Electronic transport in the Koch fractal lattice

Abstract

In this work we extend the algebraic approach introduced in the context of general Fibonacci systems [E. Maciá and F. Domínguez-Adame, Phys. Rev. Lett. 76, 2957 (1996)] to analytically study the transmission coefficient of a subset of states in the fractal Koch lattice. We report on the existence of extended states whose transmission coefficients periodically oscillate as the Koch curve approaches its fractal limit.