Electronic transport in a Cantor stub waveguide network

TL;DR

This paper explores how electronic states and transmission behave in a one-dimensional Cantor-structured waveguide network, revealing resonant and extended states with potential for wave trapping in hierarchical geometries.

Contribution

It introduces a theoretical analysis of electronic eigenstates and transmission in a Cantor stub array using RSRG and transfer matrix methods, highlighting extended states with power-law decay.

Findings

Identification of resonant transmission states.

Discovery of extended wave-functions with power-law decay.

Potential for wave trapping in hierarchical structures.

Abstract

We investigate theoretically, the character of electronic eigenstates and transmission properties of a one dimensional array of stubs with Cantor geometry. Within the framework of real space re-normalization group (RSRG) and transfer matrix methods we analyze the resonant transmission and extended wave-functions in a Cantor array of stubs, which lack translational order. Apart from resonant states with high transmittance we unravel a whole family of wave-functions supported by such an array clamped between two-infinite ordered leads, which have an extended character in the RSRG scheme, but, for such states the transmission coefficient across the lead-sample-lead structure decays following a power-law as the system grows in size. This feature is explained from renormalization group ideas and may lead to the possibility of trapping of electronic, optical or acoustic waves in such hierarchical geometries.