Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review B

I−V characteristics of an open quantum dot with a Coulomb interaction: Extension of the Landauer formula with exact scattering eigenstates

Akinori Nishino, Takashi Imamura, Naomichi Hatano

Published Jan 13, 2011• 14 citations
Publisher

Abstract

Through an extension of the Landauer formula, we study the electron transport in an open quantum dot system under a finite bias voltage. The system that we study is an interacting resonant-level model equipped with infinite two leads of a linearized dispersion relation. We explicitly construct many-electron scattering eigenstates whose incident states are free-fermionic. A remarkable feature of the scattering state is the appearance of many-body bound states after the scattering. Extending Landauer's idea, we calculate the average electric current flowing through the quantum dot. We use a renormalization-group technique to deal with the divergences that appear in the limit of the large bandwidth of the leads. As a result, the average electric current is brought to a universal form.

DOI
10.1103/physrevb.83.035306

Related papers

Renormalization group analysis of the interacting resonant-level model at finite bias: Generic analytic study of static properties and quench dynamics

Sabine Andergassen, Mikhail Pletyukhov, Dirk Schuricht +2 more

Using a real-time renormalization group method we study the minimal model of a quantum dot dominated by charge fluctuations, the two-lead interacting resonant level model, at finite bias voltage. We develop a set of RG equations to treat the case of weak and strong charge fluctuations, together with the determination of power-law exponents up to second order in the Coulomb interaction. We derive analytic expressions for the charge susceptibility, the steady-state current, and the conductance in the situation of arbitrary system parameters, in particular away from the particle-hole symmetric point and for asymmetric Coulomb interactions. In the asymmetric situation we find that power laws can be observed for the current only as a function of the level position (gate voltage) but in general not as a function of the voltage except for extremely large voltages. Furthermore, we study the quench dynamics after sudden switch-on of the level-lead couplings. The time evolution of the dot occupation and current is governed by exponential relaxation accompanied by voltage-dependent oscillations and characteristic algebraic decay.

arXiv:1010.5666•Physical Review B•May 6, 2011•69 citations

Entanglement generation through an open quantum dot: Exact two-electron scattering state in the Anderson model

Takashi Imamura, Akinori Nishino, Naomichi Hatano

We analytically study entanglement generation through an open quantum-dot system described by the two-lead Anderson model. We exactly obtain the transition rate between the nonentangled incident state in one lead and the outgoing spin-singlet state in the other lead. We find that only the spin-singlet state can transmit in the cotunneling process. To discuss such an entanglement property in the open quantum system, we construct the exact two-electron scattering state of the Anderson model. It is striking that the scattering state contains spin-singlet bound states induced by the Coulomb interaction. The bound state describes a scattering process in which the set of momenta is not conserved and hence, it is not in the form of a Bethe eigenstate.

Physical Review B•Dec 29, 2009•20 citations

Quantum transport through a quantum dot: Combining the scattering-states numerical renormalization group with nonequilibrium Green functions

Frithjof B. Anders, Sebastian Schmitt

Scattering states fulfill the correct boundary conditions of a current carrying open quantum system. Discretizing the energy continuum of these states allows for employing Wilson's numerical renormalization group approach without violating the boundary conditions by using a finite size system. We evolve the analytically known steady-state density operator for a non-interacting quantum-system at finite bias to the full interacting problem by the time-dependent numerical renormalization group after switching on the local charging energy. Using a newly developed algorithm for steady-state nonequilibrium Green functions, we can calculate the current I as function of bias voltage V for arbitrary temperature and magnetic field. A comparison with second-order and GW Kadanoff-Baym-Keldysh results shows excellent agreement for weak interaction strength U .

Journal of Physics Conference Series•Apr 1, 2010•6 citations

Scattering Bethe Ansatz approach

Sung‐Po Chao

We derive the transport properties of a quantum impurity system, often realized as a quantum dot, subject to a source-drain bias voltage at zero temperature and magnetic field. Using the Scattering Bethe Anstaz(SBA), a generalization of the traditional Thermodynamic Bethe Ansatz(TBA) to open systems out of equilibrium, we derive some transport results for the small quantum dot, described by Anderson impurity Hamiltonian. Exact dot occupation out of equilibrium and the nonlinear conductance are obtained by introducing phenomenological spin- and charge-fluctuation distribution functions in the computation of the current. The current and dot occupation as a function of voltage are evaluated numerically. We also vary the gate voltage and study the transition from the mixed valence to the Kondo regime in the presence of a non-equilibrium current. For the larger quantum dot the Interacting Resonance Level Model is used to describe the strog correlation problem in this system. We show some current vs voltage results and compare with other theoretical results. We conclude with the difficulties we encountered by using this method and suggest some future extensions related to this SBA approach.

•Jan 1, 2010•0 citations

Transport theory for interacting electrons connected to reservoirs

Akira Oguri

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.

arXiv:cond-mat/0606316•Jun 13, 2006•0 citations

Time-Dependent DMRG Study on Quantum Dot under a Finite Bias Voltage

Shunsuke Kirino, Tatsuya Fujii, Jize Zhao +1 more

Resonant tunneling through quantum dot under a finite bias voltage at zero temperature is investigated by using the adaptive time-dependent density matrix renormalization group(TdDMRG) method. Quantum dot is modeled by the Anderson Hamiltonian with the 1-D nearest-neighbor tight-binding leads. Initially the ground state wave function is calculated with the usual DMRG method. Then the time evolution of the wave function due to the slowly changing bias voltage between the two leads is calculated by using the TdDMRG technique. Even though the system size is finite, the expectation values of current operator show steady-like behavior for a finite time interval, in which the system is expected to resemble the real nonequilibrium steady state of the infinitely long system. We show that from the time intervals one can obtain quantitatively correct results for differential conductance in a wide range of bias voltage. Finally we observe an anomalous behavior in the expectation value of the double occupation operator at the dot $$ as a function of bias voltage.

arXiv:0805.0218•Journal of the Physical Society of Japan•Jul 25, 2008•48 citations
Through an extension of the Landauer formula, we study the electron transport in an open quantum dot system under a finite bias voltage. The system that we study is an interacting resonant-level model equipped with infinite two leads of a linearized dispersion relation. We explicitly construct many-electron scattering eigenstates whose incident states are free-fermionic. A remarkable feature of the scattering state is the appearance of many-body bound states after the scattering. Extending Landauer's idea, we calculate the average electric current flowing through the quantum dot. We use a renormalization-group technique to deal with the divergences that appear in the limit of the large bandwidth of the leads. As a result, the average electric current is brought to a universal form.
Using a real-time renormalization group method we study the minimal model of a quantum dot dominated by charge fluctuations, the two-lead interacting resonant level model, at finite bias voltage. We develop a set of RG equations to treat the case of weak and strong charge fluctuations, together with the determination of power-law exponents up to second order in the Coulomb interaction. We derive analytic expressions for the charge susceptibility, the steady-state current, and the conductance in the situation of arbitrary system parameters, in particular away from the particle-hole symmetric point and for asymmetric Coulomb interactions. In the asymmetric situation we find that power laws can be observed for the current only as a function of the level position (gate voltage) but in general not as a function of the voltage except for extremely large voltages. Furthermore, we study the quench dynamics after sudden switch-on of the level-lead couplings. The time evolution of the dot occupation and current is governed by exponential relaxation accompanied by voltage-dependent oscillations and characteristic algebraic decay.
We analytically study entanglement generation through an open quantum-dot system described by the two-lead Anderson model. We exactly obtain the transition rate between the nonentangled incident state in one lead and the outgoing spin-singlet state in the other lead. We find that only the spin-singlet state can transmit in the cotunneling process. To discuss such an entanglement property in the open quantum system, we construct the exact two-electron scattering state of the Anderson model. It is striking that the scattering state contains spin-singlet bound states induced by the Coulomb interaction. The bound state describes a scattering process in which the set of momenta is not conserved and hence, it is not in the form of a Bethe eigenstate.
Scattering states fulfill the correct boundary conditions of a current carrying open quantum system. Discretizing the energy continuum of these states allows for employing Wilson's numerical renormalization group approach without violating the boundary conditions by using a finite size system. We evolve the analytically known steady-state density operator for a non-interacting quantum-system at finite bias to the full interacting problem by the time-dependent numerical renormalization group after switching on the local charging energy. Using a newly developed algorithm for steady-state nonequilibrium Green functions, we can calculate the current I as function of bias voltage V for arbitrary temperature and magnetic field. A comparison with second-order and GW Kadanoff-Baym-Keldysh results shows excellent agreement for weak interaction strength U .
We derive the transport properties of a quantum impurity system, often realized as a quantum dot, subject to a source-drain bias voltage at zero temperature and magnetic field. Using the Scattering Bethe Anstaz(SBA), a generalization of the traditional Thermodynamic Bethe Ansatz(TBA) to open systems out of equilibrium, we derive some transport results for the small quantum dot, described by Anderson impurity Hamiltonian. Exact dot occupation out of equilibrium and the nonlinear conductance are obtained by introducing phenomenological spin- and charge-fluctuation distribution functions in the computation of the current. The current and dot occupation as a function of voltage are evaluated numerically. We also vary the gate voltage and study the transition from the mixed valence to the Kondo regime in the presence of a non-equilibrium current. For the larger quantum dot the Interacting Resonance Level Model is used to describe the strog correlation problem in this system. We show some current vs voltage results and compare with other theoretical results. We conclude with the difficulties we encountered by using this method and suggest some future extensions related to this SBA approach.
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.
Resonant tunneling through quantum dot under a finite bias voltage at zero temperature is investigated by using the adaptive time-dependent density matrix renormalization group(TdDMRG) method. Quantum dot is modeled by the Anderson Hamiltonian with the 1-D nearest-neighbor tight-binding leads. Initially the ground state wave function is calculated with the usual DMRG method. Then the time evolution of the wave function due to the slowly changing bias voltage between the two leads is calculated by using the TdDMRG technique. Even though the system size is finite, the expectation values of current operator show steady-like behavior for a finite time interval, in which the system is expected to resemble the real nonequilibrium steady state of the infinitely long system. We show that from the time intervals one can obtain quantitatively correct results for differential conductance in a wide range of bias voltage. Finally we observe an anomalous behavior in the expectation value of the double occupation operator at the dot $$ as a function of bias voltage.