David Logan

Abstract:

A many-body theory of paramagnetic Kondo insulators is described, focusing specifically on single-particle dynamics, scattering rates, dc transport and optical conductivities. This is achieved by development of a non-perturbative local moment approach to the symmetric periodic Anderson model within the framework of dynamical mean-field theory. Our natural focus is the strong-coupling, Kondo lattice regime, in particular the resultant 'universal' scaling behaviour in terms of the single, exponentially small low-energy scale characteristic of the problem. Dynamics/transport on all relevant (ω, T)-scales are considered, from the gapped/activated behaviour characteristic of the low-temperature insulator through to explicit connection to single-impurity physics at high ω and/or T; and for optical conductivities emphasis is given to the nature of the optical gap, the temperature scale responsible for its destruction and the consequent clear distinction between indirect and direct gap scales. Using scaling, explicit comparison is also made to experimental results for dc transport and optical conductivities of Ce3Bi4Pt3, SmB6 and YbB12. Good agreement is found, even quantitatively; and a mutually consistent picture of transport and optics results.

Abstract:

The pseudogap Anderson impurity model provides a classic example of an essentially local quantum phase transition. Here we study its single-particle dynamics in the vicinity of the symmetric quantum critical point (QCP) separating generalized Fermi-liquid and local-moment phases, via the local-moment approach. Both phases are shown to be characterized by a low-energy scale that vanishes at the QCP; and the universal scaling spectra, on all energy scales, are obtained analytically. The spectrum precisely at the QCP is also obtained; its form showing clearly the non-Fermi-liquid, interacting nature of the fixed point.

Abstract:

A non-perturbative local moment approach to single-particle dynamics of the general asymmetric Anderson impurity model is developed. The approach encompasses all energy scales and interaction strengths. It captures thereby strong coupling Kondo behaviour, including the resultant universal scaling behaviour of the single-particle spectrum; as well as the mixed valence and essentially perturbative empty orbital regimes. The underlying approach is physically transparent and innately simple, and as such is capable of practical extension to lattice-based models within the framework of dynamical mean-field theory.

Abstract:

The recently introduced local moment approach (LMA) is extended to encompass single-particle dynamics and transport properties of the Anderson impurity model at finite temperature, T. While it is applicable to arbitrary interaction strengths, primary emphasis is given to the strongly correlated Kondo regime (characterized by the T = 0 Kondo scale ωK). In particular the resultant universal scaling behaviour of the single-particle spectrum D(ω T) ≡ F(ω/ωK; T/ωK) within the LMA is obtained in closed form; leading to an analytical description of the thermal destruction of the Kondo resonance on all energy scales. Transport properties follow directly from a knowledge of D(ω; T). The (T/ωK)-dependence of the resulting resistivity ρ(T), which is found to agree rather well with numerical renormalization group calculations, is shown to be asymptotically exact at high temperatures; to concur well with the Hamann approximation for the s-d model down to T/ωK ∼ 1, and to cross over smoothly to the Fermi liquid form ρ(T) - ρ(0) ∝ - (T/ωK)2 in the low-temperature limit. The underlying approach, while naturally approximate, is moreover applicable to a broad range of quantum impurity and related models.

Abstract:

Single-particle dynamics of the Anderson impurity model in the presence of a magnetic field H are considered, using a recently developed local moment approach that encompasses all energy scales, field and interaction strengths. For strong coupling in particular, the Kondo scaling regime is recovered. Here the frequency (ω/ωK) and field (H/ωK) dependence of the resultant universal scaling spectrum is obtained in large part analytically, and the field-induced destruction of the Kondo resonance investigated. The scaling spectrum is found to exhibit the slow logarithmic tails recently shown to dominate the zero-field scaling spectrum. At the opposite extreme of the Fermi level, it gives asymptotically exact agreement with results for statics known from the Bethe ansatz. Good agreement is also found with the frequency and field-dependence of recent numerical renormalization group calculations. Differential conductance experiments on quantum dots in the presence of a magnetic field are likewise considered, and appear to be well accounted for by the theory. Some new exact results for the problem are also established.