Realization of fractal Aubry-André-Harper models in electronic circuits

Fractals, characterized by self-similarity, complexity, and fractional dimensions, have emerged as a powerful tool for exploring novel physical phenomena in non-integer-dimensional systems. Despite the absence of a conventional ``bulk'' in fractal lattices, recent research demonstrates that they can host robust topological states, thus posing a challenge to the traditional bulk-edge correspondence in topological physics. In this work, we investigate the topological properties of the two-dimensional Aubry-Andr\'e-Harper (AAH) model on a fractal lattice, unveiling higher-order corner states induced by the fractal bulk-edge correspondence. We propose a method for implementing the fractal AAH model in an electronic circuit. By analyzing the frequency spectrum of the circuit, we identify the topological features of higher-order corner states in the fractal circuit network. Our research findings enhance the understanding of topological characteristics in non-integer-dimensional systems and provide a practical physical platform for exploring phenomena related to noninteger dimensions.