Perturbative approach to the nonequilibrium Kondo effect in a quantum dot

Fujii, T.; Ueda, Kazuo

doi:10.1103/physrevb.68.155310

Cited by 100 publications

(150 citation statements)

References 25 publications

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“…It has been suggested that terms of order U 3 and U 4 might cause the peak to split. [63,64] However, a recent study with an improvement of the higher order corrections, which reproduces correctly the equilibrium expressions, indicates that the spectral density retains the qualitative features of the secondorder result. [66] Physically, one might expect that if the dot is hybridized with left and right leads at chemical potentials µ L and µ R with matrix elements V L and V R respectively, the effective distribution function fluctuates between that corresponding to µ L and µ R (at least if…”

Section: Introductionmentioning

confidence: 99%

“…Recent use of perturbation theory in U/(π∆) for V ds = 0 was limited to the symmetric case, for calculations of the current noise, [62] and other properties including terms of third and fourth order in U, [63][64][65][66] and in particular in presence of magnetic field B, [64,65] motivated by recent experiments. [14][15][16] However, even in the symmetric case, the spin current is not conserved by the approximation when V ds = 0.…”

Section: Introductionmentioning

confidence: 99%

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Nonequilibrium magnetotransport through a quantum dot: An interpolative perturbative approach

Aligia

2006

Phys. Rev. B

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We study the differential conductance, spectral density and magnetization, for a quantum dot coupled to two conducting leads as a function of bias voltage V ds , magnetic field B and temperature T . The system is modeled with the Anderson model solved using a spin dependent interpolative perturbative approximation in the Coulomb repulsion U that conserves the current. For large enough magnetic field, the differential conductance as a function of bias voltage shows split peaks. This splitting is larger than the corresponding splitting in the spectral density of states ρ d (ω), in agreement with experiment.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nonequilibrium magnetotransport through a quantum dot: An interpolative perturbative approach

Aligia

2006

Phys. Rev. B

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“…(12)(13)(14) define a set of coupled integral equations in the energy levels of the leads, ǫ k , whose solution yields the Green functions to be introduced in eq. (4). In these equations we have neglected expectation values of operators such as <χ † σχ −σĉ † k−σĉ kσ >, which…”

Section: Theorymentioning

confidence: 99%

Kondo resonance decoherence caused by an external potential

Monreal

2005

Phys. Rev. B

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The Kondo problem, for a quantum dot (QD), subjected to an external bias, is analyzed in the limit of infinite Coulomb repulsion by using a consistent equations of motion method based on a slave-boson Hamiltonian. Utilizing a strict perturbative solution in the leads-dot coupling, T , up to T 4 and T 6 orders, we calculate the QD spectral density and conductance, as well as the decoherent rate that drive the system from the strong to the weak coupling regime. Our results indicate that the weak coupling regime is reached for voltages larger than a few units of the Kondo temperature.

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“…After taking iϕ m → Φ and then iω n → ω + iη, this expression maps to the correct retarded self-energy in the Keldysh formalism [20].…”

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confidence: 99%

Imaginary-Time Formulation of Steady-State Nonequilibrium: Application to Strongly Correlated Transport

2007

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We extend the imaginary-time formulation of the equilibrium quantum many-body theory to steady-state nonequilibrium with an application to strongly correlated transport. By introducing Matsubara voltage, we keep the finite chemical potential shifts in the Fermi-Dirac function, in agreement with the Keldysh formulation. The formulation is applied to strongly correlated transport in the Kondo regime using the quantum Monte Carlo method.PACS numbers: 73.63. Kv, 72.10.Bg, 72.10.Di A coherent formulation of equilibrium and nonequilibrium is one of the ultimate goals of statistical physics. In the last two decades, this has become a particularly pressing issue with the advances in nanoelectronics. Although it has long been considered such Gibbsian description may exist in the steady-state nonequilibrium [1], implementation of time-independent nonequilibrium quantum statistics has produced limited success [2] without widely applicable algorithms.In nanoelectronics, the strong interplay between manybody interactions and nonequilibrium demands nonperturbative treatments of the quantum many-body effects. Perturbative Green function techniques [3,4] have been successful, but are often plagued by complicated diagrammatic rules and are limited to simple models. In the last few years, important advances have been made in this field to complement the diagrammatic theory. Timedependent renormalization group [5,6] and densitymatrix renormalization group method [7] were applied to calculate the real-time convergence toward the steadystate. Real-time methods [5,6,7] calculate the process toward the steady-state and therefore have clear physical interpretations. Unfortunately they often suffer from long-time behaviors associated with low energy strongly correlated states and finite size effects. Direct construction of nonequilibrium ensembles through the scattering state formalism [2,8,9, 10] and field theoretic approach [11] have provided new perspectives to the problem.The main goal of this work is to provide a critical step toward the time-independent description of equilibrium and steady-state nonequilibrium quantum statistics. In addition to the resolution of this fundamental problem, we provide a strong application. The steadystate nonequilibrium can be solved within the same formal structure as equilibrium, and therefore the powerful equilibrium many-body tools, such as the quantum Monte Carlo (QMC) method, can be easily applied to complex transport systems with many competing interactions. We demonstrate this point by applying this formalism to strongly correlated transport in the Kondo regime by using QMC. In contrast to the real-time methods, this approach starts from the steady-state and simulates the effect of many-body interaction. However, numerical analytic continuation and low temperature calculation, especially with the QMC application, are technical difficulties.In the following, we first construct a time-independent statistical ensemble of steady-state nonequilibrium [2] in the non-interacting limit with the i...

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Perturbative approach to the nonequilibrium Kondo effect in a quantum dot

Cited by 100 publications

References 25 publications

Nonequilibrium magnetotransport through a quantum dot: An interpolative perturbative approach

Nonequilibrium magnetotransport through a quantum dot: An interpolative perturbative approach

Kondo resonance decoherence caused by an external potential

Imaginary-Time Formulation of Steady-State Nonequilibrium: Application to Strongly Correlated Transport

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