Electronic transport in an anisotropic Sierpinski gasket

TL;DR

This paper investigates how anisotropy affects electronic transport in a Sierpinski gasket fractal, revealing that even minimal anisotropy enhances conductivity and creates continuous energy bands, with additional insights into magnetic field effects.

Contribution

The study provides exact results on anisotropic Sierpinski gaskets using RSRG, showing anisotropy induces continuous bands and increased conductivity, which was not previously established.

Findings

Anisotropic gasket is more conducting than isotropic.

Minimal anisotropy generates continuous eigenstate bands.

Magnetic field influences transport and persistent current.

Abstract

We present exact results on certain electronic properties of an anisotropic Sierpinski gasket fractal. We use a tight binding Hamiltonian and work within the formalism of a real space renormalization group (RSRG) method. The anisotropy is introduced in the values of the nearest neighbor hopping integrals. An extensive numerical examination of the two terminal transmission spectrum and the flow of the hopping integrals under the RSRG iterations strongly suggest that an anisotropic gasket is more conducting than its isotropic counter part and that, even a minimal anisotropy in the hopping integrals generate {\it continuous bands} of eigenstates in the spectrum for finite Sierpinski gaskets of arbitrarily large size. We also discuss the effect of a magnetic field threading the planar gasket on its transport properties and calculate the persistent current in the system. The sensitivity of the persistent current on the anisotropy and on the band filling is also discussed.