Quasiparticle Shifts Research Articles

Tuning of excitons in phosphorene atomic chains

An universal scaling between the exciton binding energy and quasiparticle (QP) band gap was first discovered in two-dimensional (2D) semiconductors such as graphene derivatives, various transition materials dichalcogenides, and black phosphorus (Choi et al 2015 Phys. Rev. Lett. 115 066403; Jiang et al 2017 Phys. Rev. Lett. 118 266401), and later extended to quasi one-dimensional (1D) systems such as carbon nanotubes and graphene nanoribbons. In this work we study the excitonic states in phosphorene atomic chains by using the exact diagonalization method and show that the linear scaling between the exciton binding energy (Ex ) and QP shift () can be easily tuned by the dielectric environment. In the presence of weak screening, Ex is seen to increase with and exhibits a similar scaling as those 2D materials. As the screening becomes stronger, however, the dependence is found to be reversed, i.e. Ex now decreases when increases. More interestingly, we also reveal that Ex may even become nearly constant, independent on the system dimension and when the screening reaches a certain strength. These abnormal scaling relations are attributed to the complex nature of excitons in the strongly correlated 1D system.

High-temperature self-energy corrections to x-ray absorption spectra

Effects of finite-temperature quasiparticle self-energy corrections on x-ray absorption spectra are investigated within the finite-temperature quasiparticle local density $GW$ approximation up to temperatures $T$ of order the Fermi temperature. To facilitate the calculations, we parametrize the quasiparticle self-energy using low-order polynomial fits. We show that temperature-driven decrease in the electron lifetime substantially broadens the spectra in the near-edge region with increasing $T$. However, the quasiparticle shift is most strongly modified near the onset of plasmon excitations.

One-dimensional excitons in long phosphorene atomic chains

The electronic structure of phosphorene atomic chains (PACs) embedded in various dielectric environments is studied theoretically by using a configuration interaction approach beyond the conventional double-excitation scheme. While the nominal single-particle gap of the PACs is shown to roughly obey an expected scaling law of ${L}^{\ensuremath{-}2}$, where $L$ measures the length of PACs, the quasiparticle shift is found to gradually converge to a value that is insensitive to the dielectric environment as $L$ increases. In the meantime, exciton binding energies are revealed to obey a simple scaling law of $0.96/(\ensuremath{\kappa}L)\ensuremath{-}0.02$, with $\ensuremath{\kappa}$ being the effective dielectric constant. As $L$ goes to infinity, the quasiparticle and excitonic effect are both found to be greatly suppressed as if the long-range electron-electron interactions are quenched in long PACs.

Finite-temperature full random-phase approximation of bandgap narrowing in quasi-neutral regions: Theory including nonparabolicity and application to silicon and InGaAs

The bandgap narrowing (BGN) in quasi-neutral regions of semiconductors is calculated in a finite-temperature full random-phase approximation formalism based on a simple isotropic dispersion model including band nonparabolicity. The total quasi-particle shift (QPS) is determined by the exchange-correlation self-energy of the free carriers and the correlation energy of the interaction between carriers and ionized dopants. At cryogenic temperatures, the latter part results in giant shifts of the minority band edge in n-type semiconductors with a large ratio of valence to conduction band density of states, as often present in III–V materials. However, at room temperature, the BGN does not exceed common values. The reason for this behavior is explained analytically. Whereas the exchange-correlation energy of free carriers is known to be insensitive to band structure details, the nonparabolicity of the conduction band (CB) has a strong effect on the ionic QPS of the minority carriers in n-type III–V materials. It strongly reduces the BGN at cryogenic temperatures compared to the case of a parabolic CB. This is demonstrated numerically and also analytically for n-type InGaAs. The BGN in n-type silicon becomes independent of temperature at high concentrations, but in p-type silicon, a weak temperature dependence re-emerges above the Mott density, which also can be attributed to the ionic QPS of the minority electrons. The calculated BGN for quasi-neutral regions in silicon is in good agreement with earlier photoluminescence and more recent photo-conductance measurements.

Negative quasiparticle shifts in phosphorene quantum dots

It is commonly believed that electron correlations would open up a quasiparticle gap in semiconductors. Contrary to this intuitive expectation, here we reveal that phosphorene quantum dots (PQDs) may exhibit just the opposite effect. By using a configuration interaction approach beyond the conventional double-excitation scheme, quasiparticle energies are calculated for hexagonal and rectangular PQDs in various dielectric environments. For the hexagonal PQD with a nominal gap of 2.26 eV, it is found that the quasiparticle shift decreases by more than 500 meV and eventually becomes negative when the effective dielectric constant is reduced from 20.0 to 5.0. For other trapezoidal, triangular, and rectangular PQDs, the quasiparticle shift exhibits a similar amount of decrement after the same change in the dielectric environment. Furthermore, the calculation by adopting the Rytova-Keldysh potential, which may be more suitable to describe two-dimensional screening, also shows a very similar result, although with smaller decrement of the quasiparticle shift. The origin of this anomalous quasiparticle shift is believed to be related to the long-range electron-electron interactions in the distinctive lattice structure of PQDs, as a similar phenomenon has never been found in graphene quantum dots.

Relationships between Orbital Energies, Optical and Fundamental Gaps, and Exciton Shifts in Approximate Density Functional Theory and Quasiparticle Theory.

The relationships between Kohn-Sham (KS) and generalized KS (GKS) density functional orbital energies and fundamental gaps or optical gaps raise many interesting questions including the physical meanings of KS and GKS orbital energies when computed with currently available approximate density functionals (ADFs). In this work, by examining three diverse databases with various ADFs, we examine such relations from the point of view of the exciton shift of quasiparticle theory. We start by calculating a large number of excitation energies by time-dependent density functional theory (TDDFT) with a large number of ADFs. To relate the exciton shift implicit in TDDFT to the exciton shift that is explicit in Green's function theory, we define the exciton shift in TDDFT as the difference of the response shift and the quasiparticle shift. We found a strong correlation between the response shift and the amount of Hartree-Fock exchange included in the density functional, with the response shift varying between -1 and 5 eV. This range is an order of magnitude larger than the mean errors of the TDDFT excitation energies. This result suggests that, with currently available functionals, the KS or GKS orbital energies should be treated as intermediate mathematical variables in the calculation of excitation energies rather than as the energies of independent-particle reference states for quasiparticle theory.

Beyond Mean-Field Corrections to the Quasiparticle Spectrum of Superfluid Fermi Gases.

We investigate the fermionic quasiparticle branch of superfluid Fermi gases in the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) crossover and calculate the quasiparticle lifetime and energy shift due to its coupling with the collective mode. The only close-to-resonance process that low-energy quasiparticles can undergo at zero temperature is the emission of a bosonic excitation from the phononic branch. Close to the minimum of the branch we find that the quasiparticles remain undamped, allowing us to compute corrections to experimentally relevant quantities such as the energy gap, location of the minimum, effective mass, and Landau critical velocity.

Quasiparticle and excitonic effects in the optical response of KNbO3

The cubic, tetragonal, and orthorhombic phase of potassium niobate (${\mathrm{KNbO}}_{3}$) are studied based on density-functional theory. Starting from the relaxed atomic geometries, we analyze the influence of self-energy corrections on the electronic band structure within the $GW$ approximation. We find that quasiparticle shifts widen the direct (indirect) band gap by 1.21 (1.44), 1.58 (1.55), and 1.67 (1.64) eV for the cubic, tetragonal, and orthorhombic phase, respectively. By solving the Bethe-Salpeter equation, we obtain the linear dielectric function with excitonic and local-field effects, which turn out to be essential for good agreement with experimental data. From our results, we extract an exciton binding energy of 0.6, 0.5, and 0.5 eV for the cubic, tetragonal, and orthorhombic phase, respectively. Furthermore, we investigate the nonlinear second-harmonic generation (SHG) both theoretically and experimentally. The frequency-dependent second-order polarization tensor of orthorhombic ${\mathrm{KNbO}}_{3}$ is measured for incoming photon energies between 1.2 and 1.6 eV. In addition, calculations within the independent-(quasi)particle approximation are performed for the tetragonal and orthorhombic phase. The novel experimental data are in excellent agreement with the quasiparticle calculations and resolve persistent discrepancies between earlier experimental measurements and ab initio results reported in the literature.

Excitonic effects in third-harmonic generation: The case of carbon nanotubes and nanoribbons

Linear and nonlinear optical properties of low-dimensional nanostructures have attracted great interest from the scientific community as tools to probe the strong confinement of electrons and for possible applications in optoelectronic devices. In particular it has been shown that the linear optical response of carbon nanotubes [F. Wang et al., Science 308, 838 (2005)] and graphene nanoribbons [Nat. Commun. 5 4253 (2014)] is dominated by bounded electron-hole pairs, excitons. The role of excitons in linear response has been widely studied, but still, little is known about their effect on nonlinear susceptibilities. Using a recently developed methodology [Phys. Rev. B 88, 235113 (2013)] based on well-established ab initio many-body perturbation theory approaches, we find that quasiparticle shifts and excitonic effects significantly modify the third-harmonic generation in carbon nanotubes and graphene nanoribbons. For both systems the net effect of many-body effects is to reduce the intensity of the main peak in the independent-particle spectrum and redistribute the spectral weight among several excitonic resonances.

Excitation spectra of aromatic molecules within a real-spaceGW-BSE formalism: Role of self-consistency and vertex corrections

We present first-principles calculations on the vertical ionization potentials (IPs), electron affinities (EAs), and singlet excitation energies on an aromatic-molecule test set (benzene, thiophene, 1,2,5-thiadiazole, naphthalene, benzothiazole, and tetrathiafulvalene) within the $GW$ and Bethe-Salpeter equation (BSE) formalisms. Our computational framework, which employs a real-space basis for ground-state and a transition-space basis for excited-state calculations, is well suited for high-accuracy calculations on molecules, as we show by comparing against ${G}_{0}{W}_{0}$ calculations within a plane-wave-basis formalism. We then generalize our framework to test variants of the $GW$ approximation that include a local density approximation (LDA)--derived vertex function (${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{LDA}}$) and quasiparticle-self-consistent (QS) iterations. We find that ${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{LDA}}$ and quasiparticle self-consistency shift IPs and EAs by roughly the same magnitude, but with opposite sign for IPs and the same sign for EAs. ${G}_{0}{W}_{0}$ and $\mathrm{QS}GW{\mathrm{\ensuremath{\Gamma}}}_{\mathrm{LDA}}$ are more accurate for IPs, while ${G}_{0}{W}_{0}{\mathrm{\ensuremath{\Gamma}}}_{\mathrm{LDA}}$ and $\mathrm{QS}GW$ are best for EAs. For optical excitations, we find that perturbative $GW$-BSE underestimates the singlet excitation energy, while self-consistent $GW$-BSE results in good agreement with previous best-estimate values for both valence and Rydberg excitations. Finally, our work suggests that a hybrid approach, in which ${G}_{0}{W}_{0}$ energies are used for occupied orbitals and ${G}_{0}{W}_{0}{\mathrm{\ensuremath{\Gamma}}}_{\mathrm{LDA}}$ for unoccupied orbitals, also yields optical excitation energies in good agreement with experiment but at a smaller computational cost.

Clusters in nuclear matter and Mott points

Light clusters (mass number A ≤ 4) in nuclear matter at subsaturation densities are described using a quantum statistical approach. In addition to self-energy and Pauli-blocking, effects of continuum correlations are taken into account to calculate the quasiparticle properties and abundances of light elements. Medium-modified quasiparticle properties are important ingredients to derive a nuclear matter equation of state applicable in the entire region of warm dense matter below saturation density. The influence of the nucleon—nucleon interaction on the quasiparticle shift is discussed.

Doping dependence of correlation effects in K1 − x Fe2 − y Se2 superconductors: LDA’ + DMFT investigation

We present detailed LDA'+DMFT investigation of doping dependence of correlation effects in novel K{1-x}Fe{2-y}Se2 superconductor. Calculations were performed at four different hole doping levels, starting from hypothetical stoichiometric composition with total number of electrons equal to 29 per unit cell through 28 and 27.2 electrons towards the case of 26.52, which corresponds to chemical composition K{0.76}Fe{1.72}Se2 studied in recent ARPES experiments. In general case the increase of hole doping leads to quasiparticle bands in wide energy window +/-2 eV around the Fermi level becoming more broadened by lifetime effects, while correlation induced compression of Fe-3d LDA' bandwidths stays almost the same and of the order of ~1.3 for all hole concentrations. However close to the Fermi level situation is more complicated. Here in the energy interval from -1.0 eV to 0.4 eV the bare Fe-3d LDA' bands are compressed by significantly larger renormalization factors up to 5 with hole doping increase, while the value of Coulomb interaction remains the same. This fact manifests the increase of correlation effects with hole doping in K{1-x}Fe{2-y}Se2 system. Moreover in contrast to typical pnictides K{1-x}Fe{2-y}Se2 does not have well defined quasiparticle bands on the Fermi leves but pseudogap like "dark" region instead. We also find that with the growth of hole doping Fe-3d orbitals of various symmetries are affected by correlations in a different way in different parts of Brillouin zone. To illustrate this we determine quasiparticle mass renormalization factors and energy shifts, which transform the bare Fe-3d LDA' bands of various symmetries into LDA'+DMFT quasiparticle bands. These renormalization factors effectively mimic more complicated energy dependent self-energy effects and can be used to analyze the available ARPES data.

Electronic Spectra of Iron Pnictide Superconductors: Influence of Multi-orbitals Hopping and Hund’s Coupling

We present a theoretical study of the electronic spectral function of iron-pnictide superconductors like LaFeAs(O, F) material. We have attempted two-band tight-binding model Hamiltonian containing various orbitals hopping energies, intra- and inter-band electronic correlations and Hund’s coupling energy in Fe 3d orbitals. The expression of a single particle spectral function within BCS-mean-field Green’s function approach for superconducting state of iron pnictides is obtained. The spectral function at different points of the Brillouin zone is numerically calculated for extended s-wave pairing symmetry as a function of various model parameters applicable for these systems. It is pointed out through numerical analysis that on increasing nearest-neighbor hopping (t1) between (dxz/dyz) σ-orbitals, the spectral function A(k,ω) shifts towards the Fermi level and provides favorable conditions for band splitting effects in the form of two well separated peaks in the electronic spectral as observed in iron pnictides angle-resolved photoemission spectroscopic (ARPES) measurements. On increasing t2 (nearest-neighbor hopping between dxz/dyzπ-orbitals), the spectral function shows prominent peak with increase in spectral weight close to the Fermi level at the (π,0) and (0,0) points of the Brillouin zone, while the quasi-particle peak shifts away from the Fermi level at the (π,π) point with decreased spectral weight. The bonding peak of spectral function get suppressed while the antibonding spectral peak becomes prominent with increasing t3 (next nearest-neighbor hopping between same orbitals of dxz/dyz) at (π,π) of the Brillouin zone. Further, intra-band Coulomb correlations shift the spectral peak downward with respect to Fermi level along with suppression of the spectral weight. The Hund’s coupling term try to pile up spectral weight close to Fermi level and support to stabilize superconducting state in these systems. The variation of the spectral function within the two-band model is in qualitative accordance with existing ARPES measurements and theoretical investigations in iron-pnictide superconductors.

2-Aminopyrimidine-silver(I) based organic semiconductors: Electronic structure and optical response

Calculations based on (occupation constrained) density functional theory using local as well as hybrid functionals to describe the electron-electron exchange and correlation are combined with many-body perturbation theory in order to determine and rationalize the electronic and optical excitation properties of 2-aminopyrimidine-silver(I) based organic semiconductors and their parent molecules. Large quasiparticle shifts and exciton binding energies of about 4 eV are found in the aminopyrimidine molecules. Both the quasiparticle blueshift and the excitonic redshift are reduced upon crystal formation. They cancel each other partially and thus allow for a meaningful description of the molecular and crystal optical response within the independent-particle approximation. We find a surprisingly strong influence of local-field effects as well as resonant-nonresonant coupling terms in the electron-hole Hamiltonian on the optical properties. The calculations reproduce well measured data and allow for identifying chemical trends with respect to the organic building blocks of the crystals.

Parametrization of light nuclei quasiparticle energy shifts and composition of warm and dense nuclear matter

Correlations and the formation of bound states (nuclei) are essential for the properties of nuclear matter in equilibrium as well as in nonequilibrium. In a quantum statistical approach, quasiparticle energies are obtained for the light elements that reflect the influence of the medium. We present analytical fits for the quasiparticle energy shifts of light nuclei that can be used in various applications. This is a prerequisite for the investigation of warm and dense matter that reproduces the nuclear statistical equilibrium and virial expansions in the low-density limit as well as relativistic mean field and Brueckner Hartree-Fock approaches near saturation density.

LIGHT CLUSTERS IN NUCLEAR MATTER

Nuclei in dense matter are influenced by the medium. In the cluster mean-field approximation, an effective Schrodinger equation for the A-nucleon cluster is obtained accounting for the effects of the surrounding medium, such as self-energy and Pauli blocking. Similar to the single-baryon states (free protons and neutrons), the light elements (A ≤ 4) are treated as quasiparticles. Fit formulae are given for the quasiparticle shifts as function of temperature, density, asymmetry, and momentum. Composition, quantum condensates and thermodynamic functions are considered. The relevance for nuclear structure, heavy ion collisions and supernova astrophysics is shown.

Many-bodyGWcalculation of the oxygen vacancy in ZnO

Density functional theory (DFT) calculations of defect levels in semiconductors based on approximate functionals are subject to considerable uncertainties, in particular due to inaccurate band gap energies. Testing previous correction methods by many-body GW calculations for the O vacancy in ZnO, we find that: (i) The GW quasi-particle shifts of the VO defect states increase the spitting between occupied and unoccupied states due to self-interaction correction, and do not reflect the conduction versus valence band character. (ii) The GW quasi-particle energies of charged defect states require important corrections for supercell finite size effects. (iii) The GW results are robust with respect to the choice of the underlying DFT or hybrid-DFT functional, and the (2+/0) donor transition lies below mid-gap, close to our previous prediction employing rigid band edge shifts.

Light nuclei quasiparticle energy shifts in hot and dense nuclear matter

Nuclei in dense matter are influenced by the medium. In the cluster mean-field approximation, an effective Schr\odinger equation for the $A$-particle cluster is obtained accounting for the effects of the correlated medium such as self-energy, Pauli blocking, and Bose enhancement. Similar to the single-baryon states (free neutrons and protons), the light elements ($2\ensuremath{\leqslant}A\ensuremath{\leqslant}4$, internal quantum state \ensuremath{\nu}) are treated as quasiparticles with energies ${E}_{A,\ensuremath{\nu}}(\mathbf{P};T,{n}_{n},{n}_{p})$. These energies depend on the center-of-mass momentum $\mathbf{P}$, as well as temperature $T$ and the total densities ${n}_{n}$, ${n}_{p}$ of neutrons and protons, respectively. No $\ensuremath{\beta}$ equilibrium is considered so that ${n}_{n}$, ${n}_{p}$ (or the corresponding chemical potentials ${\ensuremath{\mu}}_{n}$, ${\ensuremath{\mu}}_{p}$) are fixed independently. For the single-nucleon quasiparticle energy shift, different approximate expressions such as Skyrme or relativistic mean-field approaches are well known. Treating the $A$-particle problem in appropriate approximations, results for the cluster quasiparticle shifts are given. Properties of dense nuclear matter at moderate temperatures in the subsaturation density region considered here are influenced by the composition. This in turn is determined by the cluster quasiparticle energies, in particular the formation of clusters at low densities when the temperature decreases and their dissolution due to Pauli blocking as the density increases. Our finite-temperature Green function approach covers different limiting cases: the low-density region where the model of nuclear statistical equilibrium and virial expansions can be applied and the saturation-density region where a mean-field approach is possible.

Strain influence on valence-band ordering and excitons in ZnO: An ab initio study

Modern parameter-free methods to treat single- and two-particle electronic excitations are applied to compute the band structure and the lowest optical transitions of wurtzite ZnO under biaxial strain. The calculations are based on density functional theory with a spatially nonlocal exchange and correlation functional and include spin-orbit interaction. Quasiparticle shifts and excitonic effects are computed. In addition to the band parameters, also their dependence on biaxial strain and the ordering of the A, B, and C excitons are investigated. While the crystal-field splitting is very sensitive to strain, the spin-orbit splittings and the exciton binding energies remain unaffected.

Angle‐resolved photoemission on ZnSe(001): determination of conduction band quasiparticle shifts

AbstractAngle‐resolved photoemission measurements have been performed on the ZnSe(001) surface and analyzed using ab initio LDA and GW calculations. The key point of this analysis consists of a comparison between measured and calculated photoemission spectra. We suggest that matching the main dispersive peaks in experiment and theory leads to the determination of quasiparticle shifts of the conduction bands relative to their LDA position. It is found that these experimental shifts largely exceed the calculated GW‐quasiparticle shifts leading to an increased free‐electron‐like character of the photoemission final states as compared to the LDA calculations. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)