Electronic Transport on the Sierpinski Fractals

Abstract

Abstract In this thesis, the effects on the electronic properties of a system are studied due to changing the geometry from ideal lattices to the Sierpinski fractals. To this end the electronic transport is determined through the transmission function T (E), obtained through the Landauer-Büttiker formalism in a tightbinding model. Simulations are performed numerically with the use of supercomputers at ICHEC for system sizes in the order of L^2 = 10^4. Through iterative use of Dyson's equation the processing time is drastically lowered through the recursive Green's function method. For the Sierpinski carpet the theory of diffusive transmission is tested and it is found that the transmission obeys disorder-dependent powerlaw behavior of the form T / L^-0.45. As a second result the 2D Chern insulator is modeled onto the triangular lattice and it is found that the surface states present in such a system survive the transition to the geometry of the Sierpinski gasket with transmission resisting small disorder.