  In this paper we study the generation of very high energy (VHE) emission in
Crab-like pulsars driven by means of the feedback of Cherenkov drift waves on
distribution of magnetospheric electrons. We have found that the unstable
Cherenkov drift modes lead to the quasi-linear diffusion (QLD), keeping the
pitch angles from vanishing, which in turn, maintains the synchrotron
mechanism. Considering the Crab-like pulsars it has been shown that the growth
rate of the Cherenkov drift instability (ChDI) is quite high, indicating high
efficiency of the process. Analyzing the mechanism for the typical parameters
we have found that the Cherenkov drift emission from the extreme UV to hard
$X$-rays is strongly correlated with the VHE synchrotron emission in the GeV
band.
