Quantum Transport through Hierarchical Structures

Details Quantum Transport through Hierarchical Structures Quantum Transport through Hierarchical Structures

2010-11-29

arxiv.org/abs/1011.6348v1

Phys. Rev. E 83, 041106 (2011)

Physics

Condensed Matter

Disordered Systems and Neural Networks

15 pages, RevTex, 10 figures, for related work, see http://www.physics.emory.edu/faculty/boettcher/

Scientific paper

10.1103/PhysRevE.83.041106

The transport of quantum electrons through hierarchical lattices is of interest because such lattices have some properties of both regular lattices and random systems. We calculate the electron transmission as a function of energy in the tight binding approximation for two related Hanoi networks. HN3 is a Hanoi network with every site having three bonds. HN5 has additional bonds added to HN3 to make the average number of bonds per site equal to five. We present a renormalization group approach to solve the matrix equation involved in this quantum transport calculation. We observe band gaps in HN3, while no such band gaps are observed in linear networks or in HN5.

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