The modern theory of electric polarization in crystals associates the dipolemoment of an insulator with a Berry phase of its electronic ground state [1,2]. This concept constituted a breakthrough that not only solved thelong-standing puzzle of how to calculate dipole moments in crystals, but alsolies at the core of the theory of topological band structures in insulators andsuperconductors, including the quantum anomalous Hall insulator [3, 4] and thequantum spin Hall insulator [5-7], as well as quantized adiabatic pumpingprocesses [8-10]. A recent theoretical proposal extended the Berry phaseframework to account for higher electric multipole moments [11], revealing theexistence of topological phases that have not previously been observed. Here wedemonstrate the first member of this predicted class -a quantized quadrupoletopological insulator- experimentally produced using a GHz-frequencyreconfigurable microwave circuit. We confirm the non-trivial topological phasethrough both spectroscopic measurements, as well as with the identification ofcorner states that are manifested as a result of the bulk topology. Weadditionally test a critical prediction that these corner states are protectedby the topology of the bulk, and not due to surface artifacts, by deforming theedge between the topological and trivial regimes. Our results provideconclusive evidence of a unique form of robustness which has never previouslybeen observed.
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