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We study oscillations of the high energy atmospheric neutrinos in the Earthinto sterile neutrinos with the eV-scale mass. The MSW resonance and parametricenhancement of the $\bar{\nu}_\mu\to\bar{\nu}_s$ oscillations lead todistortion of the zenith angle distribution of the muon-track events which canbe observed by IceCube. Due to matter effect, the IceCube signal depends notonly on the mixing element $U_{\mu 4}$ relevant for LSND and MiniBooNE but alsoon $U_{\tau 4}$ and the CP-violating phase $\delta_{24}$. We show that the casewith $U_{\tau 4} = \delta_{24} = 0$ leads to the weakest IceCube signal andtherefore should be used to bound $U_{\mu 4}$. We compute the zenith angledistributions of the $\nu_\mu-$events for different energy intervals in therange (0.1 - 10) TeV and find that inclusion of the energy information (binningin energy) improves the sensitivity to $\nu_s$ drastically. We estimate thatwith already collected (during 3 - 4 years) IceCube statistics the bound$|U_{\mu 4}|^2 < 0.01$ ($99\%$ C.L.) can be established and the mixing requiredby LSND and MiniBooNE can be excluded at $(4 - 6) \sigma$ confidence level.

Restricting the LSND and MiniBooNE sterile neutrinos with the IceCube atmospheric neutrino data