  Motivated by the emergence of higher-order van Hove singularities (VHS) with
power-law divergent density of states (DOS)
($\rho_c(\omega)=\rho_0/|\omega|^{r}$, $0<r<1$) in materials, we investigate a
multichannel Kondo model involving conduction electrons near the higher-order
van Hove filling. This model considers $M$ channel and $N$ spin degrees of
freedom. Employing a renormalization group analysis and dynamical large-$N$
approach, our results reveal a crossover from a non-Fermi liquid to pseudogap
behavior in the spectral properties of the local impurity at the overscreened
fixed point. We precisely determine the conditions under which the crossover
occurs, either by tuning the exponent $r$ or the ratio $\kappa=M/N$ to a
critical value. This pseudogap phase of spinon exhibits distinct physical
properties that could have an impact on the properties of real systems. The
results of this study provide novel insights into the non-Fermi liquid and
pseudogap behaviors observed in strongly correlated systems and offer a
playground to study the interplay between higher-order van Hove singularities
and multichannel Kondo physics.
