deposit of the falling materials onto the polar cap area. We thus address that [*except for very young pulsars, the polar caps of the strange stars with massive atmospheres are likely to be completely bare when they act as pulsars*]{}.

Note that in the above estimate (eq.\[\[tau\]\]), we have assumed that only the matter in the polar cap regions is stripped out. This can be justified as follows. The magnetic field energy density at the pole is $\epsilon_{\rm B} = {B^2\over 8\pi}\sim 4.0\times 10^{22}B_{12}^2$ ergs cm$^{-3}$. The energy density of the matter, which is essentially the electron degenerate energy density, could be estimated as $\epsilon_{\rm e} = \epsilon_{\rm F} n_{\rm e}$, where $\epsilon_{\rm F}$ is the electron Fermi energy, $\epsilon_{\rm F}=2 \pi^4\hbar^4 c^2 n_e^2/
(e^2 B^2 m)\sim 1.03\times 10^{-63}B_{12}^{-2}n_e^2$[@r71], and $m$ and ${n_{\rm e}}$ are the mass and number density of the electrons, respectively. For $n_{\rm e}$, we adopt the electron number density at the “effective” pulsar surface of a BPCSS (eq.\[\[ne\]\] for $z=z_c$), i.e., $n_e \sim 10^{27} {\rm cm}^{-3}$. This gives $\epsilon_{\rm e} 
\sim 10^{18} {\rm ergs~ cm^{-3}}$, which is much smaller than $\epsilon_{\rm B}$. This prohibits the rapid penetration of the electrons across the magnetic field lines. However, 