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Green’s Functions for Tight Binding Hamiltonians

Chapter
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 7)

Abstract

In this chapter we introduce the Tight Binding Hamiltonian (TBH)
$$ H = \sum\limits_{\underline \ell } {|\ell > \varepsilon \underline {_\ell } < \ell |} + \sum\limits_{\underline \ell \underline m } {|\ell > V_{\underline \ell \underline m } < m|} $$
(5.8)
where each state |l> is an atomic like orbital centered at the site l. The sites {l} form a regular lattice. The quantity ε l is the energy of an electron located at the site l in the absence of V.. The quantity V lm is the amplitude for transfering an electron from the site l to the site m. The electronic motion governed by the TBH (5.8) is mathematically equivalent to the motion of a coupled set of pendulums (see Table 5.1).

Keywords

Matrix Element Brillouin Zone Band Edge Tight Binding Logarithmic Singularity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of VirginiaCharlottesvilleUSA

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