Method Of Effective Charges Research Articles

Physical mechanism of Ge doping enhanced Ruddlesden-Popper structure quasi-2D Sr<sub>3</sub>Sn<sub>2</sub>O<sub>7</sub> ceramic hybrid improper ferroelectricity

Hybrid improper ferroelectricity with quasi-two-dimensional (quasi-2D) structure has attracted much attention recently due to its great potential in realizing strong magnetoelectric coupling and room-temperature multiferroicity in a single phase. However, recent studies show that there appears high coercive field and low remnant polarization in ceramics, which severely hinders the applications of this material. In this work, high-quality Sr<sub>3</sub>Sn<sub>2</sub>O<sub>7</sub> and Sr<sub>3</sub>Sn<sub>1.99</sub>Ge<sub>0.01</sub>O<sub>7</sub> ceramics with a Ruddlesden-Popper (R-P) structure are successfully prepared, and their crystal structures and electrical properties are investigated in detail. It is found that the Sr<sub>3</sub>Sn<sub>2</sub>O<sub>7</sub> ceramic exhibits a lower coercive field that is close to that of Sr<sub>3</sub>Sn<sub>2</sub>O<sub>7</sub> single crystal. Moreover, via a small amount of Ge doping, the polarization reaches 0.34 μC/cm<sup>2</sup> for Sr<sub>3</sub>Sn<sub>2</sub>O<sub>7</sub> and 0.61 μC/cm<sup>2</sup> for Sr<sub>3</sub>Sn<sub>1.99</sub>Ge<sub>0.01</sub>O<sub>7</sub>. Combining crystal lattice dynamic studies, we analyze the Raman and infrared responses of the samples, showing the information about the tilting and rotation of the oxygen octahedra in the samples. The improved ferroelectricity after doping may be attributed to the increased amplitude of the tilt mode and the reduced amplitude of rotation mode. Besides, the enhanced ferroelectric properties through Ge doping and its mechanism are further investigated by the Berry phase approach and the Born effective charge method. Furthermore, via the UV-visible spectra, the optical bandgap is determined to be 3.91 eV for Sr<sub>3</sub>Sn<sub>2</sub>O<sub>7</sub> ceramic and 3.95 eV for Sr<sub>3</sub>Sn<sub>1.99</sub>Ge<sub>0.01</sub>O<sub>7</sub> ceramic. Using the Becke-Johnson potential combined with the local density approximation correlation, the bandgap is calculated and is found to be in close agreement with the experimental result. And the electronic excitations can be assigned to the charge transfer excitation from O 2p to Sn 5s (Ge 4s). The effects of Ge doping on the ability of Sr<sub>3</sub>Sn<sub>2</sub>O<sub>7</sub> to gain and lose electrons and the bonding strength of Sn-O bond are analyzed via two-dimensional charge density difference. In conclusion, this study provides insights into the synthesis method and modulation of ferroelectric properties of hybrid improper ferroelectrics Sr<sub>3</sub>Sn<sub>2</sub>O<sub>7</sub>, potentially facilitating their widespread applications in various capacitors and non-volatile memory devices.

First-principle investigation of hybrid improper ferroelectricity of <i>n</i> = 2 Ruddlesden-Popper Sr<sub>3</sub><i>B</i><sub>2</sub>Se<sub>7</sub> (<i>B</i> = Zr, Hf)

Recently, perovskite ferroelectric photovoltaic materials have been studied extensively. Traditional photovoltaic device usually uses the internal electric field formed by PN junction to realize the separation of photogenerated carriers to form the photovoltaic effect, while ferroelectric material, due to the existence of spontaneous polarization, can spontaneously realize the separation of photogenerated electrons and holes without the formation of PN junction, presenting the ferroelectric photovoltaic effect. Chalcogenide perovskite with suitable band gap and visible light absorption is expected to be a new generation of ferroelectric photovoltaic materials. However, its application is limited due to the lack of ferroelectric properties. Hybrid improper ferroelectricity (HIF) in layered perovskites has opened a new way for developing the new ferroelectrics. In contrast to the proper ferroelectricity in which the polarization is the main order parameter as the driving force, the improper ferroelectricity possesses the ferroelectric polarization that becomes a secondary order parameter induced by other orders. In this work, we study the ground state, electronic structure and hybrid improper ferroelectricity of <i>n</i> = 2 Ruddlesden-Popper (RP) Sr<sub>3</sub><i>B</i><sub>2</sub>Se<sub>7</sub> (<i>B</i> = Zr, Hf ) based on the first principles. The total energy calculations and phonon spectrum analysis show that the ground state of Sr<sub>3</sub><i>B</i><sub>2</sub>Se<sub>7</sub> (B = Zr, Hf ) is of <i>A</i>2<sub>1</sub><i>am</i> polar phase. The hybrid improper ferroelectricity originates from the coupling between two rotation modes of <i>B</i>Se<sub>6</sub> octahedron. Electronic structure calculations show that Sr<sub>3</sub>Zr<sub>2</sub>Se<sub>7</sub> and Sr<sub>3</sub>Hf<sub>2</sub>Se<sub>7</sub> are semiconductors with direct band-gaps, which are around 1.56 eV and 1.84 eV, respectively. The ferroelectric polarization values calculated by the Berry phase method are around 12.75 μC/cm<sup>2</sup> and 9.69 μC/cm<sup>2</sup>, respectively. The contribution of each atomic layer to the ferroelectric polarization is investigated when the Born effective charge method is used. The results show that the polarization of Sr<sub>3</sub><i>B</i><sub>2</sub>Se<sub>7</sub> (<i>B</i> = Zr, Hf ) mainly comes from the Sr-Se atomic layers. To sum up, Sr<sub>3</sub><i>B</i><sub>2</sub>Se<sub>7</sub> (<i>B</i> = Zr, Hf ) show strong ferroelectric polarization and good visible light absorption characteristics and they are expected to be candidates of a new generation of ferroelectric photovoltaic materials.

The evolution of polarization inside ultrathin PbTiO3 films: a theoretical study

How to control the material properties by manipulating the unitcell thickness is crucial for applications of ferroelectric ultrathin films. To understand the polarization behaviour of ultrathin PbTiO3 (PTO) films grown on SrTiO3 (STO) substrate, we have systematically explored the strength and direction of polarization in each unitcell layer, using density functional theory combined with Born effective charge method. Strikingly, we find that the polar state of ultrathin PTO films is a composite result depending not only on thickness but also on boundary condition, initial polarization direction, etc. Besides, we also studied the surface effect on the polarization in the thicker PTO films for comparison with the ultrathin ones, which suggests that the surface effect is basically confined in a small range (3–5 unitcells thick at surface region) no matter what kinds of surface terminations and polarization directions.

Improved analysis of moments of [formula omitted] in neutrino–nucleon scattering using the Bernstein polynomial method

We use recently calculated next-to-next-to-leading order (NNLO) anomalous dimension coefficients for the moments of the x F 3 structure function in νN scattering, together with the corresponding three-loop Wilson coefficients, to obtain improved QCD predictions for both odd and even moments of F 3 . To investigate the issue of renormalization scheme dependence, the Complete Renormalization Group Improvement (CORGI) approach is used, in which all dependence on renormalization and factorization scales is avoided by a complete resummation of RG-predictable scale logarithms. We also consider predictions using the method of effective charges, and compare with the standard ‘physical scale’ choice. The Bernstein polynomial method is used to construct experimental moments (from the x F 3 data of the CCFR Collaboration) that are insensitive to the value of x F 3 in the region of x which is inaccessible experimentally. Direct fits for Λ MS ¯ ( 5 ) ( α s ( M Z ) ) are then performed. The CORGI fits including target mass corrections give a value α s ( M Z ) = 0.1189 −0.0019 +0.0019 , consistent with the world average. The effective charge and physical scale fits give slightly smaller values, which are still consistent within the errors.

Resummation of large logarithms within the method of effective charges

We show how the resummation of large logarithms can be incorporated into the method of effective charges. As an example this approach is applied to the event shape variables thrust and heavy-jet mass in e + e − annihilation. Whilst there are some problems with the behaviour of the effective charge in the two-jet region, smaller power corrections are required to fit the data compared to the standard approach.

Resummation of large logarithms within the method of effective charges

We show how the resummation of large logarithms can be incorporated into the method of effective charges. As an example, we apply this approach to the event shape variables thrust and heavy-jet mass in e + e − annihilation. We find that, although the resummation creates problems with the behaviour of the effective charge in the 2-jet limit, smaller power corrections are required to fit the data compared to the standard approach. In addition, increasing the logarithmic accuracy reduces the size of the power corrections further. We also consider “predicting” the sub-leading logarithms in the MS ¯ scheme, obtaining surprisingly good results for the first few NLL terms.

Infrared features of the Landau gauge QCD

The infrared features of Landau gauge QCD are studied by the lattice simulation of $\beta=6.0, 16^4, 24^4, 32^4$ and $\beta=6.4, 32^4, 48^4$. We adopt two definitions of the gauge field; 1) $U-$linear 2) $\log U$ and measured the gluon propagator and ghost propagator. Infrared singularity of the gluon propagator is less than that of tree level result but the gluon propagator at 0 momentum remains finite. The infrared singularity of ghost propagator is stronger than the tree level. The QCD running coupling measured by using the gluon propagator and the ghost propagator has a maximum $\alpha_s(p)\simeq 1$ at around $p=0.5GeV$ and decreases as $p$ approaches 0. The data are analyzed in use of formula of the principle of minimal sensitivity(PMS), the effective charge method and the contour-improved perturbation method, which suggest necessity of the resummation of perturbation series in the infrared region together with existence of the infrared fixed point. Kugo-Ojima parameter saturates at about -0.8 in contrast to the theoretically expected value -1.

Disentangling running coupling and conformal effects in QCD

We investigate the relation between a postulated skeleton expansion and the conformal limit of QCD. We begin by developing some consequences of an Abelian-like skeleton expansion, which allows one to disentangle running-coupling effects from the remaining skeleton coefficients. The latter are by construction renormalon-free, and hence hopefully better behaved. We consider a simple ansatz for the expansion, where an observable is written as a sum of integrals over the running-coupling. We show that in this framework one can set a unique Brodsky-Lepage-Mackenzie (BLM) scale-setting procedure as an approximation to the running-coupling integrals, where the BLM coefficients coincide with the skeleton ones. Alternatively, the running-coupling integrals can be approximated using the effective charge method. We discuss the limitations in disentangling running coupling effects in the absence of a diagrammatic construction of the skeleton expansion. Independently of the assumed skeleton structure we show that BLM coefficients coincide with the conformal coefficients defined in the small $\beta_0$ (Banks-Zaks) limit where a perturbative infrared fixed-point is present. This interpretation of the BLM coefficients should explain their previously observed simplicity and smallness. Numerical examples are critically discussed.

Scale- and scheme-independent extension of Padé approximants: Bjorken polarized sum rule as an example

A renormalization-scale-invariant generalization of the diagonal Pad\'e approximants (dPA), developed previously, is extended so that it becomes renormalization-scheme-invariant as well. We do this explicitly when two terms beyond the leading order (NNLO, $\sim \alpha_s^3$) are known in the truncated perturbation series (TPS). At first, the scheme dependence shows up as a dependence on the first two scheme parameters $c_2$ and $c_3$. Invariance under the change of the leading parameter $c_2$ is achieved via a variant of the principle of minimal sensitivity. The subleading parameter $c_3$ is fixed so that a scale- and scheme-invariant Borel transform of the resummation approximant gives the correct location of the leading infrared renormalon pole. The leading higher-twist contribution, or a part of it, is thus believed to be contained implicitly in the resummation. We applied the approximant to the Bjorken polarized sum rule (BjPSR) at $Q^2_{\rm ph}=5$ and $3 GeV^2$, for the most recent data and the data available until 1997, respectively, and obtained ${\alpha}_s^{\bar MS}(M_Z^2)=0.119^{+0.003}_{-0.006}$ and $0.113^{+0.004}_{-0.019}$, respectively. Very similar results are obtained with the Grunberg's effective charge method and Stevenson's TPS principle of minimal sensitivity, if we fix $c_3$-parameter in them by the aforementioned procedure. The central values for ${\alpha}_s^{\bar MS}(M_Z^2)$ increase to 0.120 (0.114) when applying dPA's, and 0.125 (0.118) when applying NNLO TPS.

Complete renormalization group improvement — avoiding factorization and renormalization scale dependence in QCD predictions

For moments of leptoproduction structure functions we show that all dependence on the renormalization and factorization scales disappears provided that all the ultraviolet logarithms involving the physical energy scale Q are completely resummed. The approach is closely related to Grunberg's method of effective charges. A direct and simple method for extracting Λ MS from experimental data is advocated.

A convergent reformulation of QCD perturbation theory

We propose a generalization of Grunberg's method of effective charges in which, starting with the effective charge for some dimensionless QCD observable dependent on the single energy scale $Q, R(Q)$, we introduce an infinite set of auxiliary effective charges, each one describing the sub-asymptotic Q-evolution of the immediately preceding effective charge. The corresponding infinite set of coupled integrated effective charge beta-function equations may be truncated. The resulting approximations for $R(Q)$ are the convergents of a continued function. They are manifestly RS-invariant and converge to a limit equal to the Borel sum of the standard asymptotic perturbation series in $\alpha_s({\mu^2})$, with remaining ambiguities due to infra-red renormalons. There are close connections with Pad{\'e} approximation.

Non-perturbative calculation of the mass-gap in the Gross-Neveu model

We calculate a fully renormalizable effective action for local composite operators in the U(N) Gross-Neveu model, recently introduced by one of us, to two loop order. We obtain results for the massgap in one and two loops which are optimized using the Grunberg method of effective charges. At one loop the accuracy is of the order of 2% or less (except for N = 2). At two loops the accuracy is significantly improved for N ≥ 5.

Correlated scattering states of N-body Coulomb systems

For N charged particles of equal masses moving in the field of a heavy residual charge, an approximate analytical solution of the many-body time-independent Schrodinger equation is derived at a total energy above the complete fragmentation threshold. All continuum particles are treated on equal footing. The proposed correlated wave function represents, to leading order, an exact solution of the many-body Schrodinger equation in the asymptotic region defined by large interparticle separations. Thus, in this asymptotic region the N-body Coulomb modifications to the plane-wave motion of free particles are rigorously estimated. It is shown that the Kato cusp conditions are satisfied by the derived wave function at all two-body coalescence points. An expression of the normalization of this wave function is also given. To render possible the calculations of scattering amplitudes for transitions leading to a four-body scattering state, an effective-charge method is suggested in which the correlations between the continuum particles are completely subsumed into effective interactions with the residual charge. Analytical expressions for these effective interactions are derived and discussed for physical situations. @S1050-2947~97!01103-7#

Anharmonic force constants of helical molecules

AbstractCentral to our anharmonic potential–effective charge method of computing relative Raman intensities of large helical molecules, such as DNA, are the anharmonic force constants of such molecules. We have thus been led to derive explicit expressions of them and to study their properties. These properties prove to be indispensable in carrying out the computational steps leading to the final Raman intensity expressions for helical molecules. A general expression of cubic force constants of a helical molecule is presented and its properties discussed. Explicit expressions are listed for the cases of stretch and anglebend contributions. Other uses of the anharmonic force constants are also discussed. © 1995 John Wiley & Sons, Inc.

THE GENERALIZED HARTREE-FOCK METHOD IN THE GROSS-NEVEU MODEL

In the generalized Hartree-Fock scheme one can incorporate nonperturbative effects from the beginning of a diagrammatic expansion. In order to make a detailed analysis of the method, we apply it to the Gross-Neveu model as an example and calculate the chiral condensate at large N by using a direct diagrammatic expansion. The unperturbed Gaussian kernel is adjusted to be massive by adding fermion mass terms and the mass terms are subtracted from the interaction part, thus not changing the full Lagrangian. The chiral condensate <gσ> is expanded in powers of the renormalized coupling constant and then improved by the method of effective charges. We find that our diagrammatic expansion is compatible with renormalization. By using the principle of minimal sensitivity, we evaluate <gσ> and show that the exact broken and unbroken solutions for the discrete γ5 symmetry are obtained at each order of the expansion.

ELECTROSTATIC INTERACTIONS FOR PARTICLE ARRAYS IN ELECTRORHEOLOGICAL FLUIDS I: CALCULATIONS

A simple effective charge method and the principle of superposition were used to calculate the total system interaction energy of two-dimensional rectangular and hexagonal arrays of particles in electrorheological suspensions. The calculations gave for static conditions (no shear) that a close-packed hexagonal array of particles was energetically favored over a rectangular array and that for very dilute suspensions a structure consisting of separated single chains was favored over one consisting of clusters. For shearing and assuming that no rotation of the polarization vector takes place, no difference in the maximum force per chain occurred for a two-chain system compared to a single-chain system in either the rectangular or close-packed hexagonal array. This was also the case with rotation of the polarization vector in the rectangular array, although the force was less with rotation compared to without rotation for this array. However, in the case of the dose-packed hexagonal array with rotation of the polarization vector there occurred an order of magnitude enhancement of the maximum force for the two-chain system compared to the single-chain system. This enhancement is comparable to the ratio of the measured strength of ER fluids to that predicted for the structure consisting of separated single chains.

Spontaneous symmetry breaking in QCD

We study dynamical chiral symmetry breaking in massless QCD by the use of the generalized Hartree-Fock method. As the order parameter of chiral symmetry we choose the dynamical quark mass in the zero momentum limit which we call low energy quark mass. We calculate the low energy mass to the second order of diagrammatic expansion around shifted perturbative vacuum. We then show that the mass is finite and renormalization group invariant. After the improvement of the result by the method of effective charges we estimate the mass in the true vacuum under the gap and stationarity conditions and demonstrate that both of them produce non-zero mass proportional to a conventional scale, which breaks down the chiral symmetry.

Method of effective charges and Brodsky-Lepage-Mackenzie criterion.

A renormalization-scheme-invariant method to improve the QCD perturbative series when the Brodsky-Lepage-Mackenzie (BLM) criterion indicates large perturbative corrections is presented. The method, which is a variant of the effective-charge scheme, is specific to QCD and relies on a new renormalization-group equation describing the response of a physical quantity to a change in the BLM next-to-leading-order coefficient ${r}_{1}^{*}$. Two alternative methods are also discussed: one of them consists in an improvement of the perturbative series for the effective charge $\ensuremath{\beta}$ function, which also yields, as a byproduct, an improvement of the series for the perturbative infrared fixed point of QCD at $f\ensuremath{\approx}\frac{33}{2}$ flavors; the other represents an improvement of the perturbative series specific to the BLM choice of renormalization point.

On some ambiguities in the method of effective charges.

In response to the preceding paper by Chyla, the status of some remaining ambiguities in the method of effective charges is reviewed and the specific example of the static potential in QCD is discussed. A criterion for convergence of perturbation theory is suggested, and shown to be satisfied by the recent /ital O/(/alpha//sub /ital s///sup 3/) calculation of /sigma/(/ital e//sup +/e/sup /minus///r arrow/hadrons) of Gorishny, Kataev, and Larin.

Effective charges in QCD: Where has all the ambiguity gone?

The method of effective charges has been proposed by Grunberg as a natural solution to the problem of renormalization-scheme dependence of finite-order perturbation-theory results. In this paper I shall argue that this solution relies in a crucial way on certain rather ad hoc assumptions. Some statements contained in his paper are furthermore commented upon and the peculiarities of the renormalization-scheme ambiguity for perturbation expansions which are divergent when considered in a fixed renormalization scheme briefly mentioned.