Anomalous High-Energy Second Plateau in High Harmonic Generation from Fullerenes

We explore with ab-initio theory high harmonic generation (HHG) from a series of gas-phase fullerenes (from C$_{20}$ to C$_{60}$, including isomers) under varying laser conditions (different ellipticities, angular orientations, intensities and wavelengths). We find that HHG emission from fullerenes exhibits a prominent high-energy second plateau, extending well above the expected semi-classical cutoff, e.g. for an 800 nm driving laser with a peak intensity of $10^{14}$ W/cm$^2$, the anomalous $2^{nd}$ plateau cutoff is 115 eV. We theoretically analyze the underlying $2^{nd}$ plateau physical mechanism and determine that: (i) It differs from the standard SFA-like mechanism; (ii) It is recombination- based; (iii) It has an unusual inverted cutoff scaling with wavelength (whereby the cutoff decreases with increasing wavelength, until reaching a saturation); and (iv) It exhibits a linear cutoff dependence with electric field amplitude E$_0$ . We further rule out real-space trajectory based pictures, indicating that the most likely culprits are sharp quantum mechanical resonances in the fullerene family. Our work establishes a new route for high energy coherent broadband emission without requiring mid-IR driving and uncovers a novel HHG mechanism in complex structure quantum systems.