  The excitation of quasi-particles near the extrema of the electronic band
structure is a gateway to electronic phase transitions in condensed matter. In
a many-body system, quasi-particle dynamics are strongly influenced by the
electronic single-particle structure and have been extensively studied in the
weak optical excitation regime. Yet, under strong optical excitation, where
light fields coherently drive carriers, the dynamics of many-body interactions
that can lead to new quantum phases remain largely unresolved. Here, we induce
such a highly non-equilibrium many-body state through strong optical excitation
of charge carriers near the van Hove singularity in graphite. We investigate
the system's evolution into a strongly-driven photo-excited state with
attosecond soft X-ray core-level spectroscopy. Surprisingly, we find an
enhancement of the optical conductivity of nearly ten times the quantum
conductivity and pinpoint it to carrier excitations in flat bands. This
interaction regime is robust against carrier-carrier interaction with coherent
optical phonons acting as an attractive force reminiscent of superconductivity.
The strongly-driven non-equilibrium state is markedly different from the
single-particle structure and macroscopic conductivity and is a consequence of
the non-adiabatic many-body state.
