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

Abstract

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.

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• Probing non-Hermitian phase transitions in curved space via quench dynamics
• Microwave photonic crystals as an experimental realization of a combined honeycomb-kagome lattice
• Properties of the eigenmodes and quantum-chaotic scattering in a superconducting microwave Dirac billiard with threefold rotational symmetry
• Study on the effects of anisotropic effective mass on electronic properties, magnetization and persistent current in semiconductor quantum ring with conical geometry