  Chiral anomaly or Adler-Bell-Jackiw anomaly in Weyl semimetals (WSMs) has a
significant impact on the electron transport behaviors, leading to remarkable
longitudinal or planar electrical and thermoelectric transport phenomena in the
presence of electromagnetic gauge fields. These phenomena are consequences of
the imbalanced chiral charge and energy induced by chiral anomaly in the
presence of parallel electric ($\mathbf{E}$) and magnetic ($\mathbf{B}$) fields
($\mathbf{E \cdot B }\neq 0$) or $(\mathbf{B \cdot \nabla }T\neq 0)$
($\mathbf{\nabla}T$ is the thermal gradient). We here propose another two
fascinating transport properties, namely, the nonlinear planar Nernst effect
and nonlinear planar thermal Hall effect induced by chiral anomaly in the
presence of $\mathbf{B \cdot \nabla}T\neq 0$ in WSMs. Using the semiclassical
Boltzmann transport theory, we derive the analytical expressions for the chiral
anomaly induced nonlinear Nernst and thermal Hall transport coefficients and
also evaluate the fundamental mathematical relations among them in the
nonlinear regime. The formulas we find in this current work are consistent with
that predicted for the nonlinear anomalous electrical and thermoelectric
effects induced by Berry curvature dipole recently. Additionally, in contrast
to the recent work, by utilizing the lattice Weyl Hamiltonian with intrinsic
chiral chemical potential, we find that the chiral anomaly induced nonlinear
planar effects can exist even for a pair of oppositely tilted or non-tilted
Weyl cones in both time reversal and inversion broken WSMs. The chiral anomaly
induced nonlinear planar effects predicted here along with the related
parameter dependencies are hence possible to be realized in realistic WSMs in
experiment.
