Higher-order topological electric circuits and topological corner resonance on the breathing Kagome and pyrochlore lattices

Electric circuits are known to realize topological quadrupole insulators. We explore electric circuits made of capacitors and inductors forming the breathing Kagome and pyrochlore lattices. They are known to possess three phases (trivial insulator, higher-order topological insulator and metallic phases) in the tight-binding model. The topological phase is characterized by the emergence of zero-energy corner states. A topological phase transition is induced by tuning continuously the capacitance, which is possible by using variable capacitors. It is found that the two-point impedance yields huge resonance peaks when one node is taken at a corner in the topological phase. It is a good signal to detect a topological phase transition. We also show that the topological corner resonance is robust against randomness of capacitance and inductance. Furthermore, the size of electric circuits can be quite small to realize the topological phase together with topological phase transitions.