d+s波超导体磁掺杂转变

研究了Anderson掺杂极限Δs/Δd《1的情况下,d+s波对称下的超导态。此模型包括哈密顿量中类似BSC项和自恰平均场似下的Anderson掺杂。随着掺杂中心数的增加或比率Δs/Δd的减小,可推出从低能下在费米能级附近具有双峰的态到N(0)≈(Δs/Δd)2态的转变。如果掺杂共振的能量为最小能量标度,则转变不连续。     

Electron-electron correlation in disordered binary alloys: The T-matrix approximation

Dynamical electron-electron correlation in paramagnetic disordered binary alloys described by the Hubbard-type Hamiltonian is studied using the T-matrix approximation (TMA) valid for low concentration of particles ( $\text{\$}\text{?}$0.6/atom). We introduce the terminal-point approximation for the many-body quantities, which allows us to solve the random part of the problem within the single-site approximation (CPA). The one-centre version of the TMA is used in numerical calculations. Results are compared with those of the Hartree-Fock approximation, and with the model of a pair of interacting electrons in a random alloy (CPA II).     

Metal-insulator transition in many valley semiconductors in the spirit of the Hubbard model

The metal-insulator transition using different dielectric functions is investigated for a many valley semiconductor system within the effective mass approximation. The critical concentration as well the value of the Mott constant is enhanced when the Hartree-Fock dielectric function is used with the inclusion of exchange and correlation effects. In the absence of localization, the obtained value of Mott constant is critically examined in terms of Hubbard model. The effects of Anderson localization, exchange and correlation in the Hubbard model are included in a simple way. The relationship between the present model and the Mott criterion in terms of Hubbard model is also brought out. The critical concentration is enhanced when a random distribution of impurities is considered. The value of α is fixed demanding the vanishing of the donor binding energy with the donor concentration for several donors in Si and Ge. Results are compared with the existing data available and discussed in the light of existing literature.     

The high temperature resistivity of dilute alloys

Recently measured anomalies in the high temperature resistivity of dilute alloys (transition metals in copper) are interpreted on the basis of the Anderson model. Assuming that the anomalies are caused by phonons the Anderson hamiltonian extended to the case of many impurities is treated, electron-phonon coupling being included. Using the equation-of-motion technique for theGreen's functions, the free electron relaxation time, and the resistivity are calculated. The approximations consist in neglecting impurity correlations and taking into account only terms linear in the temperature and the impurity concentration. We find that in most cases the calculated additional resistivity caused by the impurities show the measuredT-dependance as related to the occurrence of magnetic moments of the impurities in the host metal.     

Effect of atomic disorder and temperature on incommensurate helical spin waves in the Anderson–Hubbard model

Based on the single-band t–t' Anderson–Hubbard model, the effect of disorder on the parameters and ranges of existence of incommensurate helical spin waves is studied. The problem is solved within the functional integration theory in static approximation, taking into account longitudinal fluctuations of the magnetic moment. Magnetic phase diagrams and parameters of incommensurate helical spin waves are obtained as functions of temperatures and electron and impurity concentrations. It is shown that disorder can lead to the first-order transition from the antiferromagnetic phase to the (Q, π) phase and the metal–dielectric transition from antiferromagnetic metal to antiferromagnetic dielectric far from the half-filled band. The results obtained are used to explain the incommensurate magnetic order observed in cuprates in the overdoped mode.     

Mott-Hubbard transition and Anderson localization: A generalized dynamical mean-field theory approach

The DOS, the dynamic (optical) conductivity, and the phase diagram of a strongly correlated and strongly disordered paramagnetic Anderson-Hubbard model are analyzed within the generalized dynamical mean field theory (DMFT + Σ approximation). Strong correlations are taken into account by the DMFT, and disorder is taken into account via an appropriate generalization of the self-consistent theory of localization. The DMFT effective single-impurity problem is solved by a numerical renormalization group (NRG); we consider the three-dimensional system with a semielliptic DOS. The correlated metal, Mott insulator, and correlated Anderson insulator phases are identified via the evolution of the DOS and dynamic conductivity, demonstrating both the Mott-Hubbard and Anderson metal-insulator transition and allowing the construction of the complete zero-temperature phase diagram of the Anderson-Hubbard model. Rather unusual is the possibility of a disorder-induced Mott insulator-to-metal transition. The text was submitted by the authors in English.     

Ab initio many-body treatment of the electronic structure of metals

We propose and apply a combination of an ab initio (band-structure) calculation with a many-body treatment including screening effects. We start from a linearized muffin-tin orbital (LMTO) calculation to determine the Bloch functions for the Hartree one-particle Hamiltonian, from which we calculate the static susceptibility and dielectric function within the standard random phase approximation (RPA). From the Bloch functions we obtain maximally localized Wannier functions, using a method proposed by Marzari and Vanderbilt. Within this Wannier basis all relevant one-particle and unscreened and screened Coulomb matrix elements are calculated. This yields a multi-band Hamiltonian in second quantization with ab initio parameters, for which screening has been taken into account within the simplest standard approximation. Then, established methods of many-body theory are used. We apply this concept to a simple metal, namely lithium (Li). Here the maximally localized Wannier functions turn out to be of the sp³-orbital kind. Furthermore, only the on-site contributions of the screened Coulomb matrix elements are relevant, and a generalized, four-band Hubbard model is justified. The screened on-site Coulomb matrix elements are considerably smaller than the band width because of which it is sufficient to calculate the selfenergy in weak-coupling approximation. We compare results obtained within the screened Hartree-Fock approximation (HFA) and within the second-order perturbation theory (SOPT) in the Coulomb matrix elements for Li and find that many-body effects are small but not negligible even for this simple metal.     

The limitimg behaviour of the well width of a quantum two-dimensional metal–insulator transition

Metal–Insulator transition using an exact two-dimensional (2D) dielectric function is investigated for a shallow donor in an isolated well of a GaAs/Ga_1−xAl_sAs superlattice system within the effective mass approximation. Vanishing of the donor ionization energy as a function of well width and the donor concentration suggests that a phase transition is not possible even below a well width of 10 Å, supporting the scaling theory of localization. The effects of Anderson localization, exchange and correlation in the Hubbard model are included in a simple way. The relationship between the present model and the Mott criterion in terms of Hubbard model is also brought out. The critical concentration appears to be enhanced when a random distribution of impurities is considered. The limiting behaviour of the well width for a quantum 2D well is brought out. A simple expression is derived for a Mott constant in 2D, a*N_c^1/2 exp (9.86 exp (−L/a*))=0.123, where N_c is the critical concentration per area. Results are compared with the existing data available and discussed in the light of existing literature.     

Effect of laser intensity on the semiconductor–metal transition in a doped Quantum Well

We demonstrate laser induced semiconductor–metal transition through an abrupt change in diamagnetic susceptibility of a donor at critical concentration in a GaAs/Al_xGa_1−xAs Quantum Well for finite barrier model in the effective mass approximation using variational principle. We have considered Anderson‘s localization due to the random distribution of impurities in our calculation. The nonparabolicity of the conduction band is also considered. Our results without laser field agree with the earlier theoretical results and also with the recent experimental results.     

Two-dimensional Anderson-Hubbard model in the DMFT + Σ approximation

The density of states, the dynamic (optical) conductivity, and the phase diagram of the paramagnetic two-dimensional Anderson-Hubbard model with strong correlations and disorder are analyzed within the generalized dynamical mean field theory (DMFT + Σ approximation). Strong correlations are accounted by the DMFT, while disorder is taken into account via the appropriate generalization of the self-consistent theory of localization. We consider the two-dimensional system with the rectangular “bare” density of states (DOS). The DMFT effective single-impurity problem is solved by numerical renormalization group (NRG). The “correlated metal,” Mott insulator, and correlated Anderson insulator phases are identified from the evolution of the density of states, optical conductivity, and localization length, demonstrating both Mott-Hubbard and Anderson metal-insulator transitions in two-dimensional systems of finite size, allowing us to construct the complete zero-temperature phase diagram of the paramagnetic Anderson-Hubbard model. The localization length in our approximation is practically independent of the strength of Hubbard correlations. But the divergence of the localization length in a finite-size two-dimensional system at small disorder signifies the existence of an effective Anderson transition.     

Experimental evidence for many-body effects in dilute alloys

The macroscopic and local properties of 3d transition metal impurities in normal metals are reviewed and compared with the theoretical situation in this field.

The parameters of the Anderson and s-d exchange models are derived from direct and indirect experimental data using as a guide the Hartree-Fock approximation of the non-degenerate Anderson model. The basic observations about the magnetic-non-magnetic transition, and the behaviour of the magnetic, thermal and transport properties when going through the transition region are demonstrated for specific examples. A detailed comparison between the present status of theory and experiment is performed by inspecting the large body of experimental data of two typical alloys, which served as testing materials for the development of the existing theories. CuFe is often regarded as a typical ‘yes moment’ system, and the experiments are therefore compared with the predictions based on the s-d exchange model; in the case of AlMn, the spin-fluctuation concept was chosen as a theoretical basis. It is shown that various approaches of the models fail to describe the fine experimental details. Evidence is presented which calls for a unified theory with no distinction between magnetic (Kondo-type) and non-magnetic (spin-fluctuation) alloys. It is suggested that the range of applicability of a model depends not only on the basic parameters of the dilute alloy but on the temperature, too, and the question of the relevance of the models to the actual state of affairs is to be answered by inspecting the temperature regions where the various approximations of the models are expected to work; the T≥T_K properties are compared with the Kondo approach, the Tˇ-T_K properties with the spin fluctuation model, although in the latter case the analysis is based on the concept of a narrow resonance level, which is not a feature of the spin-fluctuation concept only.

Finally, the basic experimental facts and indications are absorbed into a phenomenological model, which describes both the single-particle resonances and the many-body effects involved in resonance formation in classical dilute alloys.     

Self-consistent alloy treatment of the periodic anderson model: Susceptibility and specific heat of intermediate valence compounds

To describe the electronic properties of mixed valence compounds we study the periodic Anderson model within the frame of the alloy analog approximation. In this approach the model Hamiltonian is replaced by the sum of two single-particle alloy Hamiltonians the parameters of which have to be determined self-consistently. The alloy problem is solved within the coherent potential approximation. In contrast to other treatments of the periodic Anderson model this approximation scheme is exact in both trivially solvable limits of vanishing hybridization and Coulomb repulsion, respectively. For model parameters corresponding to a mixed valence situation only nonmagnetic solutions of the self-consistency equations exist. After discussing the limit of small hybridization analytically we numerically calculate the magnetic susceptibility and the electronic specific heat as a function of temperature for realistic values of the hybridization and Coulomb repulsion. The results are in very good qualitative agreement with experimental data.Work performed within the research program of the Sonderforschungsbereich 125 Aachen/Jülich/Köln     

Transition temperature of a superconductor containing magnetic impurities in the spin fluctuation limit

Renormalization group techniques are used to calculate the transition temperature of a BCS-Superconductor containing magnetic impurities described by the symmetric one orbital Anderson model for small U/πΓ. The suppression of superconductivity is related to the static spin fluctuation susceptibility. Superconductivity is quenched above a critical impurity concentration c_cr = λ?²πΓ/[U_effχ(0)].     

Pressure induced valence transitions in the Anderson lattice model

We apply the equation of motion method to the Anderson lattice model, which describes the physical properties of heavy fermion compounds. In particular, we focus here on the variation of the number of f electrons with pressure, associated to the crossover from the Kondo regime to the intermediate valence regime. We treat here the non-magnetic case and introduce an improved approximation, which consists of an alloy analogy based decoupling for the Anderson lattice model. It is implemented by partial incorporation of the spatial correlations contained in higher-order Green's functions involved in the problem that have been formerly neglected. As it has been verified in the framework of the Hubbard model, the alloy analogy avoids the breakdown of sum rules and is more appropriate to explore the asymmetric case of the periodic Anderson Hamiltonian. The densities of states for a simple cubic lattice are calculated for various values of the model parameters V, t, E_f, and U.     

Threshold behaviour of the three-particle scattering amplitude and gas approximation in the many-body problem

It is established by investigation of the gas approximation for the ground state energy in many-body problem how the low energy parameters of the two-particle and essentially three-particle scattering amplitude determine the dominant terms of the energy expansion in series of gas parameter. The correspondence to the gas approximation in the Faddeev integral equations in the form of the three-particle amplitude low energy behaviour near the threshold E → 0 is obtained.     

On the role of image forces in chemisorption theory

The Extended Anderson Hamiltonian is used to study the effect of fluctuations of an adatom charge Q on the ionic part of the chemisorption energy. It is shown that dynamical effects essentially modify the classical expression E = ? ?Q² for the energy of interaction between a static charge Q and a metal (? is the interaction energy for a unit charge). The exact solution for the one-electron two-level model as well as a variational solution for the Extended Anderson Hamiltonian model are given. Validity conditions for a variety of approximate schemes are studied. The results are presented for the Extended Anderson Hamiltonian model parameterized so as to describe some aspects of the Li/W and Li/Mo chemisorption systems.     

Random Matrix Theory and the Anderson Model

This paper is devoted to a discussion of possible strategies to prove rigorously the existence of a metal-insulator Anderson transition for the Anderson model in dimension d≥3. The possible criterions used to define such a transition are presented. It is argued that at low disorder the lowest order in perturbation theory is described by a random matrix model. Various simplified versions for which rigorous results have been obtained in the past are discussed. It includes a free probability approach, the Wegner n-orbital model and a class of models proposed by Disertori, Pinson, and Spencer, Comm. Math. Phys. 232:83–124 (2002). At last a recent work by Magnen, Rivasseau, and the author, Markov Process and Related Fields 9:261–278 (2003) is summarized: it gives a toy modeldescribing the lowest order approximation of Anderson model and it is proved that, for d=2, its density of states is given by the semicircle distribution. A short discussion of its extension to d≥3 follows.     

One-dimensional spin glass with oscillating long-range interaction

In this paper a long-range interacgion approximation for spin glasses is proposed as an alternative to the Sherrington-Kirkpatrick model. The one-dimensional model of Ising spins with the interaction κV _O cosQ x exp (?κ|x|), where κ?c?Q (c is the spin concentration) is studied in detail. The long-range approximation enables one to describe the spin configuration in terms of slowly varying in space fields of the type of amplitude (ρ) and phase (ψ); the ψ-dependent part of the Hamiltonian is analogous to the Hamiltonian, describing the weak pinning of the charge density waves by impurities. As a result, the phase variable apears to be gaples in equilibrium thermodynamics and parametrizes different metastable states under quasiequilibrium conditions. In the mean field approximation (MFA) (κ»0) in the vicinity of the transition pointT _c =cV ₀, there is a symmetric cusp of the magnetic susceptibility ξ; at low temperatures the heat capacity is proportional toT, whereas the susceptibility does not depend on temperature. The MFA cannot be applied in the close vicinity ofT _c (|τ?(κ/c)^2/3) and at very low temperaturesT?κV ₀ when a gap appears in the distribution of the molecular fielsh ath≈0.     

Time-dependent Mott transition in the periodic Anderson model with nonlocal hybridization

The time-dependent Mott transition in a periodic Anderson model with off-site,nearest-neighbor hybridization is studied within the framework of nonequilibriumself-energy functional theory. Using the two-site dynamical-impurity approximation, wecompute the real-time dynamics of the optimal variational parameter and of differentobservables initiated by sudden quenches of the Hubbard-U and identify the criticalinteraction. The time-dependent transition is orbital selective, i.e., in the final state,reached in the long-time limit after the quench to the critical interaction, the Mott gapopens in the spectral function of the localized orbitals only. We discuss the dependenceof the critical interaction and of the final-state effective temperature on thehybridization strength and point out the various similarities between the nonequilibriumand the equilibrium Mott transition. It is shown that these can also be smoothly connectedto each other by increasing the duration of a U-ramp from a sudden quench to a quasi-staticprocess. The physics found for the model with off-site hybridization is compared with thedynamical Mott transition in the single-orbital Hubbard model and with the dynamicalcrossover found for the real-time dynamics of the conventional Anderson lattice withon-site hybridization.