arXiv subjects

Akira Oguri

Publications and source records attributed to Akira Oguri.

At least 19 recordsLinked to original sources

arXiv2026

Three-body Fermi-liquid corrections for Andreev transport through quantum dots

We study crossed Andreev reflection occurring in quantum dots connected to one superconducting lead and two normal leads at low temperatures $T$. Specifically, we derive an exact formula for the conductance up to order $T^2$ in the large superconducting gap limit, which is expressed in terms of the transmission probabilities of Cooper pairs and interacting Bogoliubov quasiparticles. Our formulation is based on the latest version of Fermi-liquid theory for the Anderson impurity model, which has clarified the quasiparticle energy shifts of order $ω^2$ and $T^2$ -- namely, corrections of the same order as those arising from the finite lifetime of quasiparticles -- can be expressed exactly in terms of three-body correlations of impurity electrons. We also demonstrate how the three-body contributions evolve and affect the Cooper-pair tunneling as the Andreev level moves away from the Fermi level, using the numerical renormalization group approach. The results show that the Cooper-pair contribution to the $T^2$ terms of the local and nonlocal conductances becomes comparable to the Bogoliubov-quasiparticle contribution in the parameter region, in which superconducting proximity effects dominate over the Kondo effect.

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arXiv2026

Nonlocal Andreev transport through a quantum dot in a magnetic field: Interplay between Kondo, Zeeman, and Cooper-pair correlations

We study the nonlocal magnetotransport through a strongly correlated quantum dot, connected to multiple terminals consisting of two normal and one superconducting (SC) leads. Specifically, we present a comprehensive view on the interplay between the crossed Andreev reflection (CAR), the Kondo effect, and the Zeeman splitting at zero temperature in the large SC gap limit. The ground state of this network shows an interesting variety, which varies continuously with the system parameters, such as the coupling strength $Γ_S^{}$ between the SC lead and the quantum dot, the Coulomb repulsion $U$, the impurity level $\varepsilon_d^{}$, and the magnetic field $b$. We show, using the many-body optical theorem which is derived from the Fermi-liquid theory, that the nonlocal conductance is determined by the transmission rate of the Cooper pairs $\mathcal{T}_{\mathrm{CP}}^{} = \frac{1}{4} \sin^2 Θ\, \sin^2 \bigl(δ_{\uparrow}+ δ_{\downarrow})$ and that of the Bogoliubov particles $\mathcal{T}_{\mathrm{BG}}^{}= \frac{1}{2}\sum_σ \sin^2 δ_σ^{}$. Here, $δ_σ^{}$ is the phase shift of the renormalized Bogoliubov particles, and $Θ\equiv \cot^{-1} (ξ_d^{}/ Γ_S^{})$ is the Bogoliubov-rotation angle in the Nambu pseudo spin space, with $ξ_d^{} =\varepsilon_d^{}+U/2$. It is also demonstrated, using Wilson's numerical renormalization group approach, that the CAR is enhanced in the crossover region between the Kondo regime and the SC-proximity-dominated regime at zero magnetic field. The magnetic fields induce another crossover between the Zeeman-dominated regime and the SC-dominated regime. We find that the CAR is enhanced and becomes less sensitive to magnetic fields in the SC-dominated regime close to the crossover region spreading over the angular range of $π/4 \lesssim Θ\lesssim 3π/4$.

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arXiv2025

Role of bias and tunneling asymmetries in nonlinear Fermi-liquid transport through an SU($N$) quantum dot

We study how bias and tunneling asymmetries affect nonlinear current through a quantum dot with $N$ discrete levels in the Fermi liquid regime, using an exact low-energy expansion of the current derived up to terms of order $V^3$ with respect to the bias voltage. The expansion coefficients are described in terms of the phase shift, the linear susceptibilities, and the three-body correlation functions, defined with respect to the equilibrium ground state of the Anderson impurity model. In particular, the three-body correlations play an essential role in the order $V^3$ term, and their coupling to the nonlinear current depends crucially on the bias and tunnel asymmetries. The number of independent components of the three-body correlation functions increases with $N$ the internal degrees of the quantum dots, and it gives a variety in the low-energy transport. We calculate the correlation functions over a wide range of electron fillings of the Anderson impurity model with the SU($N$) internal symmetry, using the numerical renormalization group. We find that the order $V^3$ nonlinear current through the SU($N$) Kondo state, which occurs at electron fillings of $1$ and $N-1$ for strong Coulomb interactions, significantly varies with the three-body contributions as tunnel asymmetries increase. Furthermore, in the valence fluctuation regime toward the empty or fully occupied impurity state, a sharp peak emerges in the coefficient of $V^3$ current in the case at which bias and tunneling asymmetries cooperatively enhance the charge transfer from one of the electrodes.

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arXiv2025

Three-body Fermi liquid corrections for an infinite-$U$ SU($N$) Anderson impurity model

We study the three-body Fermi liquid effects in the SU($N$) Anderson impurity model in the strong interaction limit where the occupation number $N_d^{}$ of the impurity levels varies over the range of $0<N_d^{}<1$. The three-body correlation of impurity electrons contributes to the next-to-leading order terms of transport coefficients at low energies when the electron-hole symmetry, the time-reversal symmetries, or both are broken by external fields or potentials. Using the numerical renormalization group approach, we calculate the differential conductance and the nonlinear current noise through quantum dots, as well as the thermal conductivity of both quantum dots and magnetic alloys. Specifically, we focus on the SU(2) and SU(4) cases and demonstrate how the three-body contributions evolve in the limit of $U\to\infty$, across the $1/N$-filling Kondo regime and the valence fluctuation regime. Our results clarify how the three-body correlation affects low-energy transport, with a crucial dependence on the occupation number $N_d^{}$. We also show that the three-body correlation strongly couples with asymmetries in the tunnel couplings between quantum dots and reservoirs; in particular it significantly affects the nonlinear current through the quarter-filling Kondo state for $N=4$.

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arXiv2024

Thermoelectric transport and current noise through a multilevel Anderson impurity: Three-body Fermi-liquid corrections in quantum dots and magnetic alloys

We present a comprehensive Fermi-liquid description for thermoelectric transport and current noise, applicable to multilevel quantum dots (QD) and magnetic alloys (MA) without electron-hole or time-reversal symmetry. Our formulation for the low-energy transport is based on an Anderson model with $N$ discrete impurity levels, and is asymptotically exact at low energies, up to the next-leading order terms in power expansions with respect to temperature $T$ and bias voltage $eV$. The expansion coefficients can be expressed in terms of the Fermi-liquid parameters, which include the three-body correlation functions defined with respect to the equilibrium ground state in addition to the linear susceptibilities and the occupation number $N_d^{}$ of impurity electrons. We apply this formulation to SU($N$) symmetric QD and MA, and calculate the correlation functions for $N=4$ and $6$, using the numerical renormalization group approach. The three-body correlations are shown to be determined by a single parameter over a wide range of electron fillings $1 \lesssim N_d^{} \lesssim N-1$ for strong Coulomb interactions $U$, and they also exhibit the plateau structures due to the SU($N$) Kondo effects at integer values of $N_d^{}$. We find that the Lorenz number $L=κ/(T σ)$ for QD and MA, defined as the ratio of the thermal conductivity $κ$ to the electrical conductivity $σ$, deviates from the universal Wiedemann-Franz value $π^2/(3e^2)$ as the temperature increases from $T=0$, showing the $T^2$ dependence, the coefficient for which depends on the three-body correlations away from half filling. We also demonstrate the role of three-body correlations on the nonlinear current noise and the other transport coefficients.

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arXiv2024

Kondo Screening of Local Moments in a Triangular Triple Quantum Dot Connected to Normal and Superconducting Leads

We study the interplay between the Kondo and superconducting (SC) proximity effects, taking place in a triangular triple quantum dot (TTQD) connected to one normal and two SC leads. This system shows various quantum phases. Without the SC leads, the lowest two states that belong to the different spin sectors, $S=0$ and $S=1/2$, become energetically very close to each other near half filling. The singlet one is a Kondo-screened state by conduction electrons from the normal lead, and the doublet one is a resonating valence bond state with unpaired free spin which remains unscreened. Furthermore, when one additional electron enters the TTQD, the ground state becomes a doublet in which the $S=1$ local moment due to the Nagaoka ferromagnetism is partially screened by conduction electrons.The Cooper pairs penetrating into the TTQD from the SC leads reconstruct the wavefunctions and vary the phase boundaries between these quantum states in the parameter space. We calculate ground-state phase diagrams using the numerical renormalization group, and show that the SC proximity effect induces a reentrant transition in-between the three- and four-electron fillings.

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arXiv2023

Kondo Temperature Evaluated from Linear Conductance in Magnetic Fields

We theoretically and experimentally study the universal scaling property of the spin-1/2 Kondo state in the magnetic field dependence of bias-voltage linear conductance through a quantum dot at low temperatures. We discuss an efficient and reliable procedure to evaluate the Kondo temperature defined at the ground state from experimental or numerical data sets of the magnetic field dependence of the linear conductance or the magnetization of the quantum dot. This procedure is helpful for quantitative comparison of the theory and the experiment, and useful in Kondo-correlated systems where temperature control over a wide range is difficult, such as for cold atoms. We demonstrate its application to experimentally measured electric current through a carbon nanotube quantum dot.

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arXiv2022

Ground-state properties of a triangular triple quantum dot connected to superconducting leads

We study ground-state properties of a triangular triple quantum dot connected to two superconducting (SC) leads. In this system orbital motion along the triangular configuration causes various types of quantum phases, such as a Kondo effect with a four-fold degenerate state and the Nagaoka ferromagnetic mechanism, depending on the electron filling. The ground state also evolves as the Cooper pairs penetrate from the SC leads. We describe the phase diagram in a wide range of the parameter space, varying the gate voltage, the couplings between the dots and leads, and also the Josephson phase between the SC gaps. The results are obtained in the limit of large SC gap, carrying out exact diagonalization of an effective Hamiltonian. We also discuss a classification of the quantum states according to the fixed point of the Wilson numerical renormalization group (NRG). Furthermore, we show that the Bogoliubov zero-energy excitation determines the ground state of a $π$ Josephson junction at small electron fillings.

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arXiv2022

Current noise and Keldysh vertex function of an Anderson impurity in the Fermi liquid regime

We present a complete microscopic Fermi-liquid description for next-to-leading order transport through an Anderson impurity under a finite bias voltage $V$. It is applicable to multilevel quantum dots without particle-hole or time-reversal symmetry, and is constructed based on the nonequilibrium Keldysh formalism, taking into account the current conservation between electrons in the impurity levels and the conduction bands. Specifically, we derive the formula for the current noise generated in the steady flow up to terms of order $(eV)^3$ at zero temperature $T=0$. To this end, we calculate the Keldysh vertex functions $Γ_{σσ';σ'σ}^{ ν_1ν_2;ν_3ν_4} (ω,ω'; ω',ω)$, which depend on branches $ν_1, ν_2, ν_3$ and $ν_4$ of the time-loop contour and on spin degrees of freedom $σ$ and $σ'$, up to linear-order terms with respect to $eV$, $T$, and frequencies $ω$ and $ω'$. The coefficients of these linear-order terms are determined by a set of the parameters, defined with respect to the equilibrium ground state: the phase shift, static susceptibilities, and nonlinear three-body susceptibilities of the impurity electrons. The low-energy expressions of the vertex components are shown to satisfy the Ward identities with the Keldysh Green's functions expanded up to terms of order $ω^2$, $(eV)^2$, and $T^2$. We also find that the imaginary part of the Ward identities can be described in terms of the $eV$-dependent collision integrals for a single-quasiparticle excitation and that for a single quasiparticle-quasihole pair excitation. These collision integrals ensure the current conservation of the next-to-leading order Fermi-liquid transport due to the quasiparticles with a finite damping rate.

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arXiv2021

Nonlinear Fermi-liquid transport through a quantum dot in asymmetric tunnel junctions

We study the nonlinear conductance through a quantum dot, specifically its dependence on the asymmetries in the tunnel couplings and bias voltages $V$, at low energies. Extending the microscopic Fermi-liquid theory for the Anderson impurity model, we obtain an exact formula for the steady current $I$ up to terms of order $V^3$ in the presence of these asymmetries. The coefficients for the nonlinear terms are described in terms of a set of the Fermi-liquid parameters: the phase shift, static susceptibilities, and three-body correlation functions of electrons in the quantum dots, defined with respect to the equilibrium ground state. We calculate these correlation functions, using the numerical renormalization group approach (NRG), over a wide range of impurity-electron filling that can be controlled by a gate voltage in real systems. The NRG results show that the order $V^2$ nonlinear current is enhanced significantly in the valence fluctuation regime. It is caused by the order $V$ energy shift of the impurity level, induced in the presence of the tunneling or bias asymmetry. Furthermore, in the valence fluctuation regime, we also find that the order $V^3$ nonlinear current exhibits a shoulder structure, for which the three-body correlations that evolve for large asymmetries play an essential role.

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arXiv2021

Three-body correlations in nonlinear response of correlated quantum liquid

Behavior of quantum liquids is a fascinating topic in physics. Even in a strongly correlated case, the linear response of a given system to an external field is described by the fluctuation-dissipation relations based on the two-body correlations in the equilibrium. However, to explore nonlinear non-equilibrium behaviors of the system beyond this well-established regime, the role of higher order correlations starting from the three-body correlations must be revealed. In this work, we experimentally investigate a controllable quantum liquid realized in a Kondo-correlated quantum dot and prove the relevance of the three-body correlations in the nonlinear conductance at finite magnetic field, which validates the recent Fermi liquid theory extended to the non-equilibrium regime.

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arXiv2020

Fermi liquid theory for nonlinear transport through a multilevel Anderson impurity

We present a microscopic Fermi-liquid view on the low-energy transport through an Anderson impurity with $N$ discrete levels, at arbitrary electron filling $N_d$. It is applied to nonequilibrium current fluctuations, for which the two-quasiparticle collision integral and the three-body correlations that determine the quasiparticle energy shift play important roles. Using the numerical renormalization group up to $N=6$, we find that for strong interactions the three-body fluctuations are determined by a single parameter other than the Kondo energy scale in a wide filling range $1 \lesssim N_d \lesssim N-1$. It significantly affects the current noise for $N>2$ and the behavior of noise in magnetic fields.

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arXiv2020

Field-induced SU(4) to SU(2) Kondo crossover in a half-filling nanotube dot: spectral and finite-temperature properties

We study finite-temperature properties of the Kondo effect in a carbon nanotube (CNT) quantum dot using the Wilson numerical renormalization group (NRG). In the absence of magnetic fields, four degenerate energy levels of the CNT consisting of spin and orbital degrees of freedom give rise to the SU(4) Kondo effect. We revisit the universal scaling behavior of the SU(4) conductance for quarter- and half-filling in a wide temperature range. We find that the filling dependence of the universal scaling behavior at low temperatures $T$ can be explained clearly with an extended Fermi-liquid theory. This theory clarifies that a $T^{2}$ coefficient of conductance becomes zero at quarter-filling whereas the coefficient at half-filling is finite. We also study a field-induced crossover from the SU(4) to SU(2) Kondo state observed at the half-filled CNT dot. The crossover is caused by the matching of the spin and orbital Zeeman splittings, which lock two levels among the four at the Fermi level even in magnetic fields $B$. We find that the conductance shows the SU($4$) scaling behavior at $μ_{B}B<k_{B}T_{K}^{\mathrm{SU(4)}}$ and it exhibits the SU($2$) universality at $μ_{B}B\gg k_{B}T_{K}^{\mathrm{SU(4)}}$, where $T_{K}^{\mathrm{SU(4)}}$ is the SU($4$) Kondo temperature. To clarify how the excited states evolve along the SU(4) to SU(2) crossover, we also calculate the spectral function. The results show that the Kondo resonance width of the two states locked at the Fermi level becomes sharper with increasing fields. The spectral peaks of the other two levels moving away from the Fermi level merge with atomic limit peaks for $μ_{B}B \gtrsim k_{B}T_{K}^{\mathrm{SU(4)}}$.

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arXiv2020

Higher-order Fermi-liquid corrections for an Anderson impurity away from half-filling III: non-equilibrium transport

We extend the microscopic Fermi-liquid theory for the Anderson impurity [Phys.\ Rev.\ B {\bf 64}, 153305 (2001)] to explore non-equilibrium transport at finite magnetic fields. Using the Ward identities in the Keldysh formalism with the analytic and anti-symmetric properties of the vertex function, the spin-dependent Fermi-liquid corrections of order $T^2$ and $(eV)^2$ are determined at low temperatures $T$ and low bias voltages $eV$. Away from half-filling, these corrections can be expressed in terms of the linear and non-linear static susceptibilities which represent the two-body and three-body fluctuations, respectively. We calculate the non-linear susceptibilities using the numerical renormalization group, to explore the differential conductance $dI/dV$ through a quantum dot. We find that the two-body fluctuations dominate the corrections in the Kondo regime at zero magnetic field. The contribution of the three-body fluctuations become significant far away from half-filling, especially in the valence-fluctuation regime and empty-orbital regimes. In finite magnetic fields, the three-body contributions become comparable to the two-body contributions, and play an essential role in the splitting of the zero-bias conductance peak occurring at a magnetic field of the order of the Kondo energy scale. We also apply our microscopic formulation to the magneto-resistance and thermal conductivity of dilute magnetic alloys away from half-filling.

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arXiv2020

Higher-order Fermi-liquid corrections for an Anderson impurity away from half-filling II: equilibrium properties

We study the low-energy behavior of the vertex function of a single Anderson impurity away from half-filling for finite magnetic fields, using the Ward identities with careful consideration of the anti-symmetry and analytic properties. The asymptotic form of the vertex function $Γ_{σσ';σ'σ}^{}(iω,iω';iω',iω)$ is determined up to terms of linear order with respect to the two frequencies $ω$ and $ω'$, as well as the $ω^2$ contribution for anti-parallel spins $σ'\neq σ$ at $ω'=0$. From these results, we also obtain a series of the Fermi-liquid relations beyond those of Yamada-Yosida. The $ω^2$ real part of the self-energy $Σ_σ^{}(iω)$ is shown to be expressed in terms of the double derivative $\partial^2Σ_σ^{}(0)/\partial ε_{dσ}^{2}$ with respect to the impurity energy level $ε_{dσ}^{}$, and agrees with the formula obtained recently by Filippone, Moca, von Delft, and Mora in the Nozières phenomenological Fermi-liquid theory [Phys.\ Rev.\ B {\bf 95}, 165404 (2017)]. We also calculate the $T^2$ correction of the self-energy, and find that the real part can be expressed in terms of the three-body correlation function $χ_{\uparrow\downarrow,-σ}^{[3]} = \partial χ_{\uparrow\downarrow}/\partial ε_{d,-σ}^{}$. We also provide an alternative derivation of the asymptotic form of the vertex function. Specifically, we calculate the skeleton diagrams for the vertex function $Γ_{σσ;σσ}^{}(iω,0;0,iω)$ for parallel spins up to order $U^4$ in the Coulomb repulsion $U$. It directly clarifies the fact that the analytic components of order $ω$ vanish as a result of the cancellation of four related Feynman diagrams which are related to each other through the anti-symmetry operation.

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arXiv2019

Quantum noise in carbon nanotubes as a probe of correlations in the Kondo regime

Most of the time, electronic excitations in mesoscopic conductors are well described, around equilibrium, by non-interacting Landau quasi-particles. This allows a good understanding of the transport properties in the linear regime. However, the role of interaction in the non-equilibrium properties beyond this regime has still to be established. A paradigmatic example is the Kondo many body state, which can be realized in a carbon nanotube (CNT) quantum dot for temperatures below the Kondo temperature $T_K$. As CNT possess spin and orbital quantum numbers, it is possible to investigate the twofold degenerate SU(2) Kondo effect as well as the four fold degenerate SU(4) state by tuning the degeneracies and filling factor. This article aims at providing a comprehensive review on our recent works on the Kondo correlations probed by quantum noise measurement both at low and high frequencies and demonstrate how current noise measurements yield new insight on interaction effects and dynamics of a Kondo correlated state.

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arXiv2018

Current cross-correlation in the Anderson impurity model with exchange interaction

We study spin-entanglement of the quasiparticles of the local Fermi liquid excited in nonlinear current through a quantum dot described by the Anderson impurity model with two degenerate orbitals coupled to each other via an exchange interaction. Applying the renormalized perturbation theory, we obtain the precise form of the cumulant generating function and cross-correlations for the currents with spin angled to arbitrary directions, up to third order in the applied bias voltage. It is found that the exchange interaction gives rise to spin-angle dependency in the cross-correlation between the currents through the two different orbitals, and also brings an intrinsic cross-correlation of currents with three different angular momenta.

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arXiv2018

Bell-state correlations in current of local Fermi liquid

We study Bell-state correlations for quasiparticle pairs excited in nonlinear current through a double quantum dot in the Kondo regime. Exploiting the renormalized perturbation expansion in the residual interactions of the local Fermi liquid and Bell's inequality for cross correlation of spin currents through distinct conduction channels, we derive an asymptotically exact form of Bell's correlation for the double dot at low bias voltages. We find that pairs of quasiparticles and holes excited by the residual exchange interaction can violate Bell's inequality for the cross correlations of the spin currents.

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