Octupole corner state in a three-dimensional topological circuit

Higher-order topological insulators (HOTIs) represent a new family of topological materials featuring quantized bulk polarizations and zero-dimensional corner states. In recent years, zero-dimensional corner states have been demonstrated in two-dimensional systems in the form of quadrupole modes or dipole modes. Due to the challenges in designing and constructing three-dimensional systems, octupole corner modes in 3D have not been observed. In this work, we experimentally investigate octupole topological phases in a three-dimensional electrical circuit, which can be viewed as a cubic lattice version of the Hofstadter model with a π -flux threading each plaquette. We experimentally observe in our higher-order topological circuit a 0D corner state manifested as a localized impedance peak. The observed corner state in the electrical circuit is induced by the octupole moment of the bulk circuit and is topologically protected by anticommuting spatial symmetries of the circuit lattice. Our work provides a platform for investigating higher-order topological effects in three-dimensional electrical circuits. Viewing topological effects in a 3D electrical circuit An electrical circuit mimicking the characteristics of a topological insulator (TI) allows the experimental realization of exotic quantum conducting states. TIs, which have applications in the burgeoning fields of spintronics and quantum computing, act as conductors in their bulk but have two-dimensional conducting states on their surfaces. Shuang Zhang at the University of Birmingham, UK and co-workers are using electrical components to mimic the atoms in higher-order TIs, which feature zero-dimensional corner states topologically protected by three anticommuting reflection symmetries of the bulk lattice. The researchers built a 3D topological circuit comprising a cubic lattice of capacitors and inductors and observed a localized peak in impedance spectrum caused by an ‘octupole’ zero-dimensional corner state. Their circuit, which imitates the famous Hofstadter butterfly model of interacting electrons, opens up a new platform for investigating higher-order topological effects.