Coulomb blockade in molecular quantum dots

Walczak, Kamil

doi:10.1007/s11534-005-0002-x

Cited by 7 publications

(10 citation statements)

References 25 publications

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“…Above the Kondo temperature T K a good approximation for the spectral function is [39]. We verified (not shown) that N and I are in excellent agreement with the results of the Rate Equations [37,40] (RE), the orthodox theory of CB for weakly coupled systems. For the Anderson model the map (v, V ) → (N, I) is invertible for all V (infinite bias window) since the finite-bias Jacobian is…”

supporting

confidence: 73%

Steady-State Density Functional Theory for Finite Bias Conductances

Stefanucci

Kurth

2015

Nano Lett.

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In the framework of density functional theory, a formalism to describe electronic transport in the steady state is proposed which uses the density on the junction and the steady current as basic variables. We prove that, in a finite window around zero bias, there is a one-to-one map between the basic variables and both local potential on as well as bias across the junction. The resulting Kohn-Sham system features two exchange-correlation (xc) potentials, a local xc potential, and an xc contribution to the bias. For weakly coupled junctions the xc potentials exhibit steps in the density-current plane which are shown to be crucial to describe the Coulomb blockade diamonds. At small currents these steps emerge as the equilibrium xc discontinuity bifurcates. The formalism is applied to a model benzene junction, finding perfect agreement with the orthodox theory of Coulomb blockade

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supporting

confidence: 73%

Steady-State Density Functional Theory for Finite Bias Conductances

Stefanucci

Kurth

2015

Nano Lett.

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“…The resulting densities and currents are in excellent agreement with the results of the REs [116,117], the standard technique to describe CB for weakly coupled systems. In the reverseengineering procedure we numerically invert equations ( 124) and ( 125) for a given, fixed pair (N, I) both for the interacting and non-interacting system and then extract the i-DFT xc potentials according to equations ( 119) and (120).…”

Section: I-dft Functionals For the Cb Regimesupporting

confidence: 73%

Transport through correlated systems with density functional theory

Kurth¹,

Stefanucci²

2017

J. Phys.: Condens. Matter

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We present recent advances in density functional theory (DFT) for applications in the field of quantum transport, with particular emphasis on transport through strongly correlated systems. We review the foundations of the popular Landauer-Büttiker(LB) + DFT approach. This formalism, when using approximations to the exchange-correlation (xc) potential with steps at integer occupation, correctly captures the Kondo plateau in the zero bias conductance at zero temperature but completely fails to capture the transition to the Coulomb blockade (CB) regime as the temperature increases. To overcome the limitations of LB + DFT, the quantum transport problem is treated from a time-dependent (TD) perspective using TDDFT, an exact framework to deal with nonequilibrium situations. The steady-state limit of TDDFT shows that in addition to an xc potential in the junction, there also exists an xc correction to the applied bias. Open shell molecules in the CB regime provide the most striking examples of the importance of the xc bias correction. Using the Anderson model as guidance we estimate these corrections in the limit of zero bias. For the general case we put forward a steady-state DFT which is based on one-to-one correspondence between the pair of basic variables, steady density on and steady current across the junction and the pair local potential on and bias across the junction. Like TDDFT, this framework also leads to both an xc potential in the junction and an xc correction to the bias. Unlike TDDFT, these potentials are independent of history. We highlight the universal features of both xc potential and xc bias corrections for junctions in the CB regime and provide an accurate parametrization for the Anderson model at arbitrary temperatures and interaction strengths, thus providing a unified DFT description for both Kondo and CB regimes and the transition between them.

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“…The steady-state classical master equations describing the system are given by [19,29,41] Z and the P Z can be calculated as…”

Section: Theorymentioning

confidence: 99%

“…For simplicity, in this work, we will adopt the WBL approximation, which considers the self-energy due to the coupling between the system and semi-infinite right (G R ) and left (G L ) electrodes to be energy independent and purely imaginary [16,39]. In this approximation, the ET rates can be written as [29,41]:…”

Section: Theorymentioning

confidence: 99%

Deviations and similarities between landauer’s approach and the multi-electronic classical master equation in describing nanoscale transport

Moreira,

de Melo

2023

Phys. Scr.

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In this work, we show that the classical master equation (ME) treatment – with the rates obtained via the Fermi golden rule – and the elastic scattering (ES) approach give the same results for a system composed of two states/one level when considering the approximations of i) non-interacting limit, i.e., the electronic structure of the N-particle states remains frozen even in the presence of an extra particle, ii) wide-band limit (WBL) approximation, and iii) excited states are discarded. Although the predictions of these two approaches ‘deviate’ from each other when more states and/or levels are considered, under the conditions of strong coupling limit and symmetric contacts both treatments capture the same physics involved in the transport process. For other situations – such as asymmetric coupling and/or weak metal-organic coupling – the predictions of these two theories do not agree with each other. Finally, even considering that in our treatment the electronic structure of the system is described at a tight binding level, the corresponding results clearly show the situations where similarities and differences between the ME and ES approaches appears.

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Coulomb blockade in molecular quantum dots

Cited by 7 publications

References 25 publications

Steady-State Density Functional Theory for Finite Bias Conductances

Steady-State Density Functional Theory for Finite Bias Conductances

Transport through correlated systems with density functional theory

Deviations and similarities between landauer’s approach and the multi-electronic classical master equation in describing nanoscale transport

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