Yukihiro Shimizu

Single-Particle and Magnetic Excitation Spectra of Degenerate Anderson Model with Finite f–f Coulomb Interaction

Spectral densities of local single-particle, magnetic and charge excitations are calculated for the impurity Anderson Hamiltonian based on the renormalization group approach. Calculation is made in wide range of energy and for various magnitude of f – f Coulomb interaction constant, U f , and for degeneracy factor from 2 to 5. The width of the peak at the Fermi level in the single-particle spectrum has always comparable scale to the magnetic excitation energy, and is never larger than the hybridization width. In the BIS side of this sharp peak a broad satellite with large intensity appears as a shoulder when U f is large and the f -electron number is intermediate larger than 1. The band-like peak in BIS of U -compounds, which has much larger width than that of the usual band theory, is interpreted by this broad satellite.

Numerical Renormalization Group Study of Magnetic Impurities in Superconductors

A magnetic impurity doped in a superconductor produces a localized excited state within the energy gap. This problem is studied by applying Wilsons numerical renormalization group method. The ground state and the first excited state are traced by changing the exchange coupling constant relative to the energy gap. Thereby the position of the localized excited state within the energy gap is determined over the whole regime of the magnitude of T K /Δ ( T K : Kondo temperature, Δ: superconducting energy gap). A crossing of the lowest doublet and singlet is clearly observed at T K /Δ≃0.3. The ferromagnetic and Ising cases have been studied also. In the ferromagnetic case the localized excited state stays close to the gap edge since the exchange coupling is renormalized to a weak coupling. The case of the Ising-like sd coupling, which is exactly solvable, can be used to check the reliability of the present approach and the effect of the discretization.

Excitation Spectra of the Two Impurity Anderson Model.I. : Critical Transition in the Two Magnetic Impurity Problem and the Roles of the Parity Splitting

Excitation spectra of the two impurity Anderson model are calculated by using the numerical renormalization group method. The critical transition found by Jones et al. is examined based on the model that the parity splitting is induced by the f - f transfer matrix, t . The low energy scale, ω l / T K , is approximately given as (( j - j c )/1.5) 2 +( t /23 T K ) 2 , and thus t suppresses the critical transition, where j is the exchange coupling normalized by the Kondo temperature T K , j c the critical value for the model without t . The γ-coefficient is proportional to ω l -1 , while the antiferromagnetic susceptibility to ln ω l -1 . The phase shift changes continuously near j c . It tends to singular jump as t →0. The parity splitting of the single particle excitation spectrum is enhanced by the exchange coupling.

Kondo Effect in Single Quantum Dot Systems – Study with Numerical Renormalization Group Method –

The tunneling conductance is calculated as a function of the gate voltage in wide temperature range for the single quantum dot systems with Coulomb interaction. We assume that two orbitals are active for the tunneling process. We show that the Kondo temperature for each orbital channel can be largely different. The tunneling through the Kondo resonance almost fully develops in the region \(T \lesssim 0.1 T_{\rm K}^{*} \sim 0.2 T_{\rm K}^{*}\), where T K * is the lowest Kondo temperature when the gate voltage is varied. At high temperatures the conductance changes to the usual Coulomb oscillations type. In the intermediate temperature region, the degree of the coherency of each orbital channel is different, so strange behaviors of the conductance can appear. For example, the conductance once increases and then decreases with temperature decreasing when it is suppressed at T =0 by the interference cancellation between different channels. The interaction effects in the quantum dot systems lead the sensitivit...

Many Body Effects on Electron Tunneling through Quantum Dots in an Aharonov-Bohm Circuit

Tunneling conductance of an Aharonov-Bohm circuit including two quantum dots is calculated based on the general expression of the conductance in the linear response regime of the bias voltage. The calculation is performed in a wide temperature range by using numerical renormalization group method. Various types of AB oscillations appear depending on the temperature and the potential depth of the dots. Especially, AB oscillations have strong higher harmonics components as a function of the magnetic flux when the potential of the dots is deep. This is related to the crossover of the spin state due to the Kondo effect on quantum dots. When the temperature rises up, the amplitude of the AB oscillations becomes smaller reflecting the breaking of the coherency.

Numerical Renormalization-Group Study of Particle-Hole Symmetry Breaking in Two-Channel Kondo Problem : Effect of Repulsion among Conduction Electrons and Potential Scattering

Particle-hole symmetry breaking perturbation in the two-channel pseudospin Kondo problem is studied by the numerical renormalization-group method. It is shown that the repulsion among conduction electrons at the impurity site and the single particle potential are relevant perturbations against the conventional non-Fermi-liquid fixed point. Although the repulsion (potential) with realistic strength prevents the overscreening of the pseudospin, it induces in turn a real spin, which is also overscreened again. Thus the real spin susceptibility becomes anomalous, contrary to the conventional two-channel Kondo problem.

Numerical Renormalization Group Study of Magnetic Impurities in Superconductors. II. Dynamical Excitation Spectra and Spatial Variation of the Order Parameter

The Kondo problem in superconductors is studied by extending Wilsons numerical renormalization group method. As a continuation to a previous paper (J. Phys. Soc. Jpn. 61 (1992) 3239), various problems related to the localized excited state produced by a magnetic impurity are examined in detail. In particular, the binding energy of the localized excited state, its spectral weight, one-electron and magnetic excitation spectra and the spatial variation of the order parameter are studied over the whole regime of the magnitude of T K /Δ ( T K : Kondo temperature, Δ: superconducting energy gap).

Barrier Height and Film Thickness Dependence of the TMR

We calculate the tunnel magneto-resistance (TMR) ratio by employing the Keldysh formalism. The barrier height dependence of TMR has a minimum whose origin is different from that of Slonczewskis theory. The TMR decreases and saturates with increasing film thickness. When the barrier is low and thick, the barrier height dependence of modulated density of states in the electrodes is dominant to the behavior of TMR. In this case the TMR increases with increasing bias voltage. When the barrier is high and thin, the barrier height dependence of damping factor through the insulating film is dominant to the behavior of TMR. In this case the TMR decreases greatly with increasing bias voltage. The temperature dependence is small below the temperature where electrons can hop over the barrier. As the barrier becomes high, the TMR becomes weakly temperature dependent, and the bias dependence becomes large.

An extended impurity Anderson model showing divergent susceptibility and decreasing resistivity with decreasing temperature

An extended two channel Anderson model, in which an extra local spin couples to the electrons on the localized orbits by the antiferromagnetic exchange, is studied by the numerical renormalization group method. The susceptibility shows low energy divergence inherent to the over screening effect, but the scattering intensity decreases as the conduction electron energy approaches to the Fermi level. This suggests the resistivity will decrease with decreasing temperature as seen in some dilute U alloys.

Numerical Renormalization Group Study of Non-Fermi-Liquid State on Dilute Uranium Systems

We investigate the non-Fermi-liquid (NFL) behavior of the impurity Anderson model (IAM) with non-Kramers doublet ground state of the f 2 configuration under the tetragonal crystalline electric field (CEF). The low energy spectrum is explained by a combination of the NFL and the local-Fermi-liquid parts which are independent with each other. The NFL part of the spectrum has the same form to that of two-channel-Kondo model (TCKM). We have a parameter range that the IAM shows the - ln T divergence of the magnetic susceptibility together with the positive magneto resistance. We point out a possibility that the anomalous properties of U x Th 1- x Ru 2 Si 2 including the decreasing resistivity with decreasing temperature can be explained by the NFL scenario of the TCKM type. We also investigate an effect of the lowering of the crystal symmetry. It breaks the NFL behavior at around the temperature, δ/10, where δ is the orthorhombic CEF splitting. The NFL behavior is still expected above the temperature, δ/10.