Probing level renormalization by sequential transport through double quantum dots

Wünsch, Bernhard; Braun, Michael; König, Jürgen; Pfannkuche, Daniela

doi:10.1103/physrevb.72.205319

Cited by 84 publications

(129 citation statements)

References 42 publications

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“…(C.5)] are not important, because this approach preserves positivity. At the same time we note that the principal parts are required to catch important physics such as renormalization of energy levels in some systems [66,67,68,69]. By simulating different systems we also observed that with neglected principal parts the 1vN and the Redfield approaches give the same results.…”

Section: Appendix G Which Approach To Use?supporting

confidence: 65%

QmeQ 1.0: An open-source Python package for calculations of transport through quantum dot devices

Wacker

Pedersen

Karlström

et al. 2017

Computer Physics Communications

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QmeQ is an open-source Python package for numerical modeling of transport through quantum dot devices with strong electron-electron interactions using various approximate master equation approaches. The package provides a framework for calculating stationary particle or energy currents driven by differences in chemical potentials or temperatures between the leads which are tunnel coupled to the quantum dots. The electronic structures of the quantum dots are described by their single-particle states and the Coulomb matrix elements between the states. When transport is treated perturbatively to lowest order in the tunneling couplings, the possible approaches are Pauli (classical), firstorder Redfield, and first-order von Neumann master equations, and a particular form of the Lindblad equation. When all processes involving two-particle excitations in the leads are of interest, the second-order von Neumann approach can be applied. All these approaches are implemented in QmeQ. We here give an overview of the basic structure of the package, give examples of transport calculations, and outline the range of applicability of the different approximate approaches. Keywords: Open quantum systems, Quantum dots, Anderson-type model, Coulomb blockade, Python Program summaryProgram Title: QmeQ Licensing provisions: BSD 2-Clause Programming language: Python External libraries: NumPy, SciPy, Cython Nature of problem: Calculation of stationary state currents through quantum dots tunnel coupled to leads. Solution method: Exact diagonalisation of the quantum dot Hamiltonian for a given set of single particle states and Coulomb matrix elements. Numerical solution of the stationary-state master equation for a given approximate approach. Restrictions: Depending on the approximate approach the temperature needs to be sufficiently large compared to the coupling strength for the approach to be valid.

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Section: Appendix G Which Approach To Use?supporting

confidence: 65%

QmeQ 1.0: An open-source Python package for calculations of transport through quantum dot devices

Wacker

Pedersen

Karlström

et al. 2017

Computer Physics Communications

View full text Add to dashboard Cite

show abstract

“…The major approximation involved in the our master equation approach is the secondorder Born approximation for the tunnel Hamiltonian. This approximation sets restriction on valid temperature regime 40 -i.e., k B T ⌫. Fortunately, in most cases the system coupling to the electrodes is indeed very weak; then, the present formalism remains appropriate for a rather wide range of temperature.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…Thus, the system Hamiltonian is a renormalized one, with the static dispersion effect being included. 39 It is noticed that, in some cases, the dynamic dispersion may lead to some interesting phenomena, such as the negative differential conductance in coupled quantum dots system 40 and the exchange magnetic field that leads to spin procession. 13 …”

Section: ͑3͒mentioning

confidence: 99%

Calculation of the current noise spectrum in mesoscopic transport: A quantum master equation approach

Luo

Yan

2007

Phys. Rev. B

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Based on our recent work on quantum transport ͓X. Q. Li et al., Phys. Rev. B 71, 205304 ͑2005͔͒, we show how an efficient calculation can be performed for the current noise spectrum. Compared to the classical rate equation or the quantum trajectory method, the proposed approach is capable of tackling both the many-body Coulomb interaction and quantum coherence on an equal footing. The practical applications are illustrated by transport through quantum dots. We find that this alternative approach is in a certain sense simpler and more straightforward than the well-known Landauer-Büttiker scattering matrix theory.

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“…This is one of the motivations to study double quantum dots. [4][5][6][7][8][9][10][11][12][13] In particular, it is required to create entangled electron states by the interaction of an electron inside the double dot with an electron tunneling onto the double dot. Measuring this entanglement is an important experimental task, and theoretical suggestions on how to probe these states are needed.…”

Section: Introductionmentioning

confidence: 99%

Connection between noise and quantum correlations in a double quantum dot

2008

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We investigate the current and noise characteristics of a double quantum dot system. The strong correlations induced by the Coulomb interaction and the Pauli principle create entangled two-electron states and lead to signatures in the transport properties. We show that the interaction parameter , which measures the admixture of the double-occupancy contribution to the singlet state and thus the degree of entanglement, can be directly accessed through the Fano factor of super-Poissonian shot noise.

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Probing level renormalization by sequential transport through double quantum dots

Cited by 84 publications

References 42 publications

QmeQ 1.0: An open-source Python package for calculations of transport through quantum dot devices

QmeQ 1.0: An open-source Python package for calculations of transport through quantum dot devices

Calculation of the current noise spectrum in mesoscopic transport: A quantum master equation approach

Connection between noise and quantum correlations in a double quantum dot

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