Electronic transport in an anisotropic Sierpinski gasket

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 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.

Magnetic response of interacting electrons in a fractal network: A mean-field approach

“…The magnitude of the conductivity however, is sensitive to the strength of the hopping parameters. This fact has also been reported recently for non-interacting electrons [36].…”

“…The magnitude of D at any specific U of course, depends on the numerical values of the hopping strength. Interestingly, this fact is also observed [36] for non-interacting electrons on an SPG. In the half-filled band case, the Drude weight exhibits a much sharper drop in its value compared to the non-half-filled situation.…”

“…4(a) the I(φ)-φ curves exhibit multiple kinks which follows from the numerous band-crossings that are typ- ical of such hierarchical networks [3,36]. Such crossings become less in number, and global gaps open up in the spectrum, clustering the spectrum into sub-band structures in the case of an anisotropic SPG, as has recently been reported in the literature even in the case of non-interacting electrons [36]. Kinks are now expected to smooth out.…”

Exact evaluation of the causal spectrum and localization properties of electronic states on a scale-free network

“…i |i the corresponding eigenstate, where |i is the totally localized state at vertex i. The inverse participation ratios (IPR) of a state Φ (t) is defined as ξ = 1/ i (φ 4 . If we allow Φ (t) to be unnormalized, ξ is redefined as…”

“…Most physical systems living on heterogenous structure behaves quite different from those living on homogeneous backgrounds with translational invariance and other symmetries, as exemplified by the analysis of several quantum models in the past few decades [1][2][3][4][5][6]. The anomalies include, for instance, the multifractal properties of the energy spectrum, the low-dimensional Bose-Einstein condensation, and the log-periodic oscillation of thermodynamic properties [7][8][9].…”