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Abstract:

We investigate a system of three tunnel-coupled semiconductor quantum dots in a triangular geometry, one of which is connected to a metallic lead, in the regime where each dot is essentially singly occupied. Both ferromagnetic and antiferromagnetic spin- 1 2 Kondo regimes, separated by a quantum phase transition, are shown to arise on tuning the interdot tunnel couplings and should be accessible experimentally. Even in the ferromagnetically-coupled local moment phase, the Kondo effect emerges in the vicinity of the transition at finite temperatures. Physical arguments and numerical renormalization group techniques are used to obtain a detailed understanding of the problem. © 2009 The American Physical Society.

Abstract:

We consider an Anderson impurity model in which the locally correlated orbital is coupled to a host with a gapped density of states. Single-particle dynamics are studied, within a perturbative framework that includes both explicit second-order perturbation theory and self-consistent perturbation theory to all orders in the interaction. Away from particle-hole symmetry the system is shown to be a generalized Fermi liquid (GFL) in the sense of being perturbatively connectable to the non-interacting limit; and the exact Friedel sum rule for the GFL phase is obtained. We show by contrast that the particle-hole symmetric point of the model is not perturbatively connected to the non-interacting limit, and as such is a non-Fermi liquid for all non-zero gaps. Our conclusions are in agreement with NRG studies of the problem.

Abstract:

Magnetic-field effects in Kondo insulators are studied theoretically, using a local-moment approach to the periodic Anderson model within the framework of dynamical mean-field theory. Our main focus is on field-induced changes in single-particle dynamics and the associated hybridization gap in the density of states. Particular emphasis is given to the strongly correlated regime, where the dynamics is found to exhibit universal scaling in terms of a field-dependent low-energy coherence scale. Although the bare applied field is globally uniform, the effective fields experienced by the conduction electrons and the f electrons differ because of correlation effects. A continuous insulator-metal transition is found to occur on increasing the applied field, closure of the hybridization gap reflecting competition between Zeeman splitting, and screening of the f -electron local moments. For intermediate interaction strengths, the hybridization gap depends nonlinearly on the applied field, while in strong coupling its field dependence is found to be linear. For the classic Kondo insulator YbB12, good agreement is found upon direct comparison of the field evolution of the experimental transport gap with the theoretical hybridization gap in the density of states. © 2008 The American Physical Society.

Abstract:

We develop a non-perturbative local moment approach (LMA) for the gapped Anderson impurity model (GAIM), in which a locally correlated orbital is coupled to a host with a gapped density of states. Two distinct phases arise, separated by a level-crossing quantum phase transition: a screened singlet phase, adiabatically connected to the non-interacting limit and as such a generalized Fermi liquid (GFL); and an incompletely screened, doubly degenerate local moment (LM) phase. On opening a gap (δ) in the host, the transition occurs at a critical gap δ c, the GFL [LM] phase occurring for δ<δ c [ δ>δ c] . In agreement with numerical renormalization group (NRG) calculations, the critical δ c = 0 at the particle-hole symmetric point of the model, where the LM phase arises immediately on opening the gap. In the generic case by contrast δ c > 0, and the resultant LMA phase boundary is in good quantitative agreement with NRG results. Local single-particle dynamics are considered in some detail. The major difference between the two phases resides in bound states within the gap: the GFL phase is found to be characterised by one bound state only, while the LM phase contains two such states straddling the chemical potential. Particular emphasis is naturally given to the strongly correlated, Kondo regime of the model. Here, single-particle dynamics for both phases are found to exhibit universal scaling as a function of scaled frequency ω/ω m ⁰ for fixed gaps δ/ω m ⁰, where ω m ⁰ is the characteristic Kondo scale for the gapless (metallic) AIM; at particle-hole symmetry in particular, the scaling spectra are obtained in closed form. For frequencies |ω|/ω m ⁰ ≫δ/ ω m ⁰, the scaling spectra are found generally to reduce to those of the gapless, metallic Anderson model; such that for small gaps δ/ω m ⁰≪ 1 in particular, the Kondo resonance that is the spectral hallmark of the usual metallic Anderson model persists more or less in its entirety in the GAIM. © 2008 EDP Sciences/Società Italiana di Fisica/Springer-Verlag.