  Having the chiral anomaly induced magneto-transport phenomena extensively
studied in single Weyl semimetal (WSM) as characterized by topological charge
$n=1$, we here address the transport properties in the context of multi-Weyl
semimetals (m-WSMs) where $n>1$. Using semiclassical Boltzmann transport
formalism with the relaxation time approximation, we investigate several
intriguing transport properties such as longitudinal magneto-conductivity
(LMC), planar Hall conductivity (PHC), thermo-electric coefficients (TECs) and
planar Nernst coefficient (PNC) for m-WSMs in the co-planar setups with
external magnetic field, electric field and temperature gradient. Starting from
the low-energy model, we show analytically that at zero temperature both LMC
and PHC vary cubically with topological charge as $n^3$ while the finite
temperature ($T \neq 0$) correction is proportional to $(n+n^2)T^2$.
Interestingly, we find that both the longitudinal and transverse TECs vary
quadratically with topological charge as $n^2$ and the PNC is found to vary
non-monotonically as a function of $n$. Our study hence clearly suggests that
the inherent properties of m-WSMs indeed show up distinctly through the chiral
anomaly and the chiral magnetic effect induced transport coefficients in two
different setups. Moreover, in order to obtain an experimentally realizable
picture, we simultaneously verify our analytical findings through the numerical
calculations using the lattice model of m-WSMs.
