Pauli Term Research Articles

Structure of the correlation-kinetic component of the Kohn-Sham exchange potential in atoms and at metal surfaces

The Kohn–Sham density functional theory “exchange” potential vx(r)=δExKS[ρ]/δρ(r), where ExKS[ρ] is the “exchange” energy functional, is composed of a component representative of Pauli correlations and one that constitutes part of the correlation contribution to the kinetic energy. The Pauli term is the work done WxKS(r) in the field ℰxKS(r) obtained by Coulomb's law from the Fermi hole charge distribution constructed from the Kohn–Sham orbitals. The correlation–kinetic term is the work done W(1)(r) in the field Z(1)(r) derived from the kinetic-energy–density tensor involving the first-order correction to the Kohn–Sham single-particle density matrix. The sum of these fields is conservative, so that the total work done is path-independent. There is no explicit correlation–kinetic contribution to the “exchange” energy ExKS[ρ]. Its contribution is manifested via the Kohn–Sham orbitals generated via the potential vx(r). The functional ExKS[ρ] is thus expressed in virial form entirely in terms of the Pauli field ℰxKS(r). In this article, we determine and study the structure of the correlation–kinetic component field Z(1)(r) and work W(1)(r) for the nonuniform electron density system in atoms and at metal surfaces. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65: 893–906, 1997

Larkin-Ovchinnikov-Fulde-Ferrell state in d-wave superconductors

We consider the effect of Pauli interaction on the properties of unconventional superconductors with d x 2− y 2 -pairing. It is shown, that if the Pauli term is sufficiently large, then the phase transition goes from the normal state to a spatially modulated superconducting state — an analog of the Larkin-Ovchinnikov-Fulde-Ferrell state known for conventional superconductors. Possible types of the non-uniform state are considered, and a peculiar low-temperature behaviour of heat capacity is discussed.

Magnetic properties in polypyrrole doped by series of dopants

Magnetic susceptibility and ESR linewidth are measured as a function of temperature in polypyrrole (PPy) doped with PF 6−, AsF 6−, ClO 4−, BF 4−, ToS −. Spin susceptibility by Schumacher-Slichter (ESR-NMR) technique shows both the temperature independent Pauli term ranging from 0.7 to 1.4×10 −5 emu/mol-ring and the Curie term of 1 spin per 600~1500 rings, which is consistent with that obtained by SQUID measurement in the same sample. The temperature dependence of ESR linewidth is ascribed to the Elliott mechanism typical for the metallic electron spins, increasing monotonically with the temperature. This interpretation is also consistent with the ESR linewidth in polythiophene doped with ClO 4− and AsF 6−. Therefore, both the susceptibility and the ESR linewidth demonstrate the PPy's doped with several dopants to have a metallic electronic state.

Magnetic Susceptibility of the Orbitally Degenerate (J= 5/2) Periodic Anderson Model - Analysis on the Basis of the Fermi Liquid Theory -

In the orbitally degenerate ($J=5/2$) Periodic Anderson Model, the magnetic susceptibility is composed of both the Pauli term and the Van Vleck term, as is well known. The former is strongly enhanced by the strong correlation between $f$-electrons. But, for the latter, the influence of the strong correlation has been obscure for years. In this paper we give the solution of the longstanding problem. With the aid of the $d=\infty$ approximation, we study this problem on the basis of the Fermi liquid theory with degenerate orbitals, taking account of all the vertex corrections in a consistent way. As a result, we obtain the simple expression for the magnetic susceptibility, and show unambiguously that the Van Vleck term is also highly enhanced} in the strong correlation regime. This fact explains naturally the enhanced magnetic susceptibility observed in many insulating systems (i.e., Kondo insulator). Moreover, we show that the Wilson ratio takes a value around 1 in the metallic system, in good agreement with experiments.

Resisitivity, thermopower, and susceptibility of RNiO3 (R=La,Pr).

We report the resistivity, thermopower, and dc susceptibility of R${\mathrm{NiO}}_{3}$ (R=La,Pr) ceramic samples for 1.4 K\ensuremath{\le}T\ensuremath{\le}300 K. The resistivity of ${\mathrm{LaNiO}}_{3}$ shows a ${\mathit{T}}^{2}$ dependence below 80 K and changes over to a ${\mathit{T}}^{1.5}$ dependence at higher temperature (100--300 K). The resistivity of ${\mathrm{PrNiO}}_{3}$ exhibits a metal-insulator transition at ${\mathit{T}}_{\mathrm{MI}}$=130 K with a linear temperature dependence above ${\mathit{T}}_{\mathrm{MI}}$. The thermopower of both ${\mathrm{LaNiO}}_{3}$ and ${\mathrm{PrNiO}}_{3}$ is linear and negative in the metallic region. The susceptibility of ${\mathrm{LaNiO}}_{3}$ is Pauli-like with a Curie-Weiss contribution at low temperature. The Pauli term is enhanced well above the free-electron value. Our samples have smaller resistivity and larger resistivity ratio than previously reported. Thermogravimetric analysis shows that there is excess oxygen (\ensuremath{\delta}g0) in our samples of ${\mathrm{LaNiO}}_{3+\mathrm{\ensuremath{\delta}}}$, which suggests that the oxygen content of ${\mathrm{LaNiO}}_{3}$ is important for its physical properties.

Pauli principle in the theory of nonlinear electronic transport.

In approaches to the theory of electronic transport, such as the Boltzmann equation and the Landauer-B\"uttiker formalism, the problem arises as to how to take into account the exclusion principle. Usually one introduces ad hoc statistical factors to restrict the electron final states to unoccupied levels. Such a procedure in general leads to incorrect results. This is shown by a study of the friction coefficient for a localized perturbation moving in a free-electron gas. The exact expression for the friction coefficient does not include a Pauli restriction. It is only in the case where the scattering potential has inversion symmetry or for one-dimensional systems that the Pauli term vanishes identically. Therefore, we present a detailed study using a scattering potential in two dimensions without inversion symmetry. Our numerical results show a discrepancy between the exact quantum-mechanical calculation and the probabilistic approach.

Linearized gap equation for a superconductor in a strong magnetic field.

A linearized gap equation for a superconductor in the presence of a strong magnetic field incorporating the Landau-level spectrum, the Pauli term, as well as the dynamical interaction is given. The most commonly used model of a BCS-type pairing interaction of strength V\ifmmode\bar\else\textasciimacron\fi{} is a special case of the dynamical interaction, and in this case an exact solution to this linearized gap equation was obtained by us before. From this solution, several new results recently obtained by Tesanovic et al. are recovered. By expressing the solution in terms of the Landau states, the Cooper pairing is shown to involve many Landau levels.

The magnetic condensate, strong vector forces and monopoles

We study the interplay of the magnetic condensate 〈 Ψ ¯ μ v Ψ F μ v 〉, chiral symmetry breaking, strong vector forces and magnetic monopoles. Physical arguments are presented to motivate the appearance of a vacuum expectation value of the magnetic condensate in the chiral symmetry broken phase of strongly coupled quantum electrodynamics. Calculations of the magnetic condensate are presented for quenched non-compact lattice QED and linearized lattice QED. In both models a magnetic condensate is generated whose critical behavior is the same as 〈 Ψ ¯ Ψ 〉. The anomalous dimension of Ψ ¯ μ v Ψ F μ v , is extracted and the Pauli term is seen to become renormalizable together with four Fermi operators. The influence of magnetic monopole networks on fermion wave functions is studied in both non-compact and linearized lattice QED, and significant differences are found between the two models. The role of the monopoles in driving a chiral phase transition in unquenched lattice QED is argued to be enhanced as N f, the number of dynamical light fermions, is increased from zero.

Anisotropic spin susceptibility of spin-density-wave states.

The spin response of a spin-density-wave (SDW) state arises from two contributions: a Pauli term (described by spin splitting of the Fermi surface) and an interband term resulting from virtual spin-flip transitions across the SDW energy gap. Both terms are anisotropic, and so is their sum. For a linear SDW the axis of anisotropy is the SDW polarization vector; for a spiral SDW the anisotropy axis is perpendicular to the plane of polarization. In either case the algebraic sign of the anisotropy depends on whether Q/2${\mathit{k}}_{\mathit{f}}$ is greater than or less than unity, where Q is the SDW wave vector. The magnitude of the anisotropy (which is enhanced by exchange and correlation) can be as large as \ensuremath{\sim}50%. The hcp metals Ti, Zr, and Hf exhibit considerable anisotropy, but magnetic structure has not yet been discovered for them.

Fermions and solitons in the O(3) nonlinear sigma model in 2+1 space-time dimensions.

The field-theory limit of antiferromagnetism with holes is described using the O(3) nonlinear \ensuremath{\sigma} model. The minimal coupling to the spin wave gives a Pauli term that couples the hole charge density to the topological charge density for solitons. This term leads to drastic consequences: an attractive potential for holes and solitons, spin-charge coupling for the holes, and zero-momentum modes. The zero-momentum modes are exact nonperturbative solutions to the full coupled equations of motion for spin waves and holes. The effect of a Chern-Simons term, connections to other mean-field approaches, and the quantum bound-state problem are discussed. If the zero modes are the states of lowest energy, then the holes in this field-theory limit are attached to skyrmions.

Chemical and Physical Properties of Soluble Part of Emeraldine: Comparison with Insoluble Emeraldine

ABSTRACTA preliminary physical study of the soluble part of emeraldine is presented. The electrical and magnetic properties of this low weight material are very similar of those of the pristine emeraldine salt. These results emphazise the possible role of short chain species in the conduction mechanism of polyaniline. In order to clarify this point, previous magnetic investigations on insoluble emeraldine salts are revisited. It appears that the fit of the magnetic susceptibility temperature dependence of polyaniline with a Curie law plus a Pauli term might not be justified at low temperature. A T−α law with a ≈ 0.75 gives a better fit suggesting a behavior similar to the one found in Random Exchange Heisenberg Antiferromagnetic Chain (REHAC)

Finiteness of gravitational corrections to magnetic moments and supergravity embedding

We calculate the one-loop O( κ 2) contribution to the anomalous magnetic moment of a lepton in the framework of N = 1 supergravity coupled to super-QED with a charged massive scalar multiplet source, using both supersymmetry violating and preserving regularizations. Since a Pauli term is forbidden by supersymmetry, the ordinary gravity plus QED contribution must be just the negative of that given by the new supersymmetry diagrams in the latter scheme. In particular, the infinite part of the new terms' contribution vanishes; the reason for this is traced to an effective chiral-dual symmetry of our sector. Thus, the “miracle” of the moment's finiteness in ordinary gravity is accounted by supergravity embedding. The significance and implications of regularization ambiguities are also discussed.

On the microscopic origin of the Pauli term in the Interaction Boson Fermion Model (IBFM)

Several attempts have been made in order to derive the boson-fermion exchange interaction, introduced first by Mottelson (Mottelson 1967, Bohr and Mottelson 1969) from microscopic fermion Hamiltonians. Doenau and Janssen (1973) and, in the framework of the Interaction Boson Fermion Model (IBFM) (Iachello 1979), Talmi (1981) and Scholten and Dieperink (1981) considered the quadrupole-quadrupole interaction as the source of the exchange process. Scholten and Dieperink derived microscopic expressions which allow to calculate the coupling constant of the exchange term in the IBFM, often called the Pauli term, from the coupling constant of the fermion quadrupole force. A quantitative analysis, however, showed that the values obtained by means of these formulas are considerably too small compared with values obtained by the phenomenological use of the IBFM (Scholten, 1981). This surprising result suggests strongly that the question about the microscopic origin of the Pauli term is still open.

Transport, Magnetic and Structural Studies of Polyacetylene

Abstract Experimental progress is reviewed with emphasis on magnetic and transport studies. The magnetic results are fully consistent with the soliton doping mechanism; the decrease in Curie-law contribution has been demonstrated; the Pauli term remains small (Y < 0.07) and is apparently zero in the limit of completely uniform doping. The electrical conductivity (P and T dependence) and thermopower (n-type and p-type) are in excellent agreement with Kivelson's theory of intersoliton electron hopping.

Solitons in Polyacetylene: Magnetic Susceptibility

The absoulte spin susceptibility of As${\mathrm{F}}_{5}$-doped trans-polyacetylene, ${[\mathrm{CH}{(\mathrm{As}{\mathrm{F}}_{5})}_{y}]}_{x}$, was determined by spin resonance techniques for $0.0004&lt;~y&lt;~0.138$. The Curie-law contribution decreases above $y=0.001$ to a level less than 1 ppm in the highly conducting regime. The temperature-independent Pauli term is small (\ensuremath{\le}5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}8}$ emu/mole) for $y&lt;0.01$, remains small up to $y=0.05$, and shows an abrupt increase near $y=0.07$ to a value of \ensuremath{\sim} 3 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}6}$ emu/mole at higher concentrations. The results are consistent with the soliton doping mechanism.

A coupled-channels treatment of the positive-parity resonances in4He

The coupled-channels formalism, which has been previously applied successfully to interpret the negative-parity resonances in4He, has now been extended to the positiveparity 2ℏω resonances in this system. The 1p-1h approach has been modified to include coupling to the 2p-2h configurations, which also belong to 2ℏω excitations, by using the effective operator formalism. The effect of the Pauli term in thes-wave channel is examined and is found to be important in reproducing the 0+,T=0 resonance energy and width. Resonances with spins up toJπ=3+ have been studied, and the agreement with available data is satisfactory. In particular, from the good fit to the asymmetry coefficientβ(E), one establishes the presence of a 2+,T=0 resonance around 35-MeV excitation in the system.

The centre-of-mass spuriosity in continuum shell-model calculations

A method proposed previously to eliminate the centre-of-mass (CM) spuriosity in continuum shell-model (SM) calculations of 4He is generalised to adapt to the cases of heavier nuclei. It is applied to study the (p,p) and (p,n) reactions involving the one-particle-one-hole excitation of the dipole resonances in 12C and 16O. The effect is non-negligible and the results show features not observed previously. The Pauli term is also studied and is found to be less important in 16O as compared with the lighter nucleus 12C.

Solution of the Dirac equation with anomalous magnetic moment

In this note, we derive in the one-particle approximation, the normalized eigenspinor solutions of the Dirae-Pauli equation, in a homogeneous magnetic field. The constant magnetic field problem for electrons with the Pauli term has first been solved some t ime ago by STROCCHI (1) and by T~RNOV et al. (z). Since, then, a number of authors have published calculations which determined the energy eigenvalues (8.4). The derivation of the normalized eigenspinors are, however, not on record. For a number of applications such as the magnetic properties of neutron and hadron stars, it is necessary to have the explicit expressions for the spinor eigenfunctions for both kinds of charged particles and for neutral particles. An example where the eigenspinors of the ordinary Dirac equation are used to determine the equation of state is given in ref. (b).

One-loop effective potential with anomalous moment of the electron

The one-loop effective potential in QED is investigated by adding a Pauli term in the Green function equation for the electron. A modified Weisskopf-Schwinger Lagrangian is then computed up to order alpha 2.

Bloch-elektronen in antiferromagneten I. Gruppentheoretische grundlagen

The symmetry of the time-independent Schrödinger equation is investigated in antiferromagnetic single crystals using the spinor representation for the electron. The one-particle Hamiltonian depends on the assumed rigid antiferromagnetic structure via the vector potential of the magnetic induction. The Pauli term and the spin-orbit term are taken into account as well as the crystal potential. It is shown how to find the Shubnikov space group relevant to the problem. A representation of the appropriate double group gives the symmetry group of the Hamiltonian. From the lattice periodicity of the Hamiltonian an analogue of the classical Bloch theorem is obtained. The symmetry group of the Hamiltonian is used to determine the symmetry properties of the energy bands. These symmetries are examined systematically for each type of Shubnikov space groups. Special attention is paid to the validity of the Kramers symmetry. In certain antiferromagnets, the energy bands are allowed by symmetry to have terms linear in k . Such a behaviour can have measurable consequences.