Topological subspace-induced multifold topological phase transitions and large winding number in heterostructures

Large winding number as the unique characteristics of topological phenomena has been garnering widespread interest owing to its rich physics and potential applications in enhanced information capacity. In this work, we report the realization of the large winding number and multifold topological phase transitions by introducing layer degrees of freedom to construct topological heterostructures and experimentally demonstrate the topological edge states for circuit heterostructures in the circuit system. The effective decomposition of circuit heterostructures into independent subspaces is revealed. The multiple topological phase transitions and different large winding numbers for heterostructures can be triggered by tuning the topological properties of the subspace, leading to the multiple topological edge states reflecting in finite-size systems. Our work provides an intuitive and universal way to access the tunable large winding number and multifold topological phase transitions and may apply to engineering unique topological phenomena and further applications in classical wave systems.