  The recent discovery of natural biaxial hyperbolicity in van der Waals
crystals, such as $\alpha$-MoO$_3$, has opened up new avenues for mid-IR
nanophotonics due to their deep subwavelength phonon-polaritons. However, a
significant challenge is the lack of active tunability of these hyperbolic
phonon polaritons. In this work, we investigate heterostructures of graphene
and $\alpha$-MoO$_3$ for actively tunable hybrid plasmon phonon polariton modes
via electrostatic gating in the mid-infrared spectral region. We observe a
unique propagation direction dependent hybridization of graphene plasmon
polaritons with hyperbolic phonon polaritons for experimentally feasible values
of graphene chemical potential. We further report an application to tunable
valley quantum interference in this system with a broad operational bandwidth
due to the formation of these hybrid modes. This work presents a
lithography-free alternative for actively tunable, anisotropic spontaneous
emission enhancement using a sub-wavelength thick naturally biaxial hyperbolic
materials.
