  In view of searching the signature of the celebrated chiral anomaly (CA) in
Weyl semimetals (WSMs) in ongoing experiments, quantum oscillation in linear
response regime has been considered as an important signature in the magneto
transports in WSMs, due to its unique relation to CA. Investigating the
nonlinear planar effects (NPEs) starting from the semiclassical regime to the
ultra-quantum limit within the framework of Boltzmann transport theory
incorporating Landau quantization, we here propose the quantum oscillations in
NPEs can serve as a robust signature of CA in WSMs. By obtaining analytical
expressions, we show that the quantum oscillations of the nonlinear effects
exhibit two different period scales in 1/B (B is the magnetic field) compared
to the linear responses where only one period scale exists. We find that these
quantum oscillations in NPEs are attributed to the deviation of chiral chemical
potential (CCP), which is proportional to the finite band tilt as well as
transverse electric field and therefore, directly linked to CA in WSMs. In
addition, we also show that the CA-induced nonlinear magneto conductivity is
linear and independent in the magnetic field in the semiclassical and
ultraquantum regimes, respectively. We conclude that the proposed behaviors of
NPEs in different regimes uniquely signify the existence of CA and therefore,
can serve as a probe of identifying CA in WSMs in experiments.
