Formation of nonequilibrium steady states in interacting double quantum dots: When coherences dominate the charge distribution

Härtle, R.; Millis, Andrew J.

doi:10.1103/physrevb.90.245426

Cited by 44 publications

(55 citation statements)

References 127 publications

(228 reference statements)

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“…These terms describe the renormalization of the molecular energy levels due to the molecule-lead coupling [96]. In a recent study of charge-transfer dynamics in a double quantum dot system [100], it was…”

Section: B Born-markov Master Equation Approachmentioning

confidence: 99%

Effect of broadening in the weak-coupling limit of vibrationally coupled electron transport through molecular junctions and the analogy to quantum dot circuit QED systems

Härtle

Kulkarni

2015

Phys. Rev. B

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We investigate the nonequilibrium population of a vibrational mode in the steady-state of a biased molecular junction, using a rate equation approach. We focus on the limit of weak electronicvibrational coupling and show that, in the resonant transport regime and for sufficiently high bias voltages, the level of vibrational excitation increases with decreasing coupling strength, assuming a finite and non-zero value. An analytic behavior with respect to the electronic-vibrational coupling strength is only observed if the influence of environmental degrees of freedom is explicitly taken into account. We consider the influence of three different types of broadening: hybridization with the electrodes, thermal fluctuations and the coupling to a thermal heat bath. Our results apply to vibrationally coupled electron transport through molecular junctions but also to quantum dots coupled to a microwave cavity, where the photon number can be expected to exhibit a similar behavior.

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Section: B Born-markov Master Equation Approachmentioning

confidence: 99%

Effect of broadening in the weak-coupling limit of vibrationally coupled electron transport through molecular junctions and the analogy to quantum dot circuit QED systems

Härtle

Kulkarni

2015

Phys. Rev. B

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“…The first of these methods is the HQME approach [19,20,[50][51][52]. The second one is the CT-QMC method [37,39,43,44,48,49].…”

Section: B Hierarchical Master Equation Approachmentioning

confidence: 99%

“…Approximate methods, on the other hand, may miss important physics or suffer from artifacts due to the approximations involved. A combination of methods, which operate on different levels of approximation is often useful and helps to elucidate the relevant physical mechanisms [14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

“…In the presence of a short memory timescale, long time scales can be accessed by a combination of reduced dynamics techniques [44] with a short-time numerically exact scheme; or by the hierarchical master equation method [45] where the numerical effort scales linearly with the simulation time. The latter, however, can only be converged if the temperature in the electrodes is not too low [19,20].…”

Section: Introductionmentioning

confidence: 99%

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Transport through an Anderson impurity: Current ringing, nonlinear magnetization, and a direct comparison of continuous-time quantum Monte Carlo and hierarchical quantum master equations

et al. 2015

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We give a detailed comparison of the hierarchical quantum master equation (HQME) method to a continuous-time quantum Monte Carlo (CT-QMC) approach, assessing the usability of these numerically exact schemes as impurity solvers in practical nonequilibrium calculations. We review the main characteristics of the methods and discuss the scaling of the associated numerical effort.We substantiate our discussion with explicit numerical results for the nonequilibrium transport properties of a single-site Anderson impurity. The numerical effort of the HQME scheme scales linearly with the simulation time but increases (at worst exponentially) with decreasing temperature. In contrast, CT-QMC is less restricted by temperature at short times, but in general the cost of going to longer times is also exponential. After establishing the numerical exactness of the HQME scheme, we use it to elucidate the influence of different ways to induce transport through the impurity on the initial dynamics, discuss the phenomenon of coherent current oscillations, known as current ringing, and explain the non-monotonic temperature dependence of the steadystate magnetization as a result of competing broadening effects. We also elucidate the pronounced non-linear magnetization dynamics, which appears on intermediate time scales in the presence of an asymmetric coupling to the electrodes.

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“…In order to simplify our equations we will set and k B as 1. The dynamics of this model is studied via the numerically exact hierarchy equation of motion approach [36] and pronounced effects of the interdot tunneling strength are observed.…”

Section: Introductionmentioning

confidence: 99%

Finite coupling effects in double quantum dots near equilibrium

Thingna

Wang

2017

Phys. Rev. B

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A weak coupling quantum master equation provides reliable steady-state results only in the van Hove limit, i.e., when the system-lead coupling approaches zero. Recently, J. Thingna et al. [Phys. Rev. E 88, 052127 (2013)] proposed an alternative approach, based on an analytic continuation of the Redfield solution, to evaluate the steady-state reduced density matrix up to second order in the system-bath coupling. The approach provides accurate results for harmonic oscillator and spin-bosonic systems. We apply this approach to study steady-state fermionic systems and the calculation on an exactly solvable double quantum dot system shows that the method is rigorously valid up to second order in system-lead coupling only near equilibrium, i.e., linear response regime. We further compare to the Redfield and the secular Redfield (Lindblad-type) master equations that are inaccurate in all parameter regimes. Lastly, we consider the nontrivial problem of strong Coulomb interaction and illustrate the interplay between system-lead coupling, interdot tunneling, and Coulomb strength that can be captured only via the analytic continuation method.

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Formation of nonequilibrium steady states in interacting double quantum dots: When coherences dominate the charge distribution

Cited by 44 publications

References 127 publications

Effect of broadening in the weak-coupling limit of vibrationally coupled electron transport through molecular junctions and the analogy to quantum dot circuit QED systems

Effect of broadening in the weak-coupling limit of vibrationally coupled electron transport through molecular junctions and the analogy to quantum dot circuit QED systems

Transport through an Anderson impurity: Current ringing, nonlinear magnetization, and a direct comparison of continuous-time quantum Monte Carlo and hierarchical quantum master equations

Finite coupling effects in double quantum dots near equilibrium

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