  The rise of moir\'{e} materials has led to experimental realizations of
integer and fractional Chern insulators in small or vanishing magnetic fields.
At the same time, a set of minimal conditions sufficient to guarantee a Abelian
fractional state in a flat band were identified, namely "ideal" or "vortexable"
quantum geometry. Such vortexable bands share essential features with the
lowest Landau level, while excluding the need for more fine-tuned aspects such
as flat Berry curvature. A natural and important generalization is to ask if
such conditions can be extended to capture the quantum geometry of higher
Landau levels, particularly the first (1LL), where non-Abelian states at $\nu =
1/2,2/5$ are known to be competitive. The possibility of realizing these states
at zero magnetic field , and perhaps even more exotic ones, could become a
reality if we could identify the essential structure of the 1LL in Chern bands.
In this work, we introduce a precise definition of 1LL quantum geometry, along
with a figure of merit that measures how closely a given band approaches the
1LL. We apply the definition to identify two models with 1LL structure -- a toy
model of double bilayer twisted graphene and a more realistic model of strained
Bernal graphene.
