Test of the Atiyah-Singer Index Theorem for Fullerene with a Superconducting Microwave Resonator

Experiments have been performed using a spherical superconducting microwave resonator that simulates the geometric structure of the C60 fullerene molecule. The objective was to study with very high resolution the exceptional spectral properties emerging from the symmetries of the icosahedral structure of the carbon lattice. In particular, the number of zero modes has been determined to test the predictions of the Atiyah-Singer index theorem, which relates it to the topology of the curved carbon lattice. This is, to the best of our knowledge, the first experimental verification of the index theorem.