Theory of Quantum Transport at Nanoscale by Dmitry Ryndyk

Author:Dmitry Ryndyk
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(4.31)

(4.32)

or explicitly

(4.33)

where

(4.34)

The last expressions solve the problem of transformation of the tight-binding matrix elements into tunneling matrix elements.

4.1.3 Bardeen’s Matrix Elements

From the previous consideration it is clear that the left states can be considered as nonorthogonal to the right states. In this case we can choose left and right states which form two independent complete systems, this is the main idea of the method of tunneling Hamiltonian. In this section we show that both of the above mentioned problems can be overcome if we apply consistently the perturbation theory to calculate matrix elements and tunneling current.

Fig. 4.5Schematic picture of the nonorthogonal left and right states

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