  Hybrid dielectric metasurfaces have emerged as a promising approach to
enhancing near field confinement and thus achieving high optical nonlinearity
using low loss dielectrics. Additional flexibility in design and fabrication of
hybrid metasurfaces allows dynamic control of light, which is value-added for a
wider range of applications. Here, we demonstrate a tunable and efficient third
harmonic generation (THG) via hybrid metasurfaces with phase change material
Ge2Sb2Te5 (GST) deposited on top of amorphous silicon nanostructutes. Fano
resonance is excited to confine the incident light inside the hybrid
metasurfaces, and an experimental quality factor ($Q$-factor) of 125 is
achieved at the fundamental pump wavelength around 1210 nm. We demonstrate the
switching between a turn-on state of Fano resonance in the amorphous state of
GST and a turn-off state in its crystalline state and also gradual multistate
tuning of THG emission at its intermediate state. We achieve a high THG
conversion efficiency of ${\eta} = 2.9*10^{-6}$ %, which is more than ~32 times
of that of a GST-based Fabry-P\`erot cavity under a similar pump laser power,
thanks to the enhanced field confinement due to the Fano resonance. Our results
show the strong potential of GST-based hybrid dielectric metasurfaces for
efficient and tunable nonlinear optical devices.
