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

TL;DR

This study uses a superconducting microwave resonator to experimentally verify the Atiyah-Singer index theorem by analyzing the spectral properties of a model of the C60 fullerene molecule, confirming theoretical predictions.

Contribution

First experimental verification of the Atiyah-Singer index theorem using a superconducting microwave resonator simulating fullerene geometry.

Findings

Confirmed the number of zero modes matches the theorem's predictions

Demonstrated high-resolution spectral analysis of icosahedral symmetry

Validated topological aspects of curved carbon lattices

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.