David Logan

Abstract:

We consider a symmetric Anderson impurity model with a soft-gap hybridization vanishing at the Fermi level, ΔI ∝ |ω|r with r > 0. Three facets of the problem are examined. First the non-interacting limit, which despite its simplicity contains much physics relevant to the U > 0 case: it exhibits both strong coupling (SC) states (for r < 1) and local moment states (for r > 1), with characteristic signatures in both spectral properties and thermodynamic functions. Second, we establish general conditions upon the interaction self-energy for the occurence of a SC state for U > 0. This leads to a pinning theorem, whereby the modified spectral function A(ω) = |ω|r D(ω) is pinned at the Fermi level ω = 0 for any U where a SC state obtains; it generalizes to arbitrary r the pinning condition upon D(ω = 0) familiar in the normal r = 0 Anderson model. Finally, we consider explicitly spectral functions at the simplest level: second order perturbation theory in U, which we conclude is applicable for r < 1/2 and r > 1 but not for 1/2 < r < 1. Characteristic spectral features observed in numerical renormalization group calculations are thereby recovered, for both SC and LM phases; and for the SC state the modified spectral functions are found to contain a generalized Abrikosov-Suhl resonance exhibiting a characteristic low-energy Kondo scale with increasing interaction strength.

Abstract:

The dynamics of a single hole in the t-J model is solved exactly for all temperature, T, in the limit of large spatial dimensions, d = ∞, using the Feenberg renormalized perturbation series. We focus in particular on single-particle spectra, together with optical and static hole conductivities. Explicit results are illustrated for a Bethe lattice, and exemplify the continuous thermal evolution of the underlying string picture from the T = 0 string-pinned limit through to the paramagnetic phase. Quenched site-disorder is also readily incorporated, exact results thereby being obtained for the interplay between disorder and thermally-induced hole dynamics.

Abstract:

A microscopic three-band Anderson-Mott-Hubbard model for cubic disordered tungsten bronzes (Formula presented) and (Formula presented) is studied over a range of doping levels (Formula presented) at the level of an unrestricted Hartree-Fock approximation in order to understand the effects of disorder and electron interaction on the electronic ground state and their implications for the chemically induced metal-insulator transition observed at least in the latter materials. For sufficiently large U a pseudogap develops at (Formula presented) in agreement with photoemission spectra and tunneling current measurements which is found to significantly affect the localization and hybridization characteristics as well as the three-dimensional spatial distribution of quasiparticle states and thus constitutes the central feature of the model. The formation of the pseudogap is rationalized via a repulsion between occupied and unoccupied conduction band quasiparticle states induced by antiferromagnetic correlations occurring on length scales which—for the most relevant parameters—are controlled by the doping-dependent tight-binding Fermi surface. Light is shed on experimental results which hitherto have not found a satisfactory rationalization. © 1999 The American Physical Society.

Abstract:

We discuss the dynamics of a single hole in t-J model at finite temperature, in the limit of large spatial dimensions. The problem is shown to yield a simple and physically transparent solution, that exemplifies the continuous thermal evolution of the underlying string picture from the T = 0 string-pinned limit through to the paramagnetic phase.

Abstract:

A theory is developed for the single-particle spectra of the symmetric Anderson model, in which local moments are introduced explicitly from the outset. Dynamical coupling of single-particle processes to low-energy spin-flip excitations leads, within the framework of a two-self-energy description, to a theory in which both low- and high-energy spectral features are simultaneously captured, while correctly preserving Fermi liquid behaviour at low energies. The atomic limit, non-interacting limit and strong-coupling behaviour of the spectrum are each recovered. For strong coupling in particular, both the exponential asymptotics of the Kondo resonance and concomitant many-body broadening of the Hubbard satellite bands are shown to arise naturally within the present approach.