Closed-form Green functions, surface effects, and the importance of dimensionality in tight-binding metals

Journal of Chemical Physics

Volumn 133, Issue 3, 2010, Pages

  Reuter, Matthew G ^a  

^a NORTHWESTERN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CLOSED FORM; CLOSED-FORM EXPRESSION; EDGE EFFECT; GREEN FUNCTION; MATRIX; NUMBER OF LAYERS; SUBSTRATE INTERACTION; SURFACE EFFECT; THREE-DIMENSIONAL SUBSTRATES; TIGHT BINDING;

GREEN'S FUNCTION;

SUBSTRATES;

EID: 77956254763     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3447960     Document Type: Article

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37. The use of Eq. in the derivation of Eq. is only correct when the augmented Hamiltonian is Hermitian [Eq. is only valid for Hermitian Hamiltonians]. If the augmented Hamiltonian is not Hermitian, as caused by an infinite system size in this work, Eq. can be obtained from the resolvent, G (E) = [EI-H] -1, instead of the retarded Green function. In this case, solutions to Eq. are no longer guaranteed to be unique; however, we can choose the solution that satisfies the properties of the retarded Green function (Ref.).
38. σ in Eq. is three times the canonical standard deviation in the Gaussian distribution. 99% of the density is localized within (E-ε) ±σ.