Functional Theory Green Research Articles

Relativistic correction scheme for core-level binding energies from GW.

We present a relativistic correction scheme to improve the accuracy of 1s core-level binding energies calculated from Green's function theory in the GW approximation, which does not add computational overhead. An element-specific corrective term is derived as the difference between the 1s eigenvalues obtained from the self-consistent solutions to the non- or scalar-relativistic Kohn-Sham equations and the four-component Dirac-Kohn-Sham equations for a free neutral atom. We examine the dependence of this corrective term on the molecular environment and the amount of exact exchange in hybrid exchange-correlation functionals. This corrective term is then added as a perturbation to the quasiparticle energies from partially self-consistent and single-shot GW calculations. We show that this element-specific relativistic correction, when applied to a previously reported benchmark set of 65 core-state excitations [D. Golze et al., J. Phys. Chem. Lett. 11, 1840-1847 (2020)], reduces the mean absolute error (MAE) with respect to the experiment from 0.55 eV to 0.30 eV and eliminates the species dependence of the MAE, which otherwise increases with the atomic number. The relativistic corrections also reduce the species dependence for the optimal amount of exact exchange in the hybrid functional used as a starting point for the single-shot G0W0 calculations. Our correction scheme can be transferred to other methods, which we demonstrate for the delta self-consistent field (ΔSCF) approach based on density functional theory.

Level anticrossing effect in single-level or multilevel double quantum dots: Electrical conductance, zero-frequency charge susceptibility, and Seebeck coefficient

We study electrical and thermoelectrical properties for a double quantum dot system. We consider the cases of both single-level and multilevel quantum dots whatever the way they are coupled, either in a series or in a parallel arrangement. The calculations are performed by using the nonequilibrium Green function theory. In the case of a single-level double quantum dot, the problem is exactly solvable whereas for a multilevel double quantum dot, an analytical solution is obtained in the limit of energy-independent hopping integrals. { We present a detailed discussion about} the dependences of electrical conductance, zero-frequency charge susceptibility and Seebeck coefficient on the gate voltages applied to the dots, allowing us to derive the charge stability diagram. The findings are in agreement with the experimental observations notably with the occurrence of successive sign changes of the Seebeck coefficient when varying the gate voltages. We interpret the results in terms of the bonding and antibonding states produced by the level anticrossing effect which occurs in the presence of a finite interdot coupling. We show that at equilibrium the boundary lines between the domains with different dot occupancies in the charge stability diagram, take place when the bonding and antibonding state levels are aligned with the chemical potentials in the leads. Finally the total dot occupancy is found to be considerably reduced in the case in parallel compared with the case in series, { whenever} the level energies in each dot are equal. We interpret this dip as a direct manifestation of the interference effects occurring in the presence of the two electronic transmission paths provided by each dot.

Temperature scaling of two-ion anisotropy in pure and mixed anisotropy systems

Magnetic anisotropy plays an essential role in information technology applications of magnetic materials, providing a means to retain the long-term stability of a magnetic state in the presence of thermal fluctuations. Anisotropy consists of a single-ion contribution stemming from the crystal structure and two-ion terms attributed to the exchange interactions between magnetic atoms. A lack of robust theory crucially limits the understanding of the temperature dependence of the anisotropy in pure two-ion and mixed single-ion and two-ion systems. Here, we use Green's function theory and atomistic Monte Carlo simulations to determine the temperature scaling of the effective anisotropy in ferromagnets in these pure and mixed cases, from saturated to vanishing magnetization. At low temperature, we find that the pure two-ion anisotropy scales with the reduced magnetization as $k(m) \sim m^{2.28}$, while the mixed scenario describes the diversity of the temperature dependence of the anisotropy observed in real materials. The temperature dependence of the mixed anisotropy determined here is expected to considerably contribute to the understanding and the control of the thermal properties of magnetic materials.

Crossed graphene nanoribbons as beam splitters and mirrors for electron quantum optics

We analyze theoretically 4-terminal electronic devices composed of two crossed graphene nanoribbons (GNRs) and show that they can function as beam splitters or mirrors. These features are identified for electrons in the low-energy region where a single valence or conduction band is present. Our modeling is based on $p_z$ orbital tight-binding with Slater--Koster type matrix elements fitted to accurately reproduce the low-energy bands from density functional theory calculations. We analyze systematically all devices that can be constructed with either zigzag or armchair GNRs in AA and AB stackings. From Green's function theory the elastic electron transport properties are quantified as a function of the ribbon width. We find that devices composed of relatively narrow zigzag GNRs and AA-stacked armchair GNRs are the most interesting candidates to realize electron beam splitters with a close to 50-50 ratio in the two outgoing terminals. Structures with wider ribbons instead provide electron mirrors, where the electron wave is mostly transferred into the outgoing terminal of the other ribbon, or electron filters where the scattering depends sensitively on the wavelength of the propagating electron. We also test the robustness of these transport properties against variations in intersection angle, stacking pattern, lattice deformation (uniaxial strain), inter-GNR separation, and electrostatic potential differences between the layers. These generic features show that GNRs are interesting basic components to construct electronic quantum optical setups.

Many-body Green's function theory of electrons and nuclei beyond the Born-Oppenheimer approximation

The method of many-body Green's functions is developed for arbitrary systems of electrons and nuclei starting from the full (beyond Born-Oppenheimer) Hamiltonian of Coulomb interactions and kinetic energies. The theory presented here resolves the problems arising from the translational and rotational invariance of this Hamiltonian that afflict the existing many-body Green's function theories. We derive a coupled set of exact equations for the electronic and nuclear Green's functions and provide a systematic way to approximately compute the properties of arbitrary many-body systems of electrons and nuclei beyond the Born-Oppenheimer approximation. The case of crystalline solids is discussed in detail.

Micro-macro heat conduction model for the prediction of local, transient temperature in composite media

Heat flow in heterogeneous media with complex microstructure follows tortuous path and therefore the determination of local temperature distribution is a challenging task. The paper presents a micro-macro heat conduction model for the prediction of this distribution. The proposed solution is based on the prior determination of the macroscopic temperature in a quasi-homogeneous medium characterized by effective properties and then on using the relations between the macroscopic and microscopic temperatures. The Ensemble Averaging Method (EAM) was applied to derive the macroscopic transport equations while the combination of the EAM with the Green's Function Theory (GFT) was used to obtain relations between microscopic and macroscopic temperature fields. The expansion of these relations versus powers of the ratio of the micro to macro dimensions was then used to obtain a two-scale approximation of the mentioned relations. The model is applicable wherever the characteristic dimensions of the microstructure, i.e., distance between inclusions, are smaller than macro-dimension associated with time and spatial variation of macroscopic temperature distribution. The latter can be found from the respective expansion of the macroscopic temperature distribution into the Fourier series. The verification of the proposed model was carried out for 2D transient heat conduction in a periodic composite with the fixed microstructure by comparing direct numerical solution of the energy equation with the results of the approximate micro-macroscopic modelling. The model will be further extended to the prediction of temperature distribution in the case when the thermal contact resistance between constituents, species concentration in heterogeneous media, phase change phenomena and formation of a medium microstructure are present.

Superconducting transition temperatures of metallic liquids

We develop a nonperturbative approach for calculating the superconducting transition temperatures (Tc's) of liquids. The electron-electron scattering amplitude induced by electron-phonon coupling (EPC), from which an effective pairing interaction can be inferred, is related to the fluctuation of the T matrix of electron scattering induced by ions. By applying the relation, EPC parameters can be extracted from a path-integral molecular dynamics simulation. For determining Tc, the linearized Eliashberg equations are reestablished nonperturbatively. We apply the approach to estimate Tc's of metallic hydrogen liquids. It indicates that metallic hydrogen liquids in the pressure regime from 0.5 to 1.5TPa have Tc's well above their melting temperatures and therefore are superconducting liquids.1 MoreReceived 29 January 2019Revised 28 January 2020Accepted 30 January 2020DOI:https://doi.org/10.1103/PhysRevResearch.2.013340Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasElectron-phonon couplingMethods in superconductivityPressure effectsSuperconducting phase transitionTransition temperaturePhysical SystemsHigh-temperature superconductorsLiquidsUnconventional superconductorsTechniquesDensity functional theoryEliashberg theoryGreen's function methodsCondensed Matter, Materials & Applied Physics

Multiscale simulations of singlet and triplet exciton dynamics in energetically disordered molecular systems based on many-body Green's functions theory

We present a multiscale model based on many-body Green’s functions theory in the GW approximation and the Bethe–Salpeter equation (GW-BSE) for the simulation of singlet and triplet exciton transport in molecular materials. Dynamics of coupled electron–hole pairs are modeled as a sequence of incoherent tunneling and decay events in a disordered morphology obtained at room temperature from molecular dynamics. The ingredients of the rates associated to the events, i.e. reorganization energies, site energies, lifetimes, and coupling elements, are determined from a combination of GW-BSE and classical polarizable force field techniques. Kinetic Monte Carlo simulations are then employed to evaluate dynamical properties such as the excitonic diffusion tensor and diffusion lengths. Using DCV5T-Me(3,3), a crystalline organic semiconductor, we demonstrate how this multiscale approach provides insight into the fundamental factors driving the transport processes. Comparing the results obtained via different calculation models, we investigate in particular the effects of charge-transfer mediated high exciton coupling and the influence of internal site energy disorder due to conformational variations. We show that a small number of high coupling elements indicative of delocalized exciton states does not impact the overall dynamics perceptively. Molecules with energies in the tail of the excitonic density of states dominate singlet decay, independent of the level of disorder taken into account in the simulation. Overall, our approach yields singlet diffusion lengths on the order of 10 nm as expected for energetically disordered molecular materials.

Local ultraconvergence of linear and bilinear finite element method for second order elliptic problems

In this article, local ultraconvergence in gradient of the bilinear and linear finite element solutions to two-dimensional second order elliptic problems has been investigated. Special interpolation postprocessing algorithms of numerical solutions by Richardson extrapolation have been developed. The local symmetry theory and estimates of discrete Green functions are used in the analysis. Numerical experiments are provided to confirm the theoretical findings.

Quantitative predictions of photoelectron spectra in amorphous molecular solids from multiscale quasiparticle embedding

We present a first-principles-based multiscale simulation framework for quantitative predictions of the high-energy part of the Ultraviolet Photoelectron Spectroscopy (UPS) spectra of amorphous molecular solids. The approach combines a deposition simulation, many-body Green's Function Theory, polarizable film-embedding, and multimode electron-vibrational coupling and provides a molecular-level view on the interactions and processes giving rise to spectral features. This insight helps bridging the current gap between experimental UPS and theoretical models as accurate analyses are hampered by the energetic disorder, surface-sensitivity of the measurement and the complexity of excitation processes. In particular this is relevant for the unambiguous determination the highest occupied molecular orbital energy (HOMO) of organic semiconductors, a key quantity for tailoring and engineering new opto-electronic devices. We demonstrate the capabilities of the simulation approach studying the spectrum of two isomers of 2-methyl-9,10-bis(naphthalen-2-yl)anthracene (MADN) as archetypical materials showing a clearly separated HOMO peak in experiment. The agreement with experiment is excellent, suggesting that our approach provides a route for determining the HOMO energy with an accuracy better than 0.1eV.

Inorganic photovoltaic cells based on BiFeO3: spontaneous polarization, lattice matching, light polarization and their relationship with photovoltaic performance.

Inorganic ferroelectric perovskite oxides are more stable than hybrid perovskites. However, their solar energy harvesting efficiency is not so good. Here, by constructing a series of BiFeO3-based devices (solar cells), we investigated three factors that influence the photovoltaic performance, namely, spontaneous polarization, terminated ion species in the interface between BiFeO3 and the electrode, and polarized light irradiation. This work was carried out under the framework of the density functional theory combined with the non-equilibrium Green's function theory under a built-in electric field or finite bias. The results showed that (1) the photocurrent is larger only under a suitable electronic band gap rather than larger spontaneous polarization; (2) the photocurrent reaches the largest value in the Bi3+ ion-terminated interface than in the case of Fe3+ or O2- with the SrTiO3 electrode; (3) the photocurrent can be largely enhanced if the polarized direction of the monochromatic light is perpendicular to the spontaneous polarization direction. These results would deepen the understanding of some experimental results of BiFeO3-based solar cells.

Analysis of the Breakdown of Exponential Decays of Resonances

In the paper, a simple model of alpha decay with Dirac delta potential is studied. The model leads to breakdown of the exponential decay and to power law behavior at asymptotic times. Time dependence of the survival probability of the particle in the potential well is analyzed numerically with two methods: integration of Green's function representation and numerical solution of the time-dependent Schr\odinger equation. In particular, finite depth potential wells and behavior between the exponential and power law regimes, which are situations that could not be described in detail analytically, are studied. The numerical results confirm power law with exponent n = 3 after the turnover into the non-exponential decay regime. Moreover, the constructive and destructive interference is observed in the intermediate stage of the process. The simple alpha decay model is compared to the results of Rothe- Hintschich-Monkman experiment which was the first experimental proof of violation of the exponential law.

Ensemble Green's function theory for interacting electrons with degenerate ground states

An ensemble Green's function formalism, based on the von Neumann density matrix approach, to calculate one-electron excitation spectra of a many-electron system with degenerate ground states is proposed. A set of iterative equations for the ensemble Green's function and self-energy is derived and a simplest approximation corresponding to an ensemble $GW$ approximation is naturally obtained. The derivation is based on the Schwinger functional derivative technique and does not assume any adiabatic connection between a noninteracting and an interacting ground state.

Nonadiabatic dynamics in strongly driven diffusive Josephson junctions

By measuring the Josephson emission of a diffusive Superconductor-Normal metal-Superconductor (SNS) junction at a finite temperature we reveal a non-trivial sensitivity of the supercurrent to microwave irradiation. We demonstrate that the harmonic content of the current-phase relation is modified due to the energy redistribution of quasiparticles in the normal wire induced by the electromagnetic field. The distortion originates from the phase-dependent out-of-equilibrium distribution function which is strongly affected by the ac-response of the spectral supercurrent. For phases close to $\pi$, transitions accross the Andreev gap are dynamically favored leading to a supercurrent reduction. This finding is supported by a comparison with the quasiclassical Green's function theory of superconductivity in diffusive SNS junctions under microwave irradiation.

Quantum hydrodynamics for plasmas—Quo vadis?

Quantum plasmas are an important topic in astrophysics and high pressure laboratory physics for more than 50 years. In addition, many condensed matter systems, including the electron gas in metals, metallic nanoparticles, or electron-hole systems in semiconductors and heterostructures, exhibit—to some extent—plasmalike behavior. Among the key theoretical approaches that have been applied to these systems are quantum kinetic theory, Green function theory, quantum Monte Carlo, semiclassical and quantum molecular dynamics, and more recently, density functional theory simulations. These activities are in close contact with the experiments and have firmly established themselves in the fields of plasma physics, astrophysics, and condensed matter physics. About two decades ago, a second branch of quantum plasma theory emerged that is based on a quantum fluid description and has attracted a substantial number of researchers. The focus of these studies has been on collective oscillations and linear and nonlinear waves in quantum plasmas. Even though these papers pretend to address the same physical systems as the more traditional papers mentioned above, the former appear to form a rather closed community that is largely isolated from the rest of the field. The quantum hydrodynamics (QHD) results have—with a few exceptions—not found application in astrophysics or in experiments in condensed matter physics. Moreover, these results practically did not have any impact on the former quantum plasma theory community. One reason is the unknown accuracy of the QHD for dense plasmas. In this paper, we present a novel derivation, starting from reduced density operators that clearly point to the deficiencies of QHD, and we outline possible improvements. It is also to be noted that some of the QHD results have attracted negative attention being criticized as unphysical. Examples include the prediction of “novel attractive forces” between protons in an equilibrium quantum plasma, the notion of “spinning quantum plasmas,” or the new field of “quantum dusty plasmas.” In the present article, we discuss the latter system in some detail because it is a particularly disturbing case of formal theoretical investigations that are detached from physical reality despite bold and unproven claims of importance for, e.g., dense astrophysical plasmas or microelectronics. We stress that these deficiencies are not a problem of QHD itself, which is a powerful and efficient method, but rather are due to ignorance of its properties and limitations. We analyze the common flaws of these works and come up with suggestions to improve the situation of QHD applications to quantum plasmas.

Photon statistics of a quantum emitter close to a lattice of plasmonic nanoparticles

We study theoretically the statistics of photons generated by a quantum emitter located in the vicinity of a periodic plasmonic nanostructure. The presented formalism is based on a macroscopic QED formalism in conjunction with a density-matrix approach in order to obtain the second-order correlation function of the emitted photons accounting for the influence of the plasmonic environment. The metallic reservoir coupling is computed using Green's-function theory, which, for a periodic lattice of scatterers, is calculated by a multiple-scattering method. We show that the photon statistics and the antibunching of emitted photons depend very strongly on the orientation of the quantum emitter relative to the lattice, on the transition frequency of the emitter, on the intensity of the applied field, and on the geometrical parameters of the nanoparticles, such as the shell thickness.

Phonon characteristics of Si‐doped InAs grown by gas‐source molecular beam epitaxy

AbstractUsing Raman scattering spectroscopy with 514‐ and 633‐nm light sources, we have studied the phonon characteristics of Si‐doped InAs films grown on (100) n‐type InAs by gas‐source molecular beam epitaxy having charge carrier concentration (n) between 2.26 × 1018 and 1.68 × 1020 cm−3. The unscreened longitudinal optical (LO) phonon is observed near ~238 cm−1 along with two plasmon‐LO‐phonon (PLP) coupled L± modes. With increasing n, the L− mode is downshifted from the LO phonon towards the transverse optical mode frequency. This abnormal behavior is ascribed to the large scattering vector and heavy Landau damping. The L+ mode close to the plasma frequency ωP is also detected in samples with n > 1019 cm−3. The observed unscreened LO mode in the forbidden configuration is attributed to the resonance enhanced scattering induced by surface space charge. Reliable values of charge carrier density and mobility are estimated from the simulated shifts of PLP modes in the low Si‐doped InAs films. At higher doping level, a full‐line shape analysis is desired for assessing accurate values of the transport parameters. In Si‐doped InAs, we appraised the existing experimental data of localized vibrational modes (LVMs) from Raman and Fourier transform infrared spectroscopy by exploiting a sophisticated Green's function theory and incorporating lattice relaxation effects around SiIn and SiAs defects for constructing accurate perturbation models. The simulated results of LVMs for several isolated (Td) defects, nearest neighbor pair (C3v), and next‐nearest neighbor complex centers (Cs) are compared, contrasted, and discussed with the experimental data.

Quantum embedding theory in the screened Coulomb interaction: Combining configuration interaction withGW/BSE

We present a quantum embedding theory called dynamical configuration interaction (DCI) that combines wave function and Green's function theories. DCI captures static correlation in a correlated subspace with configuration interaction and couples to high-energy, dynamic correlation outside the subspace with many-body perturbation theory based on Green's functions. DCI takes the strengths of both theories to balance static and dynamic correlation in a single, fully ab initio embedding concept. The theory adds dynamic correlation around a fixed active space of orbitals with efficient $\mathcal{O}({N}^{5})$ scaling, while maintaining a multireference treatment of the active space. We show that treating high-energy correlation up to the $GW$ and Bethe-Salpeter equation level is sufficient even for challenging multireference problems. Our theory treats ground and excited states on equal footing, and we compute the dissociation curve of ${\mathrm{N}}_{2}$, the vertical excitation energies of small molecules, and the ionization spectrum of benzene in excellent agreement with high-level quantum chemistry methods and experiment.

Stochastic resolution of identity second-order Matsubara Green's function theory.

We develop a stochastic resolution of identity representation to the second-order Matsubara Green's function (sRI-GF2) theory. Using a stochastic resolution of the Coulomb integrals, the second order Born self-energy in GF2 is decoupled and reduced to matrix products/contractions, which reduces the computational cost from O(N5) to O(N3) (with N being the number of atomic orbitals). The current approach can be viewed as an extension to our previous work on stochastic resolution of identity second order Møller-Plesset perturbation theory [T. Y. Takeshita et al., J. Chem. Theory Comput. 13, 4605 (2017)] and offers an alternative to previous stochastic GF2 formulations [D. Neuhauser et al., J. Chem. Theory Comput. 13, 5396 (2017)]. We show that sRI-GF2 recovers the deterministic GF2 results for small systems, is computationally faster than deterministic GF2 for N > 80, and is a practical approach to describe weak correlations in systems with 103 electrons and more.

Determination of a Time-Dependent Free Boundary in a Two-Dimensional Parabolic Problem

The retrieval of the timewise-dependent intensity of a free boundary and the temperature in a two-dimensional parabolic problem is, for the first time, numerically solved. The measurement, which is sufficient to provide a unique solution, consists of the mass/energy of the thermal system. A stability theorem is proved based on the Green function theory and Volterra’s integral equations of the second kind. The resulting nonlinear minimization is numerically solved using the $$\textit{lsqnonlin}$$ MATLAB optimization routine. The results illustrate the reliability, in terms of accuracy and stability, of the time-dependent free surface reconstruction.