Title: Edge modes in the Sierpinski Harper Hofstadter Butterfly Fractal

Speaker: Mikael Fremling (University of Utrecht)

Abstract: We study the edge modes of the Sierpinski carpet at finite magnetic fields and characterise the transition from a Hofstadter spectrum to a Sierpinski Hofstadter spectrum. We find that there are parameter regions, which appear to be stable in the thermodynamic limit, that give rise to quantised Hall conductance. Further, we find that only edge modes related to Chern number one bands are present when the fractal is at maximal depth. We attribute this to the absence of paths though the fractal with two or more connected sites. Also, the stability of the edge modes with respect to impurities is discussed.

Time: Thursday, 09 May 2019, 3pm

Location: Lecture Room, 1st Floor, School of Theoretical Physics, DIAS, 10 Burlington Road, Dublin 4