The transport coefficients of the Anderson model are calculated by extending Wilson's numerical renormalization group method to finite-temperature Green functions. Accurate results for the frequency and temperature dependence of the single-particle spectral densities and transport time tau ( omega , T) are obtained and used to extract the temperature dependence of the transport coefficients in the strong-correlation limit of the Anderson model. Results are obtained for values of the local level position ranging from the Kondo regime to the mixed valency and empty orbital regimes. The low-temperature anomalies in the resistivity, rho (T), thermopower, S(T), thermal conductivity, kappa (T), and Hall coefficient, RH(T), are discussed in terms of the behaviour of the spectral densities. At low temperature all quantities exhibit the expected Fermi liquid behaviour, rho (T)= rho 0(1-c(T/TK)2), S(T) approximately gamma T, kappa (T)/ alpha T=1+ beta (T/TK)2, RH(T)=-Rinfinity (1- delta (T/TK)2). Analytic results based on Fermi liquid theory are derived here for the first time for beta and the numerical results are shown to be consistent with this coefficient. The range of temperatures over which universal behaviour extends is also discussed. Scattering of conduction electrons in higher-angular-momentum, l>0, channels is also considered and an expression is derived for the corresponding transport time and used to discuss the influence of the interference terms between the resonant l=0 and non-resonant l=1 channels on the transport properties. The presence of non-resonant scattering is shown to be particularly important for the thermopower at half filling, where the sign of the thermopower can depend sensitively on the non-resonant phase shift. Finally the relation of the results to experiment is discussed.

https://iopscience.iop.org/article/10.1088/0953-8984/6/13/013/pdf

Transport coefficients of the Anderson model via the numerical renormalization group

The temperature dependence of the thermoelectric power (TEP) of metallic systems with cerium and ytterbium ions exhibits characteristic features which we explain by the Coqblin-Schrieffer model (CSM). We specify a given system by the degeneracy and splitting of the crystal-field (CF) levels, the strength of the exchange and potential scattering, and the number of f electrons or f holes; for cerium and ytterbium ions we assume ${n}_{f}l~1$ and ${n}_{f}^{\mathrm{hole}}l~1,$ respectively. The Kondo temperature ${T}_{K}$ is then generated by the ``poor man's scaling''; it separates a local-moment (LM) from a Fermi-liquid (FL) regime. In the LM regime $(Tg~{T}_{K})$ we calculate the TEP by a renormalized perturbation expansion, in which the exchange coupling J is also renormalized by the poor man's scaling. This gives the TEP with a large peak at high temperatures and a sign change at ${T}_{x}\ensuremath{\simeq}\ensuremath{\alpha}{T}_{K},$ where for parameters used in this paper we have $\ensuremath{\alpha}$ between roughly 2.5 and 10. For ${n}_{f}\ensuremath{\simeq}1$ and large CF splitting, we find a broad temperature range ${T}_{K}\ensuremath{\ll}Tl~{T}_{x},$ in which the TEP of the CSM is negative. In the FL regime $(Tl~{T}_{K})$ we neglect the excited CF states, reduce the CSM to an effective spin-degenerate exchange model, map it on an effective spin-degenerate Anderson model, and calculate the TEP by an expansion in terms of $U\ensuremath{\propto}1/J.$ For cerium ions ${(n}_{f}l~1)$ we obtain in this way the TEP which follows for $T\ensuremath{\ll}{T}_{K}$ a linear FL law, attains at about ${T}_{K}/2$ a positive maximum, and changes sign above ${T}_{K}.$ The results pertaining to ytterbium ions ${(n}_{f}^{\mathrm{hole}}l~1)$ are obtained by reflecting the ${n}_{f}l~1$ curves on the temperature axis. The overall results obtained for the CSM in such a way explain the essential features of the temperature, pressure, and doping dependence of the TEP in cerium and ytterbium systems. Unfortunately, neither our high-temperature nor the low-temperature expansion provide the details or locate the minimum of the negative TEP which we find in the transition region between the FL and LM regimes.

Thermoelectric power of cerium and ytterbium intermetallics

The transport coefficients of the Anderson model are calculated by extending Wilson's NRG method to finite temperature Green's functions. Accurate results for the frequency and temperature dependence of the single--particle spectral densities and transport time $\tau(\omega,T)$ are obtained and used to extract the temperature dependence of the transport coefficients in the strong correlation limit. The low temperature anomalies in the resistivity, $\rho(T)$, thermopower, $S(T)$, thermal conductivity $\kappa(T)$ and Hall coefficient, $R_{H}(T)$, are discussed. All quantities exhibit the expected Fermi liquid behaviour at low temperature with power law dependecies on $T/T_{K}$ in very good agreement with analytic results based on Fermi liquid theory. Scattering of conduction electrons in higher, $l>0$, angular momentum channels is also considered and an expression is derived for the corresponding transport time and used to discuss the influence of non--resonant scattering on the transport properties.

https://arxiv.org/pdf/cond-mat/9310032.pdf

Transport Coefficients of the Anderson Model via the Numerical Renormalization Group

Results of calculations of residual resistivity, thermoelectric power, Dingle-temperature, changes in electronic specific heat, and superconducting critical temperature due to 3d-transition metal impurities in Al are presented. The impurities are described in terms of muffin-tin potentials, calculated with the Mattheiss construction and the Friedel sum rule. The results are compared with experimental data and show a qualitative agreement.



Es werden Berechnungen von Restwiderstand, Thermokraft, Dingletemperatur, Anderung des Elektronenanteils der spezifischen Warme und der Sprungtemperatur fur 3d-Ubergangs-metallpunktdefekte in Al vorgestellt. Die Punktdefekte werden durch muffin-tin-Potentiale beschrieben, die unter Verwendung der Mattheiss-Konstruktion und der Friedel-Summenregel berechnet wurden. Die Resultate werden mit experimentellen Werten verglichen und zeigen qualitative Ubereinstimmung.

Localized non-magnetic impurities in metals II. Application to 3d-transition metal impurities in aluminium

Recent experimental measurements such as susceptibility, specific heat, thermopower, and UPS on a wide range of intermetallic intermediate valence systems, e.g. YbCuAl, CeSn3, support a high degree of universality in the properties of such materials which apparently form a unique class of metallic compounds. The ratio χ(0)/γ≂g2μ2B (J+1) (J+1/2)/π2k2B is a good constant for compounds of a given rare earth (though g and J are rare earth dependent). A class of compounds of a given IV rare earth ion shows scaling of properties in terms of an effective temperature, or energy, scale TF, which is strong function of valence. We review the success of theoretical approaches such as perturbation theory, local Fermi liquid theory, the Bethe Ansatz technique, and large‐N perturbation theory in understanding these experimental facts. A challenge continues to be the understanding of the ground state, in which lattice periodicity plays a fundamental role, giving rise to ραT2 in some metallic, and a several meV gap in ins...

Theoretical and experimental progress in intermediate valence systems (invited)

Low temperature thermoelectric power is calculated in the LSF approximation of the Anderson model. Theoretical results are compared with the experimental data for aluminium based transition metal alloys.

V Zlatic

Papers

Low temperature thermoelectric power of dilute Al 3d alloys