  We present a systematic investigation of the magnetoresponses of the Weyl
points (WPs) with a topological charge of n = 2, 3 and 4, and with both linear
and quadratic energy tilt. The linear tilt always tends to squeeze the Landau
levels (LLs) of both conduction and valence bands of all the WPs, and
eventually leads to LL collapse in the type-II phase. However, the quadratic
energy tilt has more complex influences on the LLs of the unconventional WPs.
For charge-n (n = 2, 4) WP, the influence of the quadratic tilt on the LLs of
conduction and valence bands are opposite, i.e. if the LLs of conduction
(valence) bands are squeezed, then that of the valence (conduction) bands are
broadened, and the squeezed LL spectrum will be collapsed in type-III phase.
But, the LL collapse generally can not be found in the type-III charge-3 WP.
Moreover, for charge-n (n = 2, 3) WP, the quadratic tilt breaks the degeneracy
of the chiral LLs regardless of the direction of the magnetic field, leading to
additional optical transitions and magneto-optical conductivity peaks at low
frequencies. Interestingly, the four chiral LLs in charge-4 WP are always not
degenerate. Hence, there inevitably exist magneto-optical conductivity peaks at
low frequencies for charge-4 WP. Since the density of state of the LL spectrum
is very large, one can expect that the low-frequency magneto-optical responses
in unconventional WPs would be significant and may be used for developing
efficient terahertz photodetectors.
