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Volumn 79, Issue 1, 2009, Pages

Incompleteness of the Landauer formula for electronic transport

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EID: 58949098790     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.79.014201     Document Type: Article
Times cited : (68)

References (48)
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    • This does not exclude (and it is in fact highly possible) that the viewpoint itself championed by Landauer misses important information inherent to the true experimental problem we are considering in this paper (see, e.g., Ref.). We do not address this fundamental issue here. We simply show that even within the Landauer viewpoint to conduction (with all its assumptions) the corresponding Eq. 4 is incomplete.
    • This does not exclude (and it is in fact highly possible) that the viewpoint itself championed by Landauer misses important information inherent to the true experimental problem we are considering in this paper (see, e.g., Ref.). We do not address this fundamental issue here. We simply show that even within the Landauer viewpoint to conduction (with all its assumptions) the corresponding Eq. 4 is incomplete.
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    • This assumption is not necessary and is only relevant in the choice of definition of conductance as defined in terms of electrochemical differences or electrostatic differences (see, e.g., Ref.). In either case, the quantitative difference between the electrochemical and electrostatic potentials is small on length scales much larger than the electron screening length.
    • This assumption is not necessary and is only relevant in the choice of definition of conductance as defined in terms of electrochemical differences or electrostatic differences (see, e.g., Ref.). In either case, the quantitative difference between the electrochemical and electrostatic potentials is small on length scales much larger than the electron screening length.
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    • In the absence of a magnetic field, the following stronger conditions are found to hold (Ref.): Σα∂α σαβ (r, r′) =0 and Σβ∂′βσαβ (r, r′) =0.
    • In the absence of a magnetic field, the following stronger conditions are found to hold (Ref.): Σα∂α σαβ (r, r′) =0 and Σβ∂′ βσαβ (r, r′) =0.
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    • By contrast, the full current-current response function yields the response of the electric current to the external vector potential only. The transition from scalar electric potential to a longitudinal vector potential is done via a gauge transformation.
    • By contrast, the full current-current response function yields the response of the electric current to the external vector potential only. The transition from scalar electric potential to a longitudinal vector potential is done via a gauge transformation.
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    • Since the Kohn-Sham system is noninteracting, there is no difference between the (full) current response function χ (KS) and the proper response function χ̃(KS).
    • Since the Kohn-Sham system is noninteracting, there is no difference between the (full) current response function χ (KS) and the proper response function χ̃(KS).
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    • Notice that by virtue of the identities 2 3 the restricted matrix contains no less information than the original one.
    • Notice that by virtue of the identities 2 3 the restricted matrix contains no less information than the original one.


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