Topological phase transition between <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="double-struck">Z</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math> and second-order topological insulators in a kagome circuit
Yating Yang, Xingyu Chen, Zhenhang Pu, Jien Wu, Xueqin Huang, Weiyin Deng, Jiuyang Lu, Zhengyou Liu
Abstract
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 ${\mathbb{Z}}_{2}$ 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 ${\mathbb{Z}}_{2}$ index and spin-polarized bulk polarizations, are calculated to describe the complete phase diagram. The one-dimensional gapless helical edge states of ${\mathbb{Z}}_{2}$ 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.