Electronic transport in a Cantor stub waveguide network

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.

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Cited by in corpus (6)

• Wave propagation through Cantor-set media: Chaos, scaling, and fractal structures
• Electronic transmission in a model quantum wire with side coupled quasiperiodic chains: Fano resonance and related issues
• Wave Propagation in the Cantor-Set Media: Chaos from Fractal
• Self-similar transmission properties of aperiodic Cantor potentials in gapped graphene
• Hidden Symmetries of Electronic Transport in a Disordered One-Dimensional Lattice
• Disorder-free localization around the conduction band edge of crossing and kinked silicon nanowires