Electron transport through correlated molecules computed using the time-independent Wigner function: Two critical tests

Köppel

2009

Phys. Rev. B

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In a recent paper ͓I. Bâldea and H. Köppel, Phys. Rev. B 78, 115315 ͑2008͔͒, we showed that a variational approach ͓P. Delaney and J. C. Greer, Phys. Rev. Lett. 93, 036805 ͑2004͔͒ proposed to compute the electron transport through molecules, which is based on boundary constraints of the Wigner function, is unable to correctly describe the zero-bias conductance of the simplest uncorrelated and correlated systems. In the present paper, we extend our previous analysis of the linear response limit of that approach, by considering, instead of the Wigner function, general constraints. We demonstrate that, if, as usual in transport theories, the quasiparticle distributions in electrodes are constrained, this method yields the completely unphysical result that the zero-bias conductance vanishes. Therefore, we conclude that the variational approach itself is defective.

Section: Linear Response Approximationmentioning

confidence: 99%

Critical analysis of a variational method used to describe molecular electron transport

Köppel

2009

Phys. Rev. B

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“…The lamentable failure of the DG approach was demonstrated by explicit calculations for the simplest uncorrelated and correlated, discrete and continuous models. 4,5 They contradict well-established experimental and theoretical results, and it would make little sense to more amply document the incorrectness in many other cases. 6 By contrast, DG could not present even a single example where it is valid.…”

Section: Discussionmentioning

confidence: 96%

“…3 of Ref. 4). There are certainly many possibilities to obtain nonvanishing currents by constraining ad hoc complex Hermitian operators, since all these generally yield J = 0: see Eqs.…”

Section: Rebuttal Of the Criticism That Population Constraints Prmentioning

confidence: 88%

“…That is, the zero-bias conductance g(+ε g ) = g(−ε g ) (as well as other relevant properties not considered in Ref. 4, e. g., the whole current-voltage characteristics) should be identical irrespective whether the level is located above (+ε g ) or below (−ε g ) the electrodes' Fermi level ε F . Noteworthy, the charge carriers are electrons for positive ε g and holes for negative ε g .…”

Section: Constraints For N-type and P-type Conductionmentioning

confidence: 97%

“…In reality, we demonstrated (i) that even if, by chance, this is possible, 4 the DG current is completely unphysical, and (ii) that the DG conductance vanishes just in on-resonance cases, where the exact conductance attains its maximum (unitary limit). 4,5 To refute the false impression, which DG attempt to convey by using the superscript DG, we emphasize that they did never impose pBCs for the Au 13 -clusters, which mimic their electrodes of Refs. 3,11,12.…”

Section: Further Errors and Inaccuracies In The Commentmentioning

confidence: 99%

See 2 more Smart Citations

Reply to “Comment on ‘Critical analysis of a variational method used to describe molecular electron transport’”

Köppel²

2011

Phys. Rev. B

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We show that the failure of the Delaney-Greer (DG) variational ansatz for transport demonstrated by us in Phys. Rev. B 80, 165301 (2009) (I) is not related to an unsuitable constraint that prevents a broken time-reversal symmetry or to real orbitals, as DG incorrectly claim. The complex orbitals suggested by them as a way-out solution merely represent a particular case of the general case considered by us in I, which do not in the least affect our conclusion. In conjunction with the issues raised by the DG's Comment, we show that the DG Wigner conditions can erroneously constrain outgoing and not incoming charge carriers and present an example revealing that the sign of the "momentum" P of the Wigner function f (q, P ) is not necessarily associated with the direction of motion in the real world. We also discuss a general reason why transport approaches which, like the DG's, are solely based on information on an isolated nanocluster are incorrect.

A physical limitation of the Wigner “distribution” function in molecular transport

Köppel

2012

Physics Letters A

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We present an example revealing that the sign of the "momentum" P of the Wigner "distribution" function f (q, P ) is not necessarily associated with the direction of motion in the real world.This aspect, which is not related to the well known limitation of the Wigner function that traces back to the Heisenberg's uncertainty principle, is particularly relevant in transport studies, wherein it is helpful to distinguish between electrons flowing from electrodes into devices and vice versa.