A quantized microwave quadrupole insulator with topologically protected corner states

The modern theory of electric polarization in crystals associates the dipole moment of an insulator with a Berry phase of its electronic ground state [1, 2]. This concept constituted a breakthrough that not only solved the long-standing puzzle of how to calculate dipole moments in crystals, but also lies at the core of the theory of topological band structures in insulators and superconductors, including the quantum anomalous Hall insulator [3,...