Extended electron states and magneto-transport in a 3-simplex fractal

Abstract

We perform a real space renormalization group analysis to study the one electron eigenstates and the transmission coefficient across a 3-simplex fractal lattice of arbitrary size, in the presence of a magnetic field. In particular, we discuss the existence of extended electronic states and the influence of the magnetic field on the spectrum of the system. A general formulation is presented which enables us to deal with both the isotropic and the anisotropic cases. It is found that in general, the transmission across an anisotropic fractal is larger than its isotropic counterpart. Additionally, we point out an extremely interesting correlation between a subset of values of the external field, and the multiple fixed point cycles of the Hamiltonian corresponding to the extended eigenstates. A prescription for observing such correlations is proposed. This aspect may be important in the classification of the extended states in such deterministic structures.