arXiv subjects

Rui Sakano

Publications and source records attributed to Rui Sakano.

At least 19 recordsLinked to original sources

arXiv2024

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 $L=\kappa/(T \sigma)$ for QD and MA, defined as the ratio of the thermal conductivity $\kappa$ to the electrical conductivity $\sigma$, deviates from the universal Wiedemann-Franz value $\pi^2/(3e^2)$ 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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arXiv2023

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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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

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

Fano-Kondo resonance versus Kondo plateau in an Aharonov-Bohm ring with an embedded quantum dot

We theoretically examine the transport through an Aharonov-Bohm ring with an embedded quantum dot (QD), the so-called QD interferometer, to address two controversial issues regarding the shape of the Coulomb peaks and measurement of the transmission phase shift through a QD. We extend a previous model [B. R. Bulka and P. Stefanski, Phys. Rev. Lett. 86, 5128 (2001); W. Hofstetter, J. Konig, and H. Schoeller, ibid. 87, 156803 (2001)] to consider multiple conduction channels in two external leads, L and R. We introduce a parameter p_α (|p_α| \le 1) to characterize a connection between the two arms of the ring through lead α(=L, R), which is the overlap integral between the conduction modes coupled to the two arms. First, we study the shape of a conductance peak as a function of energy level in the QD, in the absence of electron-electron interaction U. We show an asymmetric Fano resonance for |p_{L,R}| = 1 in the case of single conduction channel in the leads and an almost symmetric Breit-Wigner resonance for |p_{L,R}| < 0.5 in the case of multiple channels. Second, the Kondo effect is taken into account by the Bethe ansatz exact solution in the presence of U. We precisely evaluate the conductance at temperature T=0 and show a crossover from an asymmetric Fano-Kondo resonance to the Kondo plateau with changing p_{L,R}. Our model is also applicable to the multi-terminal geometry of the QD interferometer. We discuss the measurement of the transmission phase shift through the QD in a three-terminal geometry by a "double-slit experiment." We derive an analytical expression for the relation between the measured value and the intrinsic value of the phase shift.

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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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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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arXiv2017

Quantum Fluctuations along Symmetry Crossover in Kondo-correlated Quantum Dot

Universal properties of entangled many-body states are controlled by their symmetry and quantum fluctuations. By magnetic-field tuning of the spin-orbital degeneracy in a Kondo-correlated quantum dot, we have modified quantum fluctuations to directly measure their influence on the many-body properties along the crossover from $SU(4)$ to $SU(2)$ symmetry of the ground state. High-sensitive current noise measurements combined with the non-equilibrium Fermi liquid theory clarify that the Kondo resonance and electron correlations are enhanced as the fluctuations, measured by the Wilson ratio, increase along the symmetry crossover. Our achievement demonstrates that non-linear noise constitutes a measure of quantum fluctuations that can be used to tackle quantum phase transitions.

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arXiv2016

Field-Enhanced Kondo Correlations in a Half-Filling Nanotube Dot: Evolution of an SU(N) Fermi-Liquid Fixed Point

We theoretically study an emergent SU(2) symmetry which is suggested by recent magneto-transport measurements, carried out near two electrons filling of a carbon nanotube quantum dot. It emerges in the case where the spin and orbital Zeeman splittings cancel each other out for two of the one-particle dot levels among four. Using the Wilson numerical renormalization group, we show that a crossover from the SU(4) to SU(2) Fermi-liquid behavior occurs at two impurity-electrons filling as magnetic field increases. We also find that the quasiparticles are significantly renormalized as the remaining two one-particle levels move away from the Fermi level and are frozen at high magnetic fields. In order to clarify how the ground state evolves during such a crossover, we also reexamine the SU(N) Kondo singlet state for M impurity-electrons filling in the limit of strong exchange interactions. We show that the nondegenerate Fermi-liquid fixed point of Nozièes and Blandin can be described as a bosonic Perron-Frobenius vector for M hard-core bosons, each of which consists of one impurity-electron and one conduction hole. This interpretation can also be applied to the Fermi-liquid fixed-point without the SU(N) symmetry.

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arXiv2015

Universality of Non-equilibrium Fluctuations in Strongly Correlated Quantum Liquids

Interacting quantum many-body systems constitute a fascinating playground for researchers since they form quantum liquids with correlated ground states and low-lying excitations, which exhibit universal behaviour. In fermionic systems, such quantum liquids are realized in helium-3 liquid, heavy fermion systems, neutron stars and cold gases. Their properties in the linear-response regime have been successfully described by the theory of Fermi liquids. However, non-equilibrium properties beyond this regime have still to be established and remain a key issue of many-body physics. Here, we show a precise experimental demonstration of Landau Fermi-liquid theory extended to the non-equilibrium regime in a 0-D system. Combining transport and ultra-sensitive current noise measurements, we have unambiguously identified the SU(2) and SU(4) symmetries of quantum liquid in a carbon nanotube tuned in the universal Kondo regime. We find that, while the electronic transport is well described by the free quasi-particle picture around equilibrium, a two-particle scattering process due to residual interaction shows up in the non-equilibrium regime. By using the extended Fermi-liquid theory, we obtain the interaction parameter "Wilson ratio" $R=1.9 \pm 0.1$ for SU(2) and $R=1.35 \pm 0.1$ for SU(4) as well as the corresponding effective charges, characterizing the quantum liquid behaviour. This result, in perfect agreement with theory, provides a strong quantitative experimental background for further developments of the many-body physics. Moreover, we discovered a new scaling law for the effective charge, signalling as-yet-unknown universality in the non-equilibrium regime. Our method to address quantum liquids through their non-equilibrium noise paves a new road to tackle the exotic nature of quantum liquids out-of-equilibrium in various physical systems.

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arXiv2015

Exact Green's function for a multi-orbital Anderson impurity at high bias voltages

We study the nonequilibrium Keldysh Green's function for an N-orbital Anderson model at high bias voltages, extending a previous work, which for the case only with the spin degrees of freedom N=2, to arbitrary N. Our approach uses an effective non-Hermitian Hamiltonian that is defined with respect to a Liouville-Fock space in the context of a thermal field theory. The result correctly captures the relaxation processes at high energies, and is asymptotically exact not only in the high-bias limit but also in the high-temperature limit at thermal equilibrium. We also present an explicit continued-fraction representation of the Green's function. It clearly shows that the imaginary part is recursively determined by the decay rate of intermediate states with at most N-1 particle-hole-pair excitations. These high-bias properties follow from the conservations of a generalized charge and current in the Liouville-Fock space. We also examine temperature dependence of the spectral function in equilibrium, comparing the exact results with both the finite-T and infinite-T results of the non-crossing approximation (NCA).

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arXiv2013

Exact interacting Green's function for the Anderson impurity at high bias voltages

We describe some exact high-energy properties of a single Anderson impurity connected to two noninteracting leads in a nonequilibrium steady state. In the limit of high bias voltages, and also in the high-temperature limit at thermal equilibrium, the model can be mapped on to an effective non-Hermitian Hamiltonian consisting of two sites, which correspond to the original impurity and its image that is defined in a doubled Hilbert space referred to as Liouville-Fock space. For this, we provide a heuristic derivation using a path-integral representation of the Keldysh contour and the thermal field theory, in which the time evolution along the backward contour is replicated by extra degrees of freedom corresponding to the image. We find that the effective Hamiltonian can also be expressed in terms of charges and currents. From this, it can be deduced that the dynamic susceptibilities for the charges and the current fluctuations become independent of the Coulomb repulsion U in the high bias limit. Furthermore, the equation of motions for the Green's function and two other higher-order correlation functions constitute a closed system. The exact solution obtained from the three coupled equations extends the atomic-limit solution such that the self-energy correctly captures the imaginary part caused by the relaxation processes at high energies. The spectral weights of the upper and lower Hubbard levels depend sensitively on the asymmetry in the tunneling couplings to the left and right leads.

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