Addition spectrum and koopmans’ theorem for disordered quantum dots

Physical Review B - Condensed Matter and Materials Physics

Volumn 60, Issue 4, 1999, Pages 2541-2553

  Gefen, Yuval ^b   Montambaux, Gilles ^a  

^a UNIVERSITÉ PARIS SUD   (France)

^b WEIZMANN INSTITUTE OF SCIENCE   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4244131857     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.60.2541     Document Type: Article

References (38)

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22. This shift can be quantified by (Formula presented) where (Formula presented) is the ground state SCHF Slater determinant of (Formula presented) particles, (Formula presented) is the (Formula presented) single-particle state of the (Formula presented) particle SCHF spectrum, and ⊗ is the antisymmetrized tensor product.
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30. This is particularly spectacular at certain special filling factors (Ref. 24).
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32. These results cannot be directly extrapolated to the thermodynamic limit, because at fixed disorder one would arrive at states that are localized on a length scale short compared to the system size in the limit (Formula presented) Here however, the noninteracting wave functions are extended over the entire sample.
33. The result that interactions become important at increasingly low (Formula presented) as (Formula presented) is increased, rather than a size independent density [e.g., (Formula presented) is an artifact of the long range of the bare interaction: The relevant interaction matrix elements grow with (Formula presented) relative to Δ. It is well known that the Coulomb interaction causes divergences (for (Formula presented) and is therefore usually screened explicitly. Here however, the (static) screening is generated self consistently. The results suggest that the screening requires increasing rearrangement as (Formula presented) is increased.
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37. In the case of one close metallic gate, the interaction is dipolar (Formula presented) at distances greater than the dot to gate separation, and in the case of two close gates (above and below the dot) the long-range interactions are exponentially small. The nearest-neighbor interaction can be considered as a model for such potentials.
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