Fullerene C(60) Simulated with a Superconducting Microwave Resonator and Test of the Atiyah-Singer Index Theorem.

We report first experiments with a macroscopic-size superconducting microwave resonator that has the geometric structure of the C(60) fullerene molecule. Our high-resolution measurements reveal the exceptional spectral properties that stem from the icosahedral symmetry of its carbon lattice. In particular, they allow us to determine the number of zero-energy modes, i.e., of modes with energy values at the Dirac point existent in the band structure due to the hexagonal arrangements of the carbon atoms, and to test the Atiyah-Singer index theorem which relates this number to the topology of the curved carbon lattice.