  The quasi two-dimensional Mott insulator $\alpha$-RuCl$_3$ is proximate to
the sought-after Kitaev quantum spin liquid (QSL). In a layer of
$\alpha$-RuCl$_3$ on graphene the dominant Kitaev exchange is further enhanced
by strain. Recently, quantum oscillation (QO) measurements of such
$\alpha$-RuCl$_3$ / graphene heterostructures showed an anomalous temperature
dependence beyond the standard Lifshitz-Kosevich (LK) description. Here, we
develop a theory of anomalous QO in an effective Kitaev-Kondo lattice model in
which the itinerant electrons of the graphene layer interact with the
correlated magnetic layer via spin interactions. At low temperatures a heavy
Fermi liquid emerges such that the neutral Majorana fermion excitations of the
Kitaev QSL acquire charge by hybridising with the graphene Dirac band. Using
ab-initio calculations to determine the parameters of our low energy model we
provide a microscopic theory of anomalous QOs with a non-LK temperature
dependence consistent with our measurements. We show how remnants of
fractionalized spin excitations can give rise to characteristic signatures in
QO experiments.
