the master or Lindblad equation, in terms of the results of the the calculation of the non-forward neutrino scattering contribution to the imaginary part of the neutrino self-energy. As a guide to estimating the decoherence effects in situations of practical interest we give explicit formulas for the decoherence terms for different background conditions, and point out some of the salient features in particular the neutrino energy dependence. To establish contact wih previous works in which the decoherence terms are treated as phenomenological parameters, we consider the solution to the evolution equation in the two-generation case. We give formulas that are useful for estimating the effects of the decoherence terms under various conditions and environments, including the typical conditions applicable to long baseline experiments, where matter effects are important. In those contexts the effects appear to be small, and indicative that if significant decoherence effects were to be found they would be due to non-standard contributions to the decoherence terms.

Anharmonic Origin of the Giant Thermal Expansion of NaBr.

All phonons in a single crystal of NaBr are measured by inelastic neutron scattering at temperatures of 10, 300, and 700K. Even at 300K, the phonons, especially the longitudinal-optical phonons, show large shifts in frequencies and show large broadenings in energy owing to anharmonicity. Abinitio computations are first performed with the quasiharmonic approximation (QHA) in which the phonon frequencies depend only on V and on T only insofar as it alters V by thermal expansion. This QHA is an unqualified failure for predicting the temperature dependence of phonon frequencies, even 300K, and the thermal expansion is in error by a factor of 4. Abinitio computations that include both anharmonicity and quasiharmonicity successfully predict both the temperature dependence of phonons and the large thermal expansion of NaBr. The frequencies of longitudinal-optical phonon modes decrease significantly with temperature owing to the real part of the phonon self-energy from explicit anharmonicity originating from the cubic anharmonicity of nearest-neighbor NaBr bonds. Anharmonicity is not a correction to the QHA predictions of thermal expansion and thermal phonon shifts but dominates the behavior.

Phonon dynamics in the Kitaev spin liquid

The search for fractionalization in quantum spin liquids largely relies on their decoupling with the environment. However, the spin-lattice interaction is inevitable in a real setting. While the Majorana fermion evades a strong decay due to the gradient form of spin-lattice coupling, the study of the phonon dynamics may serve as an indirect probe of fractionalization of spin degrees of freedom. Here we propose that the signatures of fractionalization can be seen in the sound attenuation and the Hall viscosity. Despite the fact that both quantities can be related to the imaginary part of the phonon self-energy, their origins are quite different, and the time-reversal symmetry breaking is required for the Hall viscosity. First, we compute the sound attenuation due to a phonon scattering off of a pair of Majorana fermions and show that it is linear in temperature ($\sim T$). We argue that it has a particular angular dependence providing the information about the spin-lattice coupling and the low-energy Majorana fermion spectrum. The observable effects in the absence of time-reversal symmetry are then analyzed. We obtain the phonon Hall viscosity term from the microscopic Hamiltonian with time-reversal symmetry breaking term. Importantly, the Hall viscosity term mixes the longitudinal and transverse phonon modes and renormalize the spectrum in a unique way, which may be probed in spectroscopy measurement.

Neutrino decoherence in a fermion and scalar background

We consider the decoherence effects in the propagation of neutrinos in a background composed of a scalar particle and a fermion due to the non-forward neutrino scattering processes. Using a simple model for the coupling of the form $\bar f_R\nu_L\phi$ we calculate the contribution to the imaginary part of the neutrino self-energy arising from the non-forward neutrino scattering processes in such backgrounds, from which the damping terms are determined. In the case we are considering, in which the initial neutrino state is depleted but does not actually disappear (the initial neutrino transitions into a neutrino of a different flavor but does not decay into a $f\phi$ pair, for example), we associate the damping terms with decoherence effects. For this purpose we give a precise prescription to identify the decoherence terms, as used in the context of the master or Linblad equation, in terms of the damping terms we have obtained from the calculation of the imaginary part of the neutrino self-energy from the non-forward neutrino scattering processes. The results can be directly useful in the context of Dark Matter-neutrino interaction models in which the scalar and/or fermion constitute the dark-matter, and can also serve to guide the generalizations to other models and/or situations in which the decoherence effects in the propagation of neutrinos originate from the non-forward scattering processes may be important. As a guide to estimating such decoherence effects, the contributions to the absorptive part of the self-energy and the corresponding damping terms are computed explicitly in the context of the model we consider, for several limiting cases of the momentum distribution functions of the background particles.

Effect of Phonons on the Magnetic Characteristics of Metals at Finite Temperatures

We consider the electron-phonon interaction in the framework of dynamic spin-fluctuation theory and obtain an expression for the self-energy part that depends explicitly on the spin fluctuations and lattice vibrations. We illustrate the theoretical results with the example of iron. We show that the effect of phonons on temperature dependence of the magnetic characteristics of metals is appreciable but not as large as in the static single-site approximation of the spin-fluctuation theory and spin dynamics using classical Hamiltonians.

ComDMFT: A massively parallel computer package for the electronic structure of correlated-electron systems

ComDMFT is a massively parallel computational package to study the electronic structure of correlated-electron systems (CES). Our approach is a parameter-free method based on ab initio linearized quasiparticle self-consistent GW (LQSGW) and dynamical mean field theory (DMFT). The non-local part of the electronic self-energy is treated within ab initio LQSGW and the local strong correlation is treated within DMFT. In addition to ab initio LQSGW+DMFT, charge self-consistent LDA+DMFT methodology is also implemented, enabling multiple methods in one open-source platform for the electronic structure of CES. This package can be extended for future developments to implement other methodologies to treat CES. Program summaryProgram Title: ComDMFTProgram Files doi:http://dx.doi.org/10.17632/h8vky97ncg.1Licensing provisions: GPLv3Programming language: fortran90, C++ and PythonNature of problem: There is no open-source code based on ab initio GW+EDMFT and related methodologies to support their theoretical advancement for the electronic structure of correlated electron systems.Solution method: We implemented ab initio LQSGW+DMFT methodology, as a simplification of ab initio GW+EDMFT, for the electronic structure of correlated electron systems. In addition, charge self-consistent LDA+DMFT methodology is also implemented, enabling the comparison of multiple methods for the electronic structure of correlated electron systems in one platform.Additional comments: ComDMFT is built on top of Wannier90 (Mostofi et al. 2008) and FlapwMBPT (Kutepov et al. 2017) codes.

Neutrino damping in a fermion and scalar background

We consider the propagation of a neutrino in a background composed of a scalar particle and a fermion using a simple model for the coupling of the form $\lambda\bar f_R\nu_L\phi$. In the presence of these interactions there can be damping terms in the neutrino effective potential and index of refraction. We calculate the imaginary part of the neutrino self-energy in this case, from which the damping terms are determined. The results are useful in the context of Dark Matter-neutrino interaction models in which the scalar and/or fermion constitute the dark-matter. The corresponding formulas for models in which the scalar particle couples to two neutrinos via a coupling of the form $\lambda^{(\nu\nu\phi)}\bar\nu^c_R\nu_L\phi$ are then obtained as a special case, which can be important also in the context of neutrino collective oscillations in a supernova and in the Early Universe hot plasma before neutrino decoupling. A particular feature of our results is that the damping term in a $\nu\phi$ background is independent of the antineutrino-neutrino asymmetry in the background. Therefore, the relative importance of the damping term may be more significant if the neutrino-antineutrino asymmetry in the background is small, because the leading $Z$-exchange and $\phi$-exchange contributions to the effective potential, which are proportional to the neutrino-antineutrino asymmetry, are suppressed in that case, while the damping term is not.