Topolectrical-circuit realization of a four-dimensional hexadecapole insulator

Recently, the theory of quantized dipole polarization has been extended to account for electric multipole moments, giving rise to the discovery of multipole topological insulators (TIs). Both two-dimensional quadrupole and three-dimensional (3D) octupole TIs with robust zero-dimensional corner states have been realized in various classical systems. However, due to the intrinsic 3D limitation, the higher-dimensional multipole TIs, such as four-dimensional (4D) hexadecapole TIs, are supposed to be extremely hard to construct in real space. Here, we theoretically propose and experimentally demonstrate the realization of a classical analog of 4D hexadecapole TI based on the electric circuits in fully real space. The explicit construction of 4D hexadecapole circuits, where the connection of nodes is allowed in any desired way free from constraints of locality and dimensionality, is provided. By direct circuit simulations and impedance measurements, the in-gap corner states protected by the quantized hexadecapole moment in the 4D circuit lattices are observed and the robustness of the corner state is also demonstrated. Our work offers a pathway to study the higher-order/dimensional topological physics in real space.