Topological phase transition between Z2 and second-order topological insulators in a kagome circuit

The notion of higher-order topological phases has endowed topological states of matter beyond the first order. In this work, we report the topological phase transition between the conventional Z₂ topological insulator and second-order topological insulator in a kagome circuit. Such a phase transition emerges at the competition between the spin-orbit couplings and nonequivalent nearest-neighbor hoppings without breaking symmetry. The bulk topological invariants, the Z₂ index and spin-polarized bulk polarizations, are calculated to describe the complete phase diagram. The one-dimensional gapless helical edge states of Z₂ topological phase and zero-dimensional corner states of second-order topological phase are observed in the ribbon and finite-size circuit samples, respectively. Our findings in the electric circuits provide an experimental bridge to connect the first-order and higher-order topological phases.