  Recently, time-reversal symmetric but inversion broken systems with
non-trivial Berry curvature in the presence of a built-in electric field have
been proposed to exhibit a new type of linear Hall effect in ballistic regime,
namely, the Magnus Hall effect. The transverse current here is caused by the
Magnus velocity that is proportional to the built-in electric field allowing us
to examine the Magnus Hall conductivity and Magnus Nernst conductivity with
chemical potential. Starting with two-dimensional (2D) topological systems, we
find that warping induced asymmetry in both the Fermi surface and Berry
curvature can in general enhance the Magnus Hall response for monolayer
graphene and surface states of topological insulator. Interestingly, strain can
change the Fermi surface character substantially that further results in
distinct behavior of Magnus transport coefficients as we observe in bilayer
graphene. Going beyond 2D systems, we also investigate the Magnus Hall and
Nernst responses in three-dimensional multi-Weyl semimetals (mWSMs).
Remarkably, Magnus responses can only survive for the tilted WSMs, and
therefore can be measured as a tool to distinguish between the untilted and
tilted WSMs in experiments. In addition, we find that the Magnus Hall responses
get suppressed with increasing the non-linearity associated with the band
touching around multi-Weyl node.
