  Second-order nonlinearity gives rise to many distinctive physical phenomena,
e.g., second-harmonic generation, which plays an important role in fundamental
science and various applications. Lithium niobate, one of the most widely used
nonlinear crystals, exhibits strong second-order nonlinear effects and
electro-optic properties. However, its moderate refractive index and etching
sidewall angle limit its capability in confining light into nanoscales,
restricting its application in nanophotonics. Here, we exploit nanocavities
formed by second-order circular Bragg gratings, which support resonant anapole
modes to achieve highly enhanced SHG in thin film lithium niobate. The CBG
nanocavity exhibits a record-high normalized conversion efficiency of
$1.21\times10^{-2}\mathrm{cm^2/GW}$ under the pump intensity of $1.9$
$\mathrm{MW/cm^2}$. An SHG enhancement of $42,000$ is realized compared to
TFLN. Besides, we also show s- and p-polarization independent SHG in elliptical
Bragg nanocavities. This work could inspire studying nonlinear optics at the
nanoscale on TFLN as well as other novel photonic platforms.
