  We propose a new dark-state cooling method of trapped ion systems in the
Lamb-Dicke limit. With application of microwave dressing the ion, we can obtain
two electromagnetically induced transparency structures. The heating effects
caused by the carrier and the blue sideband transition vanish due to the EIT
effects and the final mean phonon numbers can be much less than the recoil
limit. Our scheme is robust to fluctuations of microwave power and laser
intensities which provides a broad cooling bandwidth to cool motional modes of
a linear ion chain. Moreover, it is more suitable to cool four-level ions on a
large-scale ion chip.
