Two-particle Green Function Research Articles

Some exact identities connecting one- and two-particle Green's functions in spin–orbit coupling systems

Some exact identities connecting the one- and two-particle Green's functions in the presence of spin-orbit coupling have been derived. These identities is similar to the usual Ward identity in the particle or charge transport theory and a satisfying spin transport theory in spin-orbit coupling system should also preserve these identities.

Electronic excitations of theH:Si(001)−(2×1)monohydride surface: First-principles calculations

We investigate electronic excitations of the H:Si(001)-(2x1) monohydride surface using first-principles approaches. Density-functional theory is used to calculate the ground-state geometry of the system. The quasiparticle band structure is calculated within the GW approximation. Taking the electron-hole interaction into account, electron-hole pair states and optical excitations are obtained from the solution of the Bethe-Salpeter equation for the electron-hole two-particle Green's function. In this work we focus, in particular, on localized excitations of the silicon-hydrogen bonds at the surface layer. These excitations give rise to an outward-directed force on the hydrogen atoms, which may well explain their optically induced desorption from the surface as observed in recent experiments. The localization of the excitation is described by an artificial confinement potential in addition to standard many-body perturbation theory.

Polariton–polariton kinematic interaction modulation and kinematic bipolaritons in organic microcavities

We study polariton–polariton kinematic interactions in organic microcavities. Using the Agranovich–Toshich transformation, to transform the Frenkel excitons from Paulions into Bosons, the exciton–exciton kinematic interaction is derived. In the strong coupling regime, the polariton excitonic part results in the polariton–polariton kinematic interaction. The scattering amplitude is calculated and the effective potential is obtained for a scattering between two free polaritons. The effective potential can be modulated by changing the exciton-cavity photon detuning, and we show the crossover of the effective potential from attractive into repulsive one. A pole in the two-particle Green's function is the signature of the formation of polariton bound state, i.e. bipolariton. Due to the smallness of the polariton effective mass, the obtained bound state is very shallow and appears below the minimum of the lower polariton branch, and falls inside the natural bandwidth of the polariton branch.

AB-INITIOSTUDY ON THE EXCITON BINDING ENERGIES IN ORGANIC SEMICONDUCTORS

In this work, the optical properties including excitonic effects of organic semiconductors investigated within an ab-initio framework are reviewed. In particular, the imaginary part of the frequency-dependent dielectric tensor has been calculated for several organic molecular crystals consisting of short molecules and polymers, which comprise prime examples for the versatile class of organic semiconductors. The electron-hole interaction has been included by solving the Bethe–Salpeter equation for the two-particle Green's function. This approach allows for the evaluation of the exciton binding energies in such materials, which are of major interest concerning their technological application in organic opto-electronic devices. The results presented herein are compared to experimental data and surveyed together with previously reported theoretical findings, where particular emphasis is placed on analyzing the sensitivity of different approximations applied in the theoretical approaches. In this context, first the influence of the three-dimensional crystal environment versus one dimensional chains is addressed for the polymers. Second, the dependence of the exciton binding energy on the molecular size is studied by comparing the results obtained for the oligomers to those found for the polymers. As last aspect, the influence of the intermolecular interaction on the exciton binding energies is investigated by applying hydrostatic pressure.

Huge Excitonic Effects in Layered Hexagonal Boron Nitride

The all-electron GW approximation energy band gap of bulk hexagonal boron nitride is shown to be of indirect type. The resulting computed in-plane polarized optical spectrum, obtained by solving the Bethe-Salpeter equation for the electron-hole two-particle Green function, is in excellent agreement with experiment and has a strong anisotropy compared to out-of-plane polarized spectrum. A detailed analysis of the excitonic structures within the band gap shows that the low-lying excitons belong to the Frenkel class and are tightly confined within the layers. The calculated exciton binding energy is much larger than that obtained by Watanabe et al. [Nat. Mater. 3, 404 (2004).] based on a Wannier model assuming h-BN to be a direct-band-gap semiconductor.

Many-fermion generalization of the Caldeira-Leggett model

We analyze a model system of fermions in a harmonic oscillator potential under the influence of a dissipative environment: The fermions are subject to a fluctuating force deriving from a bath of harmonic oscillators. This represents an extension of the well-known Caldeira-Leggett model to the case of many fermions. Using the method of bosonization, we calculate one- and two-particle Green's functions of the fermions. We discuss the relaxation of a single extra particle added above the Fermi sea, considering also dephasing of a particle added in a coherent superposition of states. The consequences of the separation of center-of-mass and relative motion, the Pauli principle, and the bath-induced effective interaction are discussed. Finally, we extend our analysis to a more generic coupling between system and bath, that results in complete thermalization of the system.

Entanglement of electron spins in superconductors

We investigate entanglement of two electron spins forming Cooper pairs in an s-wave superconductor. The two-electron space-spin density matrix is obtained from the BCS ground state using a two-particle Green's function. It is demonstrated that a two spin state is not given by a spin singlet state but by a Werner state. It is found that the entanglement length, within which two spins are entangled, is not the order of the coherence length but the order of the Fermi wave length.

The two-particle propagator and magnetic susceptibility in the Hubbard model

We treat the two-particle Green function in the Hubbard model using the recently developedτ-CPA, a hybrid treatment that applies the coherent potential approximation (CPA) up to a timeτ related to the inverse of the bandwidth, after which the system is averaged using the virtualcrystal approximation. This model, with suitable approximations, does predict magnetismfor a modified Stoner criterion. The evaluation of the two-particle propagator in theτ-CPA requires the solution of the pure CPA, within whose formalism the vertex correctionand the weighted Green functions are obtained. The dynamical susceptibility, including thevertex correction and the weighted scattering by the residual interaction, is calculated andshows a spin wave spectrum in the ferromagnetic regime.

Minimally self-consistent T-matrix approximation to describe the low-temperature properties of the Hubbard model in the atomic limit

The atomic limit of the Hubbard model is a simple single-site problem which can be solved exactly, and all one- and two-particle Green's functions can be obtained analytically. These solutions can thus serve as a means of critiquing the success of various approximate theories which might be applied to the full Hubbard model. In particular, we have examined the $T$-matrix approximation for the attractive Hubbard model in the atomic limit, which should give reasonable results at low electronic densities, if one can avoid the spurious phase transition that results when a fully non-self-consistent $T$-matrix approximation is employed---previously we have shown that any level of self-consistency guarantees that this phase transition is correctly suppressed to zero temperature in two dimensions or less. Here, a minimally self-consistent $T$-matrix approximation is shown to be successful in reproducing the exact results for the atomic limit, while fully self-consistent $T$-matrix results do not agree with the known solutions. Of particular note is that the minimally self-consistent $T$-matrix approximation reproduces not only one- and two-particle (static) thermodynamic quantities, but it also exactly reproduces the one-particle spectral function at low but nonzero temperatures. We also make a comparison to the two-particle self-consistent approach of Vilk and Tremblay, and find that the minimally self-consistent $T$-matrix theory can give better results over a broader temperature range.

Coulomb scattering cross section in a two-dimensional electron gas and production of entangled electrons

We calculate the Coulomb scattering amplitude for two electrons injected with opposite momenta in an interacting 2DEG. We include the effect of the Fermi liquid background by solving the 2D Bethe-Salpeter equation for the two-particle Green function vertex, in the ladder and random phase approximations. This result is used to discuss the feasibility of producing spin EPR pairs in a 2DEG by collecting electrons emerging from collisions at a pi/2 scattering angle, where only the entangled spin-singlets avoid the destructive interference resulting from quantum indistinguishability. Furthermore, we study the effective 2D electron-electron interaction due to the exchange of virtual acoustic and optical phonons, and compare it to the Coulomb interaction. Finally, we show that the 2D Kohn-Luttinger pairing instability for the scattering electrons is negligible in a GaAs 2DEG.

Femtosecond dynamics of excited states ofCOadsorbed onMgO(001)‐(1×1)

We have investigated the time development of excited electronic states of $\mathrm{C}\mathrm{O}$ molecules adsorbed on the $\mathrm{Mg}\mathrm{O}(001)\text{--}(1\ifmmode\times\else\texttimes\fi{}1)$ surface using a state-of-the-art first principles approach. Density-functional theory is used to calculate the ground state geometry of the clean surface and of the molecules adsorbed on the surface. Thereafter, the quasiparticle band structures of bulk MgO, of the $\mathrm{Mg}\mathrm{O}(001)\text{--}(1\ifmmode\times\else\texttimes\fi{}1)$ surface, and of $\mathrm{C}\mathrm{O}$ adsorbed on the surface are calculated within the GW approximation. Taking the electron-hole interaction into consideration the electron-hole excitations and their optical spectrum are obtained from the solution of the Bethe-Salpeter equation for the electron-hole two-particle Green function. The optical spectra of bulk MgO, the $\mathrm{Mg}\mathrm{O}(001)\text{--}(1\ifmmode\times\else\texttimes\fi{}1)$ surface, and $\mathrm{C}\mathrm{O}$ adsorbed on the surface are calculated, yielding good agreement with available experimental data. Finally, based on the solution of the BSE for the adsorbate system $\mathrm{C}\mathrm{O}:\mathrm{Mg}\mathrm{O}(001)\text{--}(1\ifmmode\times\else\texttimes\fi{}1)$, the time propagation of molecular excitations is studied employing the time-dependent Schr\odinger equation. An initial $\mathrm{C}\mathrm{O}$ excitation exhibits a very fast decay due to its coupling to charge-transfer exciton states between the substrate and the adsorbate. The decay is characterized by a lifetime of about 1.6 fs, which is a factor of 5 faster than the decay of single-particle states.

Dispersion of the dielectric function of a charge-transfer insulator

We study the problem of dielectric response in the strong-coupling regime of a charge-transfer insulator. The frequency and wave-number dependence of the dielectric function $\ensuremath{\varepsilon}(\mathbf{q},\ensuremath{\omega})$ and its inverse ${\ensuremath{\varepsilon}}^{\ensuremath{-}1}(\mathbf{q},\ensuremath{\omega})$ is the main object of consideration. We show that the problem, in general, cannot be reduced to a calculation within the Hubbard model, which takes into account only a restricted number of electronic states near the Fermi energy. The contribution of the rest of the system to the longitudinal response [i.e., to ${\ensuremath{\varepsilon}}^{\ensuremath{-}1}(\mathbf{q},\ensuremath{\omega})]$ is essential for the whole frequency range. With the use of the spectral representation of the two-particle Green's function we show that the problem may be divided into two parts: into the contributions of the weakly correlated subsystem and the Hubbard subsystem. For the latter we propose an approach that starts from the correlated paramagnetic ground state with strong antiferromagnetic fluctuations. We obtain a set of coupled equations of motion for the two-particle Green's function that may be solved by means of the projection technique. The solution is expressed by a two-particle basis that includes the excitonic states with electron and hole separated at various distances. We apply our method to the multiband Hubbard (Emery) model that describes layered cuprates. We show that strongly dispersive branches exist in the excitonic spectrum of the ``minimal'' Emery model ${(1/U}_{d}{=U}_{p}{=t}_{\mathrm{pp}}=0)$ and consider the dependence of the spectrum on finite oxygen hopping ${t}_{\mathrm{pp}}$ and on-site repulsion ${U}_{p}.$ The relationship of our calculations to electron-energy-loss spectroscopy is discussed.

Density and current response functions in strongly disordered electron systems: diffusion, electrical conductivity and Einstein relation

We study noninteracting quantum charged particles (electron gas) subject to a strong random potential and perturbed by a weak classical electromagnetic field. We examine consequences of gauge invariance and charge conservation in the space of Bloch waves. We use two specific forms of the Ward identity between the one- and two-particle averaged Green functions to establish exact relations between the density and current response functions. In particular, we find precise conditions under which we can extract the current-current from the density-density correlation functions and vice versa. We use these results to prove a formula relating the density response and the electrical conductivity in strongly disordered systems. We introduce quantum diffusion as a response function that reduces to the diffusion constant in the static limit. We then derive Fick’s law, a quantum version of the Einstein relation and prove the existence of the diffusion pole in the quasistatic limit of the zero-temperature electron-hole correlation function. We show that the electrical conductivity controls the long-range spatial fluctuations of the electron-hole correlation function only in the static limit.

Fluctuating Order Parameter in Doped Cuprate Superconductors

We discuss the static fluctuations of the d-wave superconducting order parameter Δ in CuO 2 planes, due to quasiparticle scattering by charged dopants. The analysis of two-particle anomalous Green functions at T = 0 permits to estimate the mean-square fluctuation δ2 = <Δ2> - <Δ>2, averaged in random dopant configurations, to the lowest order in doping level c. Since Δ is found to saturate with growing doping level while δ remains to grow, this can explain the collapse of Tc at overdoping. Also we consider the spatial correlations <Δ(0)Δ(R)> for order parameter in different points of the plane.

Deconstructing the Liouvillian approach to the quantum Hall plateau transition

We examine the Liouvillian approach to the quantum Hall plateau transition, as introduced recently by Sinova, Meden, and Girvin [Phys. Rev. B {\bf 62}, 2008 (2000)] and developed by Moore, Sinova and Zee [Phys. Rev. Lett. {\bf 87}, 046801 (2001)]. We show that, despite appearances to the contrary, the Liouvillian approach is not specific to the quantum mechanics of particles moving in a single Landau level: we formulate it for a general disordered single-particle Hamiltonian. We next examine the relationship between Liouvillian perturbation theory and conventional calculations of disorder-averaged products of Green functions and show that each term in Liouvillian perturbation theory corresponds to a specific contribution to the two-particle Green function. As a consequence, any Liouvillian approximation scheme may be re-expressed in the language of Green functions. We illustrate these ideas by applying Liouvillian methods, including their extension to $N_L > 1$ Liouvillian flavors, to random matrix ensembles, using numerical calculations for small integer $N_L$ and an analytic analysis for large $N_L$. We find that behavior at $N_L > 1$ is different in qualitative ways from that at $N_L=1$. In particular, the $N_L = \infty$ limit expressed using Green functions generates a pathological approximation, in which two-particle correlation functions fail to factorize correctly at large separations of their energy, and exhibit spurious singularities inside the band of random matrix energy levels. We also consider the large $N_L$ treatment of the quantum Hall plateau transition, showing that the same undesirable features are present there, too.

Photon production in a dense medium

On the basis of diagram formalism for two-particle Green functions, the bremsstrahlung of charged particles interacting in a dense medium is investigated. In the case of production of soft photons, exact expressions for two-particle Green functions corresponding to the process of particle bremsstrahlung in the substance are obtained. The Green functions found are fully determined by the set of closed irreducible diagrams. It is shown that, in the case of radiation in a sufficiently dense medium in a far long-wave region of the spectrum, the coherent multiple particle scattering results in an additional (as compared that reported earlier in [1–13]) suppression of the bremsstrahlung photon yield.

Quasiparticle band structure and optical spectrum of LiF(001)

We present the quasiparticle band structure and the optical excitation spectrum of bulk LiF and the LiF(001)-(1\ifmmode\times\else\texttimes\fi{}1) surface. First, we calculate the ground-state geometry of the bulk and the surface using density-functional theory within the local-density approximation. Next, applying the $\mathrm{GW}$ approximation for the self-energy, we evaluate the corresponding quasiparticle band structure. Finally, we calculate the electron-hole interaction, solve the Bethe-Salpeter equation for the two-particle Green function, and investigate the optical-absorption spectrum. The obtained spectrum of bulk LiF, which is dominated by a strong exciton peak at 12.7 eV, is in good agreement with experiment. At the LiF(001)-(1\ifmmode\times\else\texttimes\fi{}1) surface, the excitonic effects are strongly modified with respect to the bulk. In particular, we observe a surface exciton at 12.3 eV, i.e., 0.4 eV below the bulk exciton.

Optical absorption spectra of semiconductors and insulators including electron-hole correlations: Anab initiostudy within the LAPW method

The solution of the Bethe-Salpeter equation (BSE) for the electron-hole two-particle Green's function has proven to yield optical absorption spectra of semiconductors and insulators beyond the independent quasiparticle approximation. The inclusion of electron-hole correlations greatly improves the accordance with experimental data. In this work we present an implementation of the BSE scheme into the linearized augmented plane-wave method, and apply our method to the semiconductor Si and to the wide band-gap insulator LiF. We discuss the effects of the electron-hole correlations and compare our results to the experimental data as well as to the previous theoretical findings.

MULTIBAND SUPERCONDUCTIVITY

Multi-band superconductivity is investigated by using two-particle Green's function techniques, and equations for coupled states are derived in the framework of a two-band model. These results suggest that superconductivity appears, even if electron–electron interaction is positive. We also present a cooperative mechanism for multi-band superconductivity.

Aharonov-Bohm ring with fluctuating flux

We consider a non-interacting system of electrons on a clean one-channel Aharonov-Bohm ring which is threaded by a fluctuating magnetic flux. The flux derives from a Caldeira-Leggett bath of harmonic oscillators. We address the influence of the bath on the following properties: one- and two-particle Green's functions, dephasing, persistent current and visibility of the Aharonov-Bohm effect in cotunneling transport through the ring. For the bath spectra considered here (including Nyquist noise of an external coil), we find no dephasing in the linear transport regime at zero temperature. PACS numbers: 73.23.-b, 73.23.Hk, 73.23.Ra, 03.65.Yz