arXiv subjects

David E. Logan

Publications and source records attributed to David E. Logan.

48 records · Page 3Linked to original sources

arXiv2007

Interaction effects in mixed-valent Kondo insulators

We study theoretically the class of mixed-valent Kondo insulators, employing a recently developed local moment approach to heavy Fermion systems using the asymmetric periodic Anderson model (PAM). Novel features in spectra and transport, observable experimentally but lying outside the scope of the symmetric PAM or the Kondo lattice model, emerge naturally within the present theory. We argue in particular that a shoulder-like feature in the optical conductivity, that is distinct from the usual mid-infrared or direct gap peak and has been observed experimentally in mixed-valent compounds such as CeOs4Sb12 and YbAl3, is of intrinsic origin. Detailed comparison is made between the resultant theory and transport/optical experiments on the filled-skutterudite compound CeOs4Sb12, and good agreement is obtained.

cond-mat.str-el↗

arXiv2006

Gate voltage effects in capacitively coupled quantum dots

We study a system of two symmetrical capacitively coupled quantum dots, each coupled to its own metallic lead, focusing on its evolution as a function of the gate voltage applied to each dot. Using the numerical renormalization group and poor man's scaling techniques, the low-energy Kondo scale of the model is shown to vary significantly with the gate voltage, being exponentially small when spin and pseudospin degrees of freedom dominate; but increasing to much larger values when the gate voltage is tuned close to the edges of the Coulomb blockade staircase where low-energy charge-fluctuations also enter, leading thereby to correlated electron physics on energy/temperature scales more accessible to experiment. This range of behaviour is also shown to be manifest strongly in single-particle dynamics and electron transport through each dot.

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arXiv2006

Dynamics of capacitively coupled double quantum dots

We consider a double dot system of equivalent, capacitively coupled semiconducting quantum dots, each coupled to its own lead, in a regime where there are two electrons on the double dot. Employing the numerical renormalization group, we focus here on single-particle dynamics and the zero-bias conductance, considering in particular the rich range of behaviour arising as the interdot coupling is progressively increased through the strong coupling (SC) phase, from the spin-Kondo regime, across the SU(4) point to the charge-Kondo regime; and then towards and through the quantum phase transition to a charge-ordered (CO) phase. We first consider the two-self-energy description required to describe the broken symmetry CO phase, and implications thereof for the non-Fermi liquid nature of this phase. Numerical results for single-particle dynamics on all frequency scales are then considered, with particular emphasis on universality and scaling of low-energy dynamics throughout the SC phase. The role of symmetry breaking perturbations is also briefly discussed.

cond-mat.str-el↗

arXiv2006

Renormalization group study of capacitively coupled double quantum dots

The numerical renormalization group is employed to study a double quantum (DQD) dot system consisting of two equivalent single-level dots, each coupled to its own lead and with a mutual capacitive coupling embodied in an interdot interaction U', in addition to the intradot Coulomb interaction U. We focus on the regime with two electrons on the DQD, and the evolution of the system on increasing U'/U. The spin-Kondo effect arising for U'=0 (SU(2) x SU(2)) is found to persist robustly with increasing U'/U, before a rapid but continuous crossover to (a) the SU(4) point U'=U where charge and spin degrees of freedom are entangled and the Kondo scale strongly enhanced; and then (b) a charge-Kondo state, in which a charge-pseudospin is quenched on coupling to the leads/conduction channels. A quantum phase transition of Kosterlitz-Thouless type then occurs from this Fermi liquid, strong coupling (SC) phase, to a broken symmetry, non-Fermi liquid charge ordered (CO) phase at a critical U'_c. Our emphasis in this paper is on the structure, stability and flows between the underlying RG fixed points, on the overall phase diagram in the (U,U')-plane and evolution of the characteristic low-energy Kondo scale inherent to the SC phase; and on static physical properties such as spin- and charge-susceptibilities (staggered and uniform), including universality and scaling behaviour in the strongly correlated regime. Some exact results for associated Wilson ratios are also obtained.

cond-mat.str-el↗

arXiv2005

Single-particle dynamics of the Anderson model: a two-self-energy description within the numerical renormalization group approach

Single-particle dynamics of the Anderson impurity model are studied using both the numerical renormalization group (NRG) method and the local moment approach (LMA). It is shown that a 'two-self-energy' description of dynamics inherent to the LMA, as well as a conventional 'single-self-energy' description, arise within NRG; each yielding correctly the same local single-particle spectrum. Explicit NRG results are obtained for the broken symmetry spectral constituents arising in a two-self-energy description, and the total spectrum. These are also compared to analytical results obtained from the LMA as implemented in practice. Very good agreement between the two is found, essentially on all relevant energy scales from the high-energy Hubbard satellites to the low-energy Kondo resonance.

cond-mat.str-el↗

arXiv2005

Quantum phase transition in capacitively coupled double quantum dots

We investigate two equivalent, capacitively coupled semiconducting quantum dots, each coupled to its own lead, in a regime where there are two electrons on the double dot. With increasing interdot coupling a rich range of behavior is uncovered: first a crossover from spin- to charge-Kondo physics, via an intermediate SU(4) state with entangled spin and charge degrees of freedom; followed by a quantum phase transition of Kosterlitz-Thouless type to a non-Fermi liquid `charge-ordered' phase with finite residual entropy and anomalous transport properties. Physical arguments and numerical renormalization group methods are employed to obtain a detailed understanding of the problem.

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arXiv2003

Dynamics and transport properties of Kondo insulators

A many-body theory of paramagnetic Kondo insulators is described, focusing specifically on single-particle dynamics, scattering rates, d.c. 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 d.c. transport and optical conductivites of Ce_3Bi_4Pt_3, SmB_6 and YbB_{12}. Good agreement is found, even quantitatively; and a mutually consistent picture of transport and optics results.

cond-mat.str-el↗

arXiv2002

Single-particle dynamics of the Anderson model: a local moment approach

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 valent 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.

cond-mat.str-el↗

arXiv2002

Finite temperature dynamics of the Anderson model

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 applicable to arbitrary interaction strengths, primary emphasis is given to the strongly correlated Kondo regime (characterized by the T=0 Kondo scale $ω_{\rm K}$). In particular the resultant universal scaling behaviour of the single-particle spectrum $D(ω; T) \equiv F(\frac{\w}{ω_{\rm K}}; \frac{T}{ω_{\rm K}})$ 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 $T / ω_{\rm K}$-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 $T/ω_{\rm K} \sim 1$, and to cross over smoothly to the Fermi liquid form $ρ(T) - ρ(0) \propto -(T/ω_{\rm K})^2$ in the low-temperature limit. The underlying approach, while naturally approximate, is moreover applicable to a broad range of quantum impurity and related models.

cond-mat.str-el↗

arXiv2002

Field-dependent dynamics of the Anderson impurity model

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 ($ω/ω_{\rm K}$) and field ($H/ω_{\rm K}$) 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.

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arXiv1998

Collective excitation spectrum of a disordered Hubbard model

We study the collective excitation spectrum of a d=3 site-disordered Anderson-Hubbard model at half-filling, via a random-phase approximation (RPA) about broken-symmetry, inhomogeneous unrestricted Hartree-Fock (UHF) ground states. We focus in particular on the density and character of low-frequency collective excitations in the transverse spin channel. In the absence of disorder, these are found to be spin-wave-like for all but very weak interaction strengths, extending down to zero frequency and separated from a Stoner-like band, to which there is a gap. With disorder present, a prominent spin-wave-like band is found to persist over a wide region of the disorder-interaction phase plane in which the mean-field ground state is a disordered antiferromagnet, despite the closure of the UHF single-particle gap. Site resolution of the RPA excitations leads to a microscopic rationalization of the evolution of the spectrum with disorder and interaction strength, and enables the observed localization properties to be interpreted in terms of the fraction of strong local moments and their site-differential distribution.

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arXiv1997

Insulating phases of the infinite-dimensional Hubbard model

A theory is developed for the T=0 Mott-Hubbard insulating phases of the infinite-dimensional Hubbard model at half-filling, including both the antiferromagnetic (AF) and paramagnetic (P) insulators. Local moments are introduced explicitly from the outset, enabling ready identification of the dominant low energy scales for insulating spin- flip excitations. Dynamical coupling of single-particle processes to the spin-flip excitations leads to a renormalized self-consistent description of the single-particle propagators that is shown to be asymptotically exact in strong coupling, for both the AF and P phases. For the AF case, the resultant theory is applicable over the entire U-range, and is discussed in some detail. For the P phase, we consider in particular the destruction of the Mott insulator, the resultant critical behaviour of which is found to stem inherently from proper inclusion of the spin-flip excitations.

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