Quasiparticle Spectral Function Research Articles

Efficient full frequency GW for metals using a multipole approach for the dielectric screening

The properties of metallic systems with important and structured excitations at low energies, such as Cu, are challenging to describe with simple models like the plasmon pole approximation (PPA), and more accurate and sometimes prohibitive full frequency approaches are usually required. In this paper we propose a numerical approach to $GW$ calculations on metals that takes into account the frequency dependence of the screening via the multipole approximation (MPA), an accurate and efficient alternative to current full-frequency methods that was recently developed and validated for semiconductors and overcomes several limitations of PPA. We now demonstrate that MPA can be successfully extended to metallic systems by optimizing the frequency sampling for this class of materials and introducing a simple method to include the $\mathbf{q}\to 0$ limit of the intra-band contributions. The good agreement between MPA and full frequency results for the calculations of quasi-particle energies, polarizability, self-energy and spectral functions in different metallic systems confirms the accuracy and computational efficiency of the method. Finally, we discuss the physical interpretation of the MPA poles through a comparison with experimental electron energy loss spectra for Cu.

Dynamical magnetic response in superconductors with finite-momentum pairs

We derive the dynamical magnetic response functions in the Fulde-Ferrell (FF) state of a superconductor with inversion symmetry. The pair momentum 2q is obtained by minimization of the condensation energy and the resulting quasiparticle states and spectral functions exhibit the segmentation into paired and unpaired regions due to the finite q. The dynamical magnetic susceptibility is then calculated in linear response formalism in the FF state with finite-q condensate resulting from s-wave or d-wave pairing. We show that quasiparticle excitations inside as well as between paired and unpaired segments contribute to the dynamical response. We discuss its dependence on frequency and momentum transfer which develops a characteristic symmetry-breaking parallel to q. Furthermore, we investigate the possible influence on Knight shift and in the case of d-wave pairing on the spin resonance formation in the FF state.

Fragile versus stable two-dimensional fermionic quasiparticles

We provide a comprehensive theoretical investigation of the Fermi liquid quasiparticle description in two-dimensional electron gas interacting via the long-range Coulomb interaction by calculating the electron self-energy within the leading-order approximation, which is exact in the high-density limit. We find that the quasiparticle energy is larger than the imaginary part of the self-energy up to very high energies, implying that the basic Landau quasiparticle picture is robust up to far above the Fermi energy. We find, however, that the quasiparticle picture becomes fragile in a small discrete region around a critical wave vector where the quasiparticle spectral function strongly deviates from the expected quasiparticle Lorentzian line shape with a vanishing renormalization factor. We show that such a non-Fermi liquid behavior arises due to the coupling of quasiparticles with the collective plasmon mode. This situation is somewhat intermediate between the one-dimensional interacting electron gas (i.e., Luttinger liquid), where the Landau Fermi liquid theory completely breaks down since only bosonic collective excitations exist, and three-dimensional electron gas, where quasiparticles are well-defined and more stable against interactions than in one and two dimensions. We use a number of complementary definitions for a quasiparticle to examine the interacting spectral function, contrasting two-dimensional and three-dimensional situations critically.

Switching of the electron-phonon interaction in 1T−VSe2 assisted by hot carriers

We apply an intense infrared laser pulse in order to perturb the electronic and vibrational states in the three-dimensional charge density wave material 1$T$-VSe$_2$. Ultrafast snapshots of the light-induced hot carrier dynamics and non-equilibrium quasiparticle spectral function are collected using time- and angle-resolved photoemission spectroscopy. The hot carrier temperature and time-dependent electronic self-energy are extracted from the time-dependent spectral function, revealing that incoherent electron-phonon interactions heat the lattice above the charge density wave critical temperature on a timescale of $(200 \pm 40)$~fs. Density functional perturbation theory calculations establish that the presence of hot carriers alters the overall phonon dispersion and quenches efficient low-energy acoustic phonon scattering channels, which results in a new quasi-equilibrium state that is experimentally observed.

Magnon-assisted dynamics of a hole doped in a cuprate superconductor

We calculate the quasiparticle dispersion and spectral weight of the quasiparticle that results when a hole is added to an antiferromagnetically ordered CuO$_2$ plane of a cuprate superconductor. We also calculate the magnon contribution to the quasiparticle spectral function. We start from a multiband model for the cuprates considered previously [Nat. Phys. \textbf{10}, 951 (2014)]. We map this model and the operator for creation of an O hole to an effective one-band generalized $t-J$ model, without free parameters. The effective model is solved using the state of the art self-consistent Born approximation. Our results reproduce all the main features of experiments. They also reproduce qualitatively the dispersion of the multiband model, giving better results for the intensity near wave vector $(\pi,\pi)$, in comparison with the experiments. In contrast to what was claimed in [Nat. Phys. \textbf{10}, 951 (2014)], we find that spin fluctuations play an essential role in the dynamics of the quasiparticle, and hence in both its weight and dispersion.

Longitudinal and anomalous Hall conductivity of a general two-band model

We derive and analyze the longitudinal and the anomalous Hall conductivity for a general momentum-block-diagonal two-band model. This model captures a broad spectrum of physically very different systems including N\'eel antiferromagnetic and spiral spin density waves as well as models that involve spin-orbit interaction and are known to show topological properties. We present a complete microscopic derivation for finite temperature and constant scattering rate $\Gamma$ that is diagonal and equal, but arbitrarily large for both bands. We identify two criteria that allow for a unique and physically motivated decomposition of the conductivities. On the one hand, we distinguish intraband and interband contributions that are defined by the involved quasiparticle spectral functions. On the other hand, we distinguish symmetric and antisymmetric contributions that are defined by the symmetry under the exchange of the current and the electric field directions. The (symmetric) intraband contributions generalize the formula of standard Boltzmann transport theory, which is valid only in the clean limit (small $\Gamma$), whereas the interband contributions capture interband coherence effects beyond independent quasiparticles. We show that the symmetric interband contribution is a correction only present for finite $\Gamma$ and is controlled by the quantum metric. The antisymmetric interband contributions generalize the formula of the anomalous Hall conductivity in terms of the Berry curvature to finite $\Gamma$. We study the clean (small $\Gamma$) and dirty (large $\Gamma$) limit analytically. The connection between the presented derivation and the Bastin and Streda formalism is given. We apply our results to a Chern insulator, a ferromagnetic multi-d-orbital, and a spiral spin density wave model.

SternheimerGW: A program for calculating [formula omitted] quasiparticle band structures and spectral functions without unoccupied states

The SternheimerGW software uses time-dependent density-functional perturbation theory to evaluate GW quasiparticle band structures and spectral functions for solids. Both the Green’s function G and the screened Coulomb interaction W are obtained by solving linear Sternheimer equations, thus overcoming the need for a summation over unoccupied states. The code targets the calculation of accurate spectral properties by convoluting G and W using a full frequency integration. The linear response approach allows users to evaluate the spectral function at arbitrary electron wavevectors, which is particularly useful for indirect band gap semiconductors and for simulations of angle-resolved photoelectron spectra. The software is parallelized efficiently, integrates with version 6.3 of Quantum Espresso, and is continuously monitored for stability using a test farm. Program summaryProgram Title:SternheimerGWProgram Files doi:http://dx.doi.org/10.17632/7ywzjng9t5.1Licensing provisions: GNU General Public License v3.0Programming language: Fortran 2003Nature of problem: The lack of the exchange–correlation discontinuity in density-functional theory (DFT) leads to a systematic underestimation of the band gap between conduction and valence states. Many-body perturbation theory in the GW approximation provides an effective solution to this problem, as well as other limitations faced by DFT in the description of electronic excitations. However, the GW method comes with its own set of limitations: (i) The perturbation of the system is typically expressed in terms of the unoccupied states, and achieving numerical convergence with respect to these states is often cumbersome. Since the underlying DFT codes rely only on the occupied states, their default behavior is often ill-suited to provide a sufficient amount of empty states. Combined with the large number of parameters that need to be converged, this limits the use of GW codes by non-expert users and automatic scripts. (ii) Currently, GW codes require that a homogeneous k-point mesh is used in the calculation. Hence, features close to the band edges are often only accessible via prohibitively expensive dense k-point meshes or interpolation techniques. (iii) To evaluate the frequency convolution of the Green’s function G and the screened Coulomb interaction W, many current GW calculations rely on approximations such as the plasmon-pole approximation, the analytic continuation, or the contour deformation. The relative merits and accuracy of the various approximations are not fully understood.Solution method: In SternheimerGW, we address (i) by replacing the summation over unoccupied states with a linear response equation. The solution depends on the occupied states only, and it employs linear response algorithms already provided by the Quantum ESPRESSO suite to compute phonons and related properties. As an additional benefit, transforming the problem in a linear response equation removes the restriction to homogeneous k-point meshes (ii), so that the GW self-energy for any arbitrary point can be evaluated. Finally (iii), we provide the possibility to perform a full frequency convolution along the real frequency axis. This feature can serve as a benchmark for approximate integrations using models or analytic continuation.

Dynamical quasiparticle properties of gapped monolayer graphene in the presence of Holstein phonons

We have calculated the quasiparticle particle self-energy and spectral function in a graphene plane when a symmetry breaking of the sublattice is occurred. Holstein model Hamiltonian has been applied to describe the electron dynamics in the presence of lattice vibrations. This model Hamiltonian takes into account the effects of interaction between electrons and Einstein phonons beyond the usual Dirac-cone approximation. Specially, the effects of gap parameter and electron-phonon coupling strength on spectral function, inelastic scattering lifetime and band gap renormalization have been studied. Also the electron density dependence of inelastic scattering lifetime for different values of gap parameter has been investigated. In order to find the quasiparticle excitation spectrum of the interacting electronic system, we have studied the frequency dependence of spectral function for different physical parameters. Our results show the intensity of broad peak in frequency dependence of spectral function reduces with electron-phonon coupling strength. However the intensity of quasiparticle particle peak increases with coupling strength. The increase of gap parameter leads to appear sharp quasiparticle peak with high intensity in spectral function. The frequency dependence of sharp peak goes to higher frequency with gap parameter. Also the gap parameter dependence of inverse of scattering life time shows a sudden change for all values of coupling constant. Finally band gap renormalization enhances with electron-phonon coupling constant at fixed electron density.

The study of dynamical quasiparticle properties of undoped graphene nanoribbon

We have calculated the quasiparticle particle self-energy and spectral function in an undoped graphene nanoribbon when a symmetry breaking of the sublattice is occurred. Hubbard model Hamiltonian has been applied to describe the electron dynamics in the structure. Using the many body G0W approach and Green's function technique, we have found the dynamical quasiparticle properties of electrons on nanoribbon structure. Also random phase approximation has been exploited to calculate electronic self-energy of the system. The difference between on-site energies of atoms on two sublattices is named gap parameter. Specially, the effects of gap parameter and Hubbard parameter on spectral function, inelastic scattering lifetime and band gap renormalization have been studied. Also the wave vector dependence of inelastic scattering lifetime for different values of gap parameter has been investigated. In order to find the quasiparticle excitation spectrum of the interacting electronic system, we have studied the frequency dependence of spectral function for different physical parameters.

T -matrix approach to quark-gluon plasma

A selfconsistent thermodynamic $T$-matrix approach is deployed to study the microscopic properties of the quark-gluon plasma (QGP), encompassing both light- and heavy-parton degrees of freedom in a unified framework. The starting point is a relativistic effective Hamiltonian with a universal color force. The input in-medium potential is quantitatively constrained by computing the heavy-quark (HQ) free energy from the static $T$-matrix and fitting it to pertinent lattice-QCD (lQCD) data. The corresponding $T$-matrix is then applied to compute the equation of state (EoS) of the QGP in a two-particle irreducible formalism including the full off-shell properties of the selfconsistent single-parton spectral functions and their two-body interaction. In particular, the skeleton diagram functional is fully resummed to account for emerging bound and scattering states as the critical temperature is approached from above. We find that the solution satisfying three sets of lQCD data (EoS, HQ free energy and quarkonium correlator ratios) is not unique. As limiting cases we discuss a weakly-coupled solution (WCS) which features color-potentials close to the free energy, relatively sharp quasiparticle spectral functions and weak hadronic resonances near $T_{\rm c}$, and a strongly-coupled solution (SCS) with a strong color potential (much larger than the free energy) resulting in broad non-quasiparticle parton spectral functions and strong hadronic resonance states which dominate the EoS when approaching $T_{\rm c}$.

Cubic scalingGW: Towards fast quasiparticle calculations

Within the framework of the full potential projector-augmented wave methodology, we present a promising low-scaling $GW$ implementation. It allows for quasiparticle calculations with a scaling that is cubic in the system size and linear in the number of $k$ points used to sample the Brillouin zone. This is achieved by calculating the polarizability and self-energy in the real space and imaginary time domain. The transformation from the imaginary time to the frequency domain is done by an efficient discrete Fourier transformation with only a few nonuniform grid points. Fast Fourier transformations are used to go from real space to reciprocal space and vice versa. The analytic continuation from the imaginary to the real frequency axis is performed by exploiting Thiele's reciprocal difference approach. Finally, the method is applied successfully to predict the quasiparticle energies and spectral functions of typical semiconductors (Si, GaAs, SiC, and ZnO), insulators (C, BN, MgO, and LiF), and metals (Cu and SrVO$_3$). The results are compared with conventional $GW$ calculations. Good agreement is achieved, highlighting the strength of the present method.

Resonant tunneling and the quasiparticle lifetime in graphene/boron nitride/graphene heterostructures

Tunneling of quasiparticles between two nearly aligned graphene sheets produces resonant current-voltage characteristics because of the quasiexact conservation of in-plane momentum. We claim that, in this regime, vertical transport in graphene/boron nitride/graphene heterostructures carries precious information on electron-electron interactions and the quasiparticle spectral function of the two-dimensional electron system in graphene. We present extensive microscopic calculations of the tunneling spectra with the inclusion of quasiparticle lifetime effects and elucidate the range of parameters (interlayer bias, temperature, twist angle, and gate voltage) under which electron-electron interaction physics emerges.

Pair–pair interactions as a mechanism for high-Tc superconductivity

The mutual interaction between Cooper pairs is proposed as a mechanism for the superconducting state. Above Tc, pre-existing but fluctuating Cooper pairs give rise to the unconventional pseudogap (PG) state, well-characterized by experiment. At the critical temperature, the pair–pair interaction induces a Bose-like condensation of these preformed pairs leading to the superconducting (SC) state. Below Tc, both the condensation energy and the pair–pair interaction β are proportional to the condensate density Noc(T), while the usual Fermi-level spectral gap is independent of temperature. The new order parameter , can be followed as a function of temperature, carrier concentration and disorder—i.e. the phase diagrams. The complexity of the cuprates, revealed by the large number of parameters, is a consequence of the coupling of quasiparticles to Cooper-pair excitations. The latter interpretation is strongly supported by the observed quasiparticle spectral function.

Heavy-impurity resonance, hybridization, and phonon spectral functions inFe1−xMxSi (M=Ir, Os)

The vibrational behavior of heavy substitutional impurities $(M=\phantom{\rule{4.pt}{0ex}}\text{Ir},\phantom{\rule{4.pt}{0ex}}\text{Os})$ in ${\text{Fe}}_{1\ensuremath{-}x}{M}_{x}\text{Si}\phantom{\rule{4.pt}{0ex}}(x=0,0.02,0.04,0.1)$ was investigated with a combination of inelastic neutron scattering (INS), transport measurements, and first-principles simulations. Our INS measurements on single crystals mapped the four-dimensional dynamical structure factor, $S(\mathbf{Q},E)$, for several compositions and temperatures. Our results show that both Ir and Os impurities lead to the formation of a weakly dispersive resonance vibrational mode, in the energy range of the acoustic phonon dispersions of the FeSi host. We also show that Ir doping, which introduces free carriers, leads to softened interatomic force constants compared to doping with Os, which is isoelectronic to Fe. We analyze the phonon $S(\mathbf{Q},E)$ from INS through a Green's-function model incorporating the phonon self-energy based on first-principles density functional theory simulations, and we study the disorder-induced lifetimes on large supercells. Calculations of the quasiparticle spectral functions in the doped system reveal the hybridization between the resonance and the acoustic phonon modes. Our results demonstrate a strong interaction of the host acoustic dispersions with the resonance mode, likely leading to the large observed suppression in lattice thermal conductivity.

Mean-field approach to unconventional superconductivity

We propose a model that connects the quasiparticle spectral function of high-Tc superconductors to the condensation energy. Given the evidence for pair correlations above Tc, we consider a coarse-grain Hamiltonian of fluctuating pairs describing the incoherent pseudogap (PG) state, together with a novel pair–pair interaction term that restores long-range superconducting (SC) coherence below Tc. A mean-field solution then leads to a self-consistent gap equation containing the new pair–pair coupling. The corresponding spectral function A(k,E) reveals the characteristic peak–dip–hump features of cuprates, now observed on iron pnictides (LiFeAs). The continuous transition from SC to PG states is discussed.

Connecting electron and phonon spectroscopy data to consistently determine quasiparticle-phonon coupling on the surface of topological insulators

Photoemission and phonon spectroscopies have yielded widely varying estimates of the electron-phonon coupling constant \lambda\ on the surfaces of topological insulators, even for a particular material and technique. We connect the results of these experiments by determining the Dirac fermion quasiparticle spectral function using information from measured spectra of a strongly-interacting, low-lying optical surface phonon band. The manifest spectral features resulting from the coupling are found to vary on energy scales < 1 meV, and are distinct from those traditionally observed in the case of acoustic phonons in metals. We explore different means of determining \lambda\ from the electron perspective and identify definitions that yield values consistent with phonon spectroscopy.

Effect of hydrogen dimers on the electronic structure of graphene

We investigate the effect of hydrogen dimers on the electronic structure of graphene. Using Greenʼs function and the T-matrix approach, we calculate the local density of states of graphene with single hydrogen dimer, as well as the quasiparticle spectral function of graphene with a finite concentration of randomly distributed hydrogen dimers. Our results show that the effect of dimer adsorption is dramatically different from that of monomer adsorption previously studied, and strongly depends on the configuration of the dimer. The features of the plotted spectral function of graphene are relevant to the band gap opening and the metal–insulator transition.

Surface polar optical phonon interaction induced many-body effects and hot-electron relaxation in graphene

We theoretically study various aspects of the electron-surface optical phonon interaction effects in graphene on a substrate made of polar materials. We calculate the electron self energy in the presence of the surface phonon-mediated electron-electron interaction focusing on how the linear chiral graphene dispersion is renormalized by the surface phonons. The electron self energy as well as the quasiparticle spectral function in graphene are calculated, taking into account electron-polar optical phonon interaction by using a many-body perturbative formalism. The scattering rate of free electrons due to polar interaction with surface optical phonons in a dielectric substrate is calculated as a function of the electron energy, temperatures, and carrier density. Effects of screening on the self energy and scattering rate are discussed. Our theory provides a comprehensive quantitative (and qualitative) picture for surface phonon interaction induced many-body effects and hot-electron relaxation in Dirac materials.

GWand beyond approaches to quasiparticle properties in metals

We perform a comparative study of the performances of some standard approaches within the many-body perturbation theory. We calculate quasiparticle dispersions, lifetimes, and spectral functions of aluminum and sodium. Calculations have been carried out in the $GW$ approximation with a plasmon pole model (PPM) or with the contour deformation technique. We also accounted for vertex corrections either only in the screening (replacing the RPA dielectric function with the TDLDA or the Hubbard one) or both in the screening and in the self-energy (using the Del Sole et al. local vertex). Results show the failure of the PPM to describe the corrections far from the Fermi energy, as well as its inability to describe quasiparticle lifetimes and spectral functions. Calculations with a more refined screened interaction decrease the bandwidths and the lifetime of the quasiparticles compared with the $GW$ as well as inducing tiny modifications in the spectral functions. The inclusion of the vertex also in the self-energy cancels the effects arising from the screening by pushing the results back toward the $GW$ ones or even enlarging the differences.

Emergence of plasmaronic structure in the near-field optical response of graphene

The finite momentum optical response $\sigma({\boldsymbol{q}},\omega)$ of graphene can be probed with the innovative technique of infrared nanoscopy where mid-infrared radiation is confined by an atomic force microscope cantilever tip. In contrast to conventional $q\sim 0$ optical absorption which primarily involves Dirac fermions with momentum near the Fermi momentum, $k\sim k_F$, for finite $q$, $\sigma({\boldsymbol{q}},\omega)$ has the potential to provide information on many body renormalizations and collective phenomena which have been found at small $k< k_F$ near the Dirac point in electron-doped graphene. For electron-electron interactions, the low energy excitation spectrum characterizing the incoherent part of the quasiparticle spectral function of Dirac electrons with $k\sim k_F$ consists of a flat, small amplitude background which scales with chemical potential and Fermi momentum. However, probing of the states with $k$ near $k=0$ will reveal plasmarons, a collective state of a charge carrier and a plasmon. These collective modes in graphene have recently been seen in angle-resolved photoemission spectroscopy and here we describe how they manifest in near field optics.