arXiv subjects

Akira Oguri

Publications and source records attributed to Akira Oguri.

At least 55 records · Page 3Linked to original sources

arXiv2008

Numerical Renormalization Group Approach to a Quantum Dot Coupled to Normal and Superconducting Leads

We study transport through a quantum dot coupled to normal and superconducting leads using the numerical renormalization group method. We show that the low-energy properties of the system are described by the local Fermi liquid theory despite of the superconducting correlations penetrated into the dot due to a proximity effect. We calculate the linear conductance due to the Andreev reflection in the presence of the Coulomb interaction. It is demonstrated that the maximum structure appearing in the conductance clearly characterizes a crossover between two distinct spin-singlet ground states, i.e. the superconducting singlet state and the Kondo singlet state. It is further elucidated that the gate-voltage dependence of the conductance shows different behavior in the superconducting singlet region from that in the Kondo singlet region.

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arXiv2008

Andreev Transport through Side-Coupled Double Quantum Dots

We study the transport through side-coupled double quantum dots, connected to normal and superconducting (SC) leads with a T-shape configuration. We find, using the numerical renormalization group, that the Coulomb interaction suppresses SC interference in the side dot, and enhances the conductance substantially in the Kondo regime. This behavior stands in total contrast to a wide Kondo valley seen in the normal transport. The SC proximity penetrating into the interfacial dot pushes the Kondo clouds, which screens the local moment in the side dot, towards the normal lead to make the singlet bond long. The conductance shows a peak of unitary limit as the cloud expands. Furthermore, two separate Fano structures appear in the gate-voltage dependence of the Andreev transport, where a single reduced plateau appears in the normal transport.

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arXiv2007

Kondo effect in asymmetric Josephson couplings through a quantum dot

Asymmetry in the Josephson couplings between two superconductors through a quantum dot is studied based on a single impurity Anderson model using the numerical renormalization group (NRG). Specifically, we examine how the difference between the couplings Γ_L and Γ_R affects the ground state, which is known to show a quantum phase transition between a nonmagnetic singlet and a magnetic doublet depending on the various parameters; the Coulomb interaction U, onsite potential ε_d, level width Γ_L, Γ_R, caused by the hybridization, and superconducting gaps Δ_L and Δ_R for the leads on the left and right. Our results show that whether the local moment is fully screened or not depends substantially on the asymmetry in the couplings Γ_L \neq Γ_R. It tends to make the singlet ground state stable, while the size and phase difference of the two superconducting gaps tend to suppress the screening. We also discuss some general symmetry properties of the system and their relation to the current conservation.

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arXiv2006

Kondo screening of a high-spin Nagaoka state in a triangular quantum dot

We study transport through a triangle triple quantum dot connected to two noninteracting leads using the numerical renormalization group (NRG). The triangle has a high-spin ground state of S=1 caused by a Nagaoka ferromagnetism, when it is isolated and has one extra electron introduced into a half-filling. The results show that the conduction electrons screen the local moment via two separate stages with different energy scales. The half of the S=1 is screened first by one of the channel degrees, and then at very low temperature the remaining half is fully screened to form a Kondo singlet. The transport is determined by two phase shifts for quasi-particles with even and odd parities, and then a two-terminal conductance in the series configuration is suppressed $g_{\rm series} \simeq 0$, while plateau of a four-terminal parallel conductance reaches a Unitary limit value $g_{\rm parallel} \simeq 4e^2/h$ of two conducting modes.

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arXiv2006

Mixed-state aspects of an out-of-equilibrium Kondo problem in a quantum dot

We reexamine basic aspects of a nonequilibrium steady state in the Kondo problem for a quantum dot under a bias voltage using a reduced density matrix, which is obtained in the Fock space by integrating out one of the two conduction channels. The integration has been carried out by discretizing the conduction channels preserving the two-fold degeneracy due to the left-going and right-going scattering states. The remaining subspace is described by a single-channel Anderson model, and the statistical weight is determined by the reduced density matrix. In the noninteracting case, it can be constructed as the mixed states that show a close similarity to the high-temperature distribution in equilibrium. Specifically, if the system has an inversion symmetry, the one-particle states in an energy window between the two chemical potentials μ_R and μ_L are occupied, or unoccupied, completely at random with an equal weight. The Coulomb interaction preserves these aspects, and the correlation functions can be expressed in a Lehmann-representation form using the mixed-state statistical weight.

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arXiv2006

NRG approach to the transport through a finite Hubbard chain connected to reservoirs

We study the low-energy properties of a Hubbard chain of finite size N_C connected to two noninteracting leads using the numerical renormalization group (NRG) method. The results obtained for N_C = 3 and 4 show that the low-lying eigenstates have one-to-one correspondence with the free quasi-particle excitations of a local Fermi liquid. It enables us to determine the transport coefficients from the fixed-point Hamiltonian. At half-filling, the conductance for even N_C decreases exponentially with increasing U showing a tendency towards the development of a Mott-Hubbard gap. In contrast, for odd N_C, the Fermi-liquid nature of the low-energy states assures perfect transmission through the Kondo resonance. Our formulation to deduce the conductance from the fixed-point energy levels can be applied to various types of interacting systems.

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arXiv2006

Transport theory for interacting electrons connected to reservoirs

We describe microscopic theory for the quantum transport through finite interacting systems connected to noninteracting leads. It can be applied to small systems such as quantum dots, quantum wires, atomic chain, molecule, and so forth. The Keldysh formalism is introduced to study the nonlinear current-voltage characteristics, and general properties of the nonequilibrium Green's functions are provided. We apply the formulated to an out-of-equilibrium Anderson model that has been used widely for the Kondo effect in quantum dots. In the linear-response regime the Kubo formalism still has an advantage, because it relates the transport coefficients directly to the correlation functions defined with respect to the thermal equilibrium, and it has no ambiguities about a profile of the inner electric field. We introduce a many-body transmission coefficient, by which the dc conductance can be expressed in a Landauer-type form, quite generally. We also discuss transport properties of the Tomonaga-Luttinger liquid, which has also been an active field of research in this decade.

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arXiv2006

Numerical renormalization group approach to a quartet quantum-dot array connected to reservoirs:gate-voltage dependence of the conductance

The ground-state properties of quartet quantum-dot arrays are studied using the numerical renormalization group (NRG) method with a four-site Hubbard model connected to two non-interacting leads. Specifically, we calculate the conductance and local charge in the dots from the many-body phase shifts, which can be deduced from the fixed-point eigenvalues of NRG. As a function of the on-site energy $ε_d$ which corresponds to the gate voltage, the conductance shows alternatively wide peak and valley. Simultaneously, the total number of electrons $N_{\rm el}$ in the four dots shows a quantized stair case behavior due to a large Coulomb interaction $U$. The conductance plateaus of the Unitary limit emerging for odd $N_{\rm el}$ are caused by the Kondo effect. The valleys of the conductance emerge for even $N_{\rm el}$, and their width becomes substantially large at half-filling. It can be regarded as a kind of the Mott-Hubbard insulating behavior manifesting in a small system. These structures of the plateaus and valleys become weak for large values of the hybridization strength $Γ$ between the chain and leads. We also discuss the parallel conductance for the array connected to four leads.

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arXiv2004

Quantum phase transition in a minimal model for the Kondo effect in a Josephson junction

We propose a minimal model for the Josephson current through a quantum dot in a Kondo regime. We start with the model that consists of an Anderson impurity connected to two superconducting (SC) leads with the gaps $Δ_α=|Δ_α| e^{i θ_α}$, where $α= L, R$ for the lead at left and right. We show that, when one of the SC gaps is much larger than the others $|Δ_L| \gg |Δ_R|$, the starting model can be mapped exactly onto the single-channel model, which consists of the right lead of $Δ_R$ and the Anderson impurity with an extra onsite SC gap of $Δ_d \equiv Γ_L e^{i θ_L}$. Here $θ_L$ and $Γ_L$ are defined with respect to the starting model, and $Γ_L$ is the level width due to the coupling with the left lead. Based on this simplified model, we study the ground-state properties for the asymmetric gap, $|Δ_L| \gg |Δ_R|$, using the numerical renormalization group (NRG) method. The results show that the phase difference of the SC gaps $ϕ\equiv θ_R -θ_L$, which induces the Josephson current, disturbs the screening of the local moment to destabilize the singlet ground state typical of the Kondo system. It can also drive the quantum phase transition to a magnetic doublet ground state, and at the critical point the Josephson current shows a discontinuous change. The asymmetry of the two SC gaps causes a re-entrant magnetic phase, in which the in-gap bound state lies close to the Fermi level.

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arXiv2004

Fermi liquid theory for the nonequilibrium Kondo effect at low bias voltages

In this report, we describe a recent development in a Fermi liquid theory for the Kondo effect in quantum dots under a finite bias voltage $V$. Applying the microscopic theory of Yamada and Yosida to a nonequilibrium steady state, we derive the Ward identities for the Keldysh Green's function, and determine the low-energy behavior of the differential conductance $dI/dV$ exactly up to terms of order $(eV)^2$ for the symmetric Anderson model. These results are deduced from the fact that the Green's function at the impurity site is a functional of a nonequilibrium distribution $f_{\text{eff}}(ω)$, which at $eV=0$ coincides with the Fermi function. Furthermore, we provide an alternative description of the low-energy properties using a renormalized perturbation theory (RPT). In the nonequilibrium state the unperturbed part of the RPT is determined by the renormalized free quasiparticles, the distribution function of which is given by $f_{\text{eff}}(ω)$. The residual interaction between the quasiparticles $\widetilde{U}$, which is defined by the full vertex part at zero frequencies, is taken into account by an expansion in the power series of $\widetilde{U}$. We also discuss the application of the RPT to a high-bias region beyond the Fermi-liquid regime.

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arXiv2003

Effects of Electron Correlation on the Transport through a Quantum Dot Superlattice

We study correlation effects on the transport through a quantum dot superlattice using a two-dimensional Hubbard model connected to two noninteracting leads. To calculate the zero-temperature conductance away from half-filling, we have used the non-magnetic solution of the Hartree-Fock approximation for the unperturbed Green's function, and then take into account the electron correlation beyond the mean field theory through the second-order self-energy corrections with respect to the residual interaction. When the value of the onsite potential $ε_d$ or the repulsion $U$ is changed, the conductance shows a number of peaks corresponding to the resonance states passing through the Fermi energy. The behavior of the resonance states for correlated electrons can be investigated using the eigenvalue of the effective Hamiltonian for a quasi-particle of a local Fermi liquid. We calculate the eigenvalue using the second-order self-energy, and show explicitly that it can be compared with the conductance peak.

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arXiv2003

On the applicability of an equation of motion method at low-temperatures: comments on cond-mat/0309458 and cond-mat/0308413

The equation of motion method (EOM) is one of the approximations to calculate transport coefficients of interacting electron systems. The method is known to be useful to examine high-temperature properties. However, sometimes a naive application of the EOM fails to capture an important physics at low-energy scale, and it happens in recent preprints cond-mat/0309458 and cond-mat/0308413 which study a series of quantum dots. These preprints concluded that a unitarity-limit transport due to the Kondo resonance, which has been deduced from a Fermi-liquid behavior of the self-energy at T=0, $ω=0$ [A.O., PRB {\bf 63}, 115305 (2001)], does not occur. We show that the EOM self-energy obtained with a finite cluster has accidentally a singular $1/ω$ dependence around the Fermi energy, and it misleads one to the result incompatible with a Fermi-liquid ground state.

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arXiv2003

Transmission Coefficient as a Three-Point Retarded Function

We show that the transmission probability through a small interacting region connected to noninteracting leads, can be written in terms of a retarded product of a three-point correlation function defined in the real time. Our proof is based on the Kubo formalism, and uses an Eliashberg theory for analytic properties of vertex functions. The aim of this short report is to add a new viewpoint to the transport theory described in the previous paper: A.O., J. Phys. Soc. Jpn. 70 (2001) 2666.

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arXiv2002

Transmission probability through small interacting systems: application to a series of quantum dots

We apply a theory for the transmission probability of small interacting systems, which was formulated based on the Kubo formalism in our previous study, to a series of quantum dots described by the N-impurity Anderson model. In this report, we present the transmission pobability for the system of N=2 calculated using the order $U^2$ self-energy and vertex corrections. Particularly, we examine the features in the two typical parameter regions, $t<Γ$ and $t>Γ$, where the Kondo effect or the inter-dot correlation dominates. Here, $t$ is the inter-dot transfer and $Γ$ is the level broadening caused by the coupling with the noninteracting leads.

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arXiv2002

Out-of-equilibrium Anderson model at high and low bias voltages

We study the high- and low-voltage properties of the out-of-equilibrium Anderson model for quantum dots, using a functional method in the Keldysh formalism. The Green's function at the impurity site can be regarded as a functional of a nonequilibrium distribution function. The dependence of the Green's function on the bias voltage V and temperature T arises through the nonequilibrium distribution function. From this behavior as a functional, it is shown that the nonequilibrium Green's function at high-voltage limit is identical to the equilibrium Green's function at high-temperature limit. This correspondence holds when the couplings of the dot and two leads, at the left and right, are equal. In the opposite limit, for small eV, the low-energy behavior of the Green's function can be described by the local Fermi-liquid theory up to terms of order $(eV)^2$. These results imply that the correlation effects due to the Coulomb interaction U can be treated adiabatically in the two limits, at high and low bias voltages.

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arXiv2002

Effects of disorder on conductance through small interacting systems

We study the effects of disorders on the transport through small interacting systems based on a two-dimensional Hubbard cluster of finite size connected to two noninteracting leads. This system can be regarded as a model for the superlattice of quantum dots or atomic network of the nanometer size. We calculate the conductance at T=0 using the order $U^2$ self-energy in an electron-hole symmetric case. The results show that the conductance is ensitive to the randomness when the resonance states are situated near the Fermi energy.

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arXiv2001

Perturbation Study of the Conductance through an Interacting Region Connected to Multi-Mode Leads

We study the effects of electron correlation on transport through an interacting region connected to multi-mode leads based on the perturbation expansion with respect to the inter-electron interaction. At zero temperature the conductance defined in the Kubo formalism can be written in terms of a single-particle Green's function at the Fermi energy, and it can be mapped onto a transmission coefficient of the free quasiparticles described by an effective Hamiltonian. We apply this formulation to a two-dimensional Hubbard model of finite size connected to two noninteracting leads. We calculate the conductance in the electron-hole symmetric case using the order $U^2$ self-energy. The conductance shows several maximums in the $U$ dependence in some parameter regions of $t_y/t_x$, where $t_x$ ($t_y$) is the hopping matrix element in the $x$- ($y$-) directions. This is caused by the resonance occurring in some of the subbands, and is related with the $U$ dependence of the eigenvalues of the effective Hamiltonian.

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arXiv2001

Fermi liquid theory for the Anderson model out of equilibrium

We study low-energy properties of the Anderson impurity under a finite bias voltage $V$ using the perturbation theory in $U$ of Yamada and Yosida in the nonequilibrium Keldysh diagrammatic formalism, and obtain the Ward identities for the derivative of the self-energy with respect to $V$. The self-energy is calculated exactly up to terms of order $ω^2$, $T^2$ and $V^2$, and the coefficients are defined with respect to the equilibrium ground state. From these results, the nonlinear response of the current through the impurity has been deduced up to order $V^3$.

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