Intermediate Coupling Theory Research Articles

Reciprocity between local moments and collective magnetic excitations in the phase diagram of BaFe2(As1\u2212xPx)2

Unconventional superconductivity arises at the border between the strong coupling regime with local magnetic moments and the weak coupling regime with itinerant electrons, and stems from the physics of criticality that dissects the two. Unveiling the nature of the quasiparticles close to quantum criticality is fundamental to understand the phase diagram of quantum materials. Here, using resonant inelastic x-ray scattering (RIXS) and {rm{Fe}}-{{rm{K}}}_{beta } emission spectroscopy (XES), we visualize the coexistence and evolution of local magnetic moments and collective spin excitations across the superconducting dome in isovalently-doped BaFe{}_{2}(As{}_{1-x}P{}_{x}){}_{2} (0.00 le x le 0.52). Collective magnetic excitations resolved by RIXS are gradually hardened, whereas XES reveals a strong suppression of the local magnetic moment upon doping. This relationship is captured by an intermediate coupling theory, explicitly accounting for the partially localized and itinerant nature of the electrons in Fe pnictides. Finally, our work identifies a local-itinerant spin fluctuations channel through which the local moments transfer spin excitations to the particle-hole (paramagnons) continuum across the superconducting dome.

Stripes, spin resonance, and nodelessd-wave pairing symmetry in Fe2Se2-based layered superconductors

We calculate RPA-BCS based spin resonance spectra of newly discovered iron-selenide superconductor using two orbitals tight-binding (TB) model. The slightly squarish electron pocket Fermi surfaces (FSs) at $(\pi,0)/(0,\pi)-$momenta produce leading interpocket nesting instability at incommensurate vector $q\sim(\pi,0.5\pi)$ in the normal state static susceptibility, pinning a strong stripe-like spin-density wave (SDW) or antiferromagnetic (AFM) order at some critical value of $U$. The same nesting also induces $d_{x^2-y^2}-$pairing. The superconducting (SC) gap is nodeless and isotropic on the FSs as they are concentric to the four-fold symmetry point of the $d-$wave gap maxima, in agreement with various measurements. This induces an slightly incommensurate spin resonance with `hour-glass'-like dispersion feature, in close agreement with neutron data of chalcogenides. We also calculate $T$ pendence of the SC gap solving BCS gap equations and find that the spin resonance follows the same $T$ evolution of $\Delta(T)$ both in energy and intensity, suggesting that an itinerant weak or intermediate pair coupling theory is relevant in this system.

Intermediate coupling theory of electronic ferroelectricity.

We calculate the quantum phase diagram of an extended Falicov-Kimball model for one- and two-dimensional systems in the intermediate coupling regime. Even though some features of the phase diagram are obtained analytically, the main results are calculated with a constrained path Monte Carlo technique. We find that this regime is dominated by a Bose-Einstein condensation of excitons with a built-in electric polarization. The inclusion of a finite hybridization between the bands removes the condensate but reinforces the ferroelectricity.

Theory of Excitation Energy Transfer in the Intermediate Coupling Case of Clusters

Previously we presented a unified theory of excitation energy transfer (EET) in dimers, which is applicable to the intermediate coupling case by self-consistently solving the stochastic Liouville equation (Kimura, A.; Kakitani, T.; Yamato, T. J. Phys. Chem. B 2000 104, 9276). However, up to the present time, proper EET theory, which is applicable to the intermediate coupling case of clusters, was not established. In this paper, we contribute to such an intermediate coupling theory in cluster systems. We utilize the method of generalized master equations (GME). In the first step, we construct the memory function by the second-order perturbation theory of the excitonic interaction from a general point of view. Eventually, it is expressed by a Fourier transform of the overlap of the time-dependent fluorescence and the absorption spectra of the constituent molecules. We show that our new theory reduces to the Kenkre-Knox theory in the limit of fast vibrational relaxation and reduces to the Sumi theory of the hot transfer mechanism in the limit of fast decay of the memory function. In the next step, we introduce a renormalization function into this memory function. This renormalization includes a correction due to the contribution of powers of combination of the fourth- and the second-order correlation functions. By numerical calculations, we illustrate how the renormalization effect becomes significant as the excitonic coupling strength U becomes large. We applied this GME method to the EET between BChla molecules in B850 of the photosynthetic antenna system LH2. We found that the memory function calculated using the experimentally obtained optical spectra initially decays very rapidly (with time constant of about 5 fs) and has a plateau in the time region 10-25 fs. Because of this specific memory function, the calculated coherence length in the steady state was about 3. This GME method should be useful for the analysis of the mechanism of EET in many kinds of biological systems.

A new formula of exciton coherence length in linear array of pigments

By solving the generalized master equation with a memory function properly expressed by using the time-correlation function of the exciton-vibration interaction, we derived an empirical formula for the exciton coherence length Ncoh in the linear array of pigments as a function of exciton coupling U and the decay factor for excitation transfer g as follows: Ncoh = 1.40 + 1.32 (U/g ) Adopting the intermediate coupling theory of exciton in dimer (Kimura et al., J. Phys. Chem. B 104 (2000) 9276), we can express the decay factor g by using the reorganization energy l and energy gap D G due to the excitation transfer between neighboring pigments. Applying this general formula to the B850 ring of LH2 of photosynthetic purple bacteria (U = 350 cm-1, l = 80 cm-1 and so g = 140 cm-1), we obtain Ncoh = 4.7. When we evaluate g by considering the Gaussian inhomogeneous broadening (HWHM 200 cm-1), we obtain Ncoh = 3.2. Namely, the exciton domain extends only 3-4 BCl units among the 18 BCl units of B850 in LH2.

Theory of the spin polaron in the t- J model

A fully analytical theory is developed for the motion of a single hole in the t-J model based on the spin-polaron idea. With a self-consistent treatment of the hole-spin-wave interaction, we are able to overcome the difficulties encountered by the intermediate-coupling theory of Barentzen and obtain a theory applicable over the full range of the coupling strength. Good agreement with numerical studies is achieved.

Intermediate-coupling theory for the spectral weight of a spin polaron

Within the intermediate-coupling theory, the quasiparticle weight $Z$ of one hole injected in the undoped antiferromagnetic ground state is studied. We find that, for the hole located at the quasiparticle band minimun with momentum ${\bf k}_0 = (\pm \frac{\pi}{2}, \pm \frac{\pi}{2})$, $Z$ is finite. By comparing the results obtained by the self-consistent Born approximation, we show that the intermediate-coupling theory for $Z$ is appropriate only when $J/t \stackrel{>}{\sim} 1.6$. Finally, the reason why this approach fails in the small-$J$ case will also be clarified.

Intermediate-coupling theory of the spin polaron in the t-J model.

The spin polaron in the t-J model, i.e., a hole dressed by a cloud of virtual magnons of the antiferromagnetic spin background, is treated within the framework of intermediate-coupling theory. To this end the original t-J model is first reformulated in terms of spinless fermions and bosons by means of the generalized Dyson-Maleev representation (DMR). The latter may be regarded as the natural extension of the ordinary DMR of pure (undoped) spin systems to the case where holes are present, and is similar to the one originally proposed by Schmitt-Rink, Varma, and Ruckenstein. The reformulated t-J model, which is reminiscent of the Fr\"ohlich Hamiltonian, is then subjected to a series of unitary transformations, analogous to those employed by Lee, Low, and Pines in their treatment of the Fr\"ohlich polaron. Our approach yields an approximate quasiparticle energy E(k) as well as the corresponding eigenvector. To explore the range of validity of the theory presented here, the analytic expressions are then further analyzed for intermediate (J/t=0.4) and strong (J/t=0.08) coupling, where special attention is paid to the quasiparticle bandwidth W. The intermediate-coupling result for E(k) is in excellent agreement with the dispersion curve recently obtained by Dagotto and co-workers by means of a Green function Monte Carlo method. Surprisingly, even in the strong-coupling range the bandshape remains qualitatively correct.The bandwidth W is rather accurate for weak coupling (J/t\ensuremath{\gtrsim}3), as expected, and still reasonable in the intermediate range 0.4\ensuremath{\lesssim}J/t\ensuremath{\le}3, where it deviates from the correct values by some 10--20 %. Our theory fails, however, to describe the proper behavior of W in the strong-coupling regime. This shows that the limitations of our approach manifest themselves in the bandwidths rather than in the shapes of the dispersion curves. Our conclusion is that intermediate-coupling theory is appropriate for J/t\ensuremath{\gtrsim}0.4, whereas a genuine strong-coupling theory is required for all other cases. \textcopyright{} 1996 The American Physical Society.

Anisotropic optical polaron in crystals with complex structure

In the context of intermediate coupling theory, the forms of the self-energy and effective-mass tensor of the optical polaron, in appropriate uniaxial crystals with complex structure, are obtained. These forms contain all sources of anisotropy; the effective-mass tensor of the "bare" electron, the electron – optical-phonon interaction, and the angular dependence of the "true" phonoic modes. A numerical application is developed in the case of the CdS crystal.

Photoionization of Kr near 4s threshold. II. Intermediate-coupling theory

The Kr 4s-electron photoionization cross section as a function of the exciting-photon energy in the range between 30 eV and 90 eV was calculated using the configuration interaction (CI) technique in intermediate coupling. In the calculations the 4p spin-orbital interaction and corrections due to higher orders of perturbation theory (the so-called Coulomb interaction correlational decrease) were considered. Energies of Kr II states were calculated and agree with spectroscopic data within less than 10 meV. For some of the Kr II states new assignments were suggested on the basis of the largest component among the calculated CI wavefunctions.

A polaron-type of treatment for 3He in superfluid 4He

A polaron-type model is proposed to describe the deformation in the superfluid 4He ground state, due to the presence of a 3He atom. The interaction matrix element of the model is expressed in terms of the structure factor of the superfluid on the basis of the hypernetted chain approximation.Both the use of an intermediate polaron coupling theory (rather than perturbation theory) and the determination of the precise interaction matrix elements are crucial ingredients to obtain an adequate theoretical description based on a polaron-type model. A generalization of Feynman's path-integral technique is used for the treatment of intermediate coupling.The present work solves i.a. an outstanding problem regarding the 3He effective mass in superfluid 4He. The theoretical result (an effective mass of 2.3123m3 as compared to the experimental value of 2.3m3 where m3 is the bare 3He mass) confirms that our formalism accurately describes the deformation cloud around the 3He atom.Also the difference between the specific heat of the mixture and the specific heat of pure superfluid 4He, and the diffusion of 3He in the superfluid, are accurately explained as the result of the interaction of 3He with the excitations of the superfluid.

The K and LMX Auguer spectra of krypton from the 83Rb decay

The K and LMX Auger spectra of krypton were analysed at an instrumental resolution of 6.5 eV using an electrostatic spectrometer and a vacuum-evaporated 83Rb source. The energies and relative intensities of the KLL, KLX, and KMX Auger transitions were determined as well as the natural widths of some of them. For the LMX transitions, only energies were obtained. Measured absolute energies of dominant Auger transitions are higher by about 13 eV than expected from semi-empirical calculations. Structures predicted by intermediate coupling theory were observed for some KLM lines. The KMM spectrum is found to be successfully described only in the frame of an intermediate coupling scheme.

Intermediate coupling in L2-L3 core excitons of MgO, Al2O3, and SiO2.

The ${\mathit{L}}_{23}$ reflection spectra for single-crystal MgO, \ensuremath{\alpha}-${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$, and \ensuremath{\alpha}-${\mathrm{SiO}}_{2}$ are measured. These reflection spectra are used to generate absorption spectra that agree well with electron-total-yield and electron-energy-loss measurements. Exciton features are shown to exist in the band gap by comparing the valence-band maximum plus optical band gap to the observed transition energies. The energy splitting of the ${\mathit{L}}_{2\mathrm{\ensuremath{-}}}$${\mathit{L}}_{3}$ excitons, as seen in reflection, is clearly resolved for ${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$ and ${\mathrm{SiO}}_{2}$, while in electron-total-yield measurements the doublets are not resolved for ${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$. This resolution allows the calculation of the exchange energy using intermediate-coupling theory.

Photoemission and Auger spectra of incompletely filled bands: intermediate-coupling theory and application to palladium metal

The theoretical analyses of photoemission and Auger XVV spectra of incompletely filled bands are developed in a coherent fashion, based on the same model Hamiltonian. The model, which had been justified previously for cases when the hole density is small, is generalised to account for band degeneracy and multiplet splittings. Accordingly, the authors extend the graph theoretical expansion of the self-energy in the low-density approximation and that of the two-hole Green function in the bare ladder approximation. They work in the intermediate-coupling scheme, in order to include the spin-orbit interaction. Assuming that to a good approximation the total angular momentum J is conserved, they apply the formalism to Pd metal; they use the same Coulomb matrix and Christensen's independent-particle density of states for both spectroscopies and obtain good agreement with the experimental lineshapes.

Intermediate coupling theory for the multidimensional polaron

The intermediate coupling theory of Lee, Low and Pines is employed to calculate the ground state energy and the effective mass of a multidimensional optical polaron. The average number of virtual phonons in the cloud around the electron in the ground state is also calculated in this approximation. The dimensional scaling relations satisfied by these quantities are obtained.

Studies of the magnetization densities in Pu compounds; determination of the degree of localization

The electronic configuration of trivalent Pu is nominally a 5f5 state in which there is a strong cancellation of the L (orbital) and S (spin) components in the J=5/2 ground state. This leads to small g factors and magnetic moments, and to unusual neutron magnetic form factors f(Q) with maxima at Q values greater than zero. We present here the results of form-factor measurements (taken on the polarized-neutron diffractometer at the ILL) on single crystals of PuSb, PuTe, and PuFe2. These results show that the form factor, which is a measure of the magnetization density of the 5f electrons around the Pu nucleus, is sensitive to the degree of localization of the 5f electrons. For example, in PuSb the 5f electrons are well localized and the form factor is in good agreement with the predictions of intermediate coupling and crystal-field theory. In PuTe f(Q) falls monotonically from a maximum at Q=0, indicating an almost spin-only system. This is produced by wide 5f bands, which give rise to the observed T-independent magnetic susceptibility. In PuFe2, however, a large maximum occurs in f(Q). We believe this arises from strong hybridization of the 5f and 3d Fe electrons, which leads to a reduction in the Pu orbital component.

Low-temperature polaron collision time.

The polaron mobility is studied in the temperature region where a Boltzmann equation applies and where resonant optical-phonon scattering is dominant. The collision frequency is computed from the forward-scattering amplitude. The approximation is that the structure function involves a single long-lived fast polaron state that is a simple extension of the slow states. In the parabolic approximation and with intermediate-coupling theory we find a modified Osaka formula that agrees with the Kadanoff-Langreth theorem. We also study the effects of nonparabolicity. The approach applies over the entire coupling range and is illustrated by doing the strong-coupling limit where there is sensitivity in the polaron form factor. In the moderate-coupling range, further detailed computations with conventional Hamiltonian theories of the polaron mass will be needed.

S−fmodel in magnetic semiconductors

In the $s\ensuremath{-}f$ model electrons in the conduction band are coupled with the lattice of localized magnetic moments by exchange interaction. In this paper the influence of the exchange interaction on electron bands and electrical resistivity is studied. An intermediate-coupling theory is presented, valid up to the region where the level broadening exceeds the average thermal energy but is small compared to the bandwidth. Using the functional-derivative method the spin correlations are expressed in terms of the connected correlation functions. The functional-derivative method also provides a decoupling recipe for the electron Green's functions. Concentrating on the two-spin correlations the single-particle Green's function is derived by a decoupling method and is shown to be equivalent to a perturbation expansion. The finite lifetime is obtained for all band energies. The absorption edge, derived from density of states, shows in ferromagnetic semiconductors the familiar red shift and in addition a blue shift of magnetic origin in the paramagnetic region. Mobility is derived from the two-particle Green's function calculated by a decoupling method. Level broadening affects both the acceleration and the scattering part, resulting generally in smaller mobilities than predicted by the weak-coupling theory. In addition, corrections to the ordinary acceleration term are obtained. Results for the ferromagnetic semiconductors EuS and EuO are presented. The narrow mobility minimum occurring at ${T}_{C}$ in the weak-coupling case is considerably broadened in temperature. The minimum mobilities are around 3 ${\mathrm{cm}}^{2}$/Vsec in both materials. The low mobility near ${T}_{C}$ is partly caused by the intense scattering and partly by the decrease in the acceleration term. The results compare reasonably well with experiments.

Radiative lifetimes and two-body deactivation rate constants for Ar(3p5, 4p) and Ar(3p5,4p′) states

The radiative lifetimes and two-body deactivation rate constants of the Ar(3p54p and 4p′) levels have been measured by a time-resolved laser-induced fluorescence technique in a flowing afterglow apparatus. The flowing afterglow produced the Ar(3p54s,3P2) metastable atoms, which subsequently were pumped by the pulsed dye laser. The measured radiative lifetimes are in excellent agreement with the calculated transition probabilities based upon intermediate-coupling theory. Radiative branching ratios of these states also were measured in order to assign the transition probabilities and the absorption oscillator strengths of the transitions between the 4s and 4p levels. The two-body deactivation rate constants range from 1×10−10 to 2×10−11 cm3 atom−1 sec−1. Specific product states from the two-body collisions between Ar(4p and 4p′) atoms and Ar were identified from the laser-induced emission spectra and rate constants for individual product states were assigned for each level. Our results show that two-body collisions do not necessarily result in cascade down the p and p′ manifold, and for the Ar(4p and 4p′) levels more than 50% of the atoms are directly converted to the Ar(4s and 4s′) manifold.

Moving acoustical-mode polarons

A general class of acoustical-phonon mode induced-polaron systems is considered. The electron-phonon interaction for these systems is described by a Fr\"ohlich-interaction Hamiltonian involving Fourier components proportional to ${q}^{\ensuremath{\gamma}}$, where $\ensuremath{\gamma}$ is an arbitrary real number. The energy versus total momentum ($E\ensuremath{-}P$) relations for these polarons are investigated. At weak coupling, in the context of the intermediate coupling theory, it is found that when $\ensuremath{-}1<\ensuremath{\gamma}\ensuremath{\le}\ensuremath{-}\frac{1}{2}$ a linear structure is present in the $E\ensuremath{-}P$ relations. As $\ensuremath{\gamma}$ decreases from -1/2 to -1, this linear structure becomes apparent only for larger and larger values of $P$. For $\ensuremath{\gamma}>\ensuremath{-}\frac{1}{2}$, this linear structure is not present, but rather the $E\ensuremath{-}P$ relations cut off at a critical value of $P$. When $\ensuremath{-}1<\ensuremath{\gamma}\ensuremath{\le}0$, the polaron mass for these systems grows large as the polaron velocity $v$ approaches the speed of sound $s$, but for $\ensuremath{\gamma}>0$ the polaron mass has a finite value as $v\ensuremath{\rightarrow}s$. As a function of $\ensuremath{\gamma}$, the self-energy reaches a maximum value for $\ensuremath{\gamma}\ensuremath{\approx}\ensuremath{-}0.73$ and the $v\ensuremath{\rightarrow}0$ polaron mass reaches a minimum value for $\ensuremath{\gamma}\ensuremath{\approx}\ensuremath{-}0.25$, independent of coupling strength. From a strong-coupling theory appropriate for moving polarons it is found that a linear structure in the $E\ensuremath{-}P$ relations is obtained for all $\ensuremath{\gamma}>\ensuremath{-}1$. At both weak and strong coupling it is unclear that the $E\ensuremath{-}P$ relations are meaningful when $\ensuremath{\gamma}\ensuremath{\le}\ensuremath{-}1$.