Direct evidence for superconductivity in the organic charge density wave compound $\alpha$-(BEDT-TTF)$_2$KHg(SCN)$_4$ under hydrostatic pressure

We present direct evidence of a superconducting state existing in the title compound below 300 mK under quasi-hydrostatic pressure. The superconducing transition is observed in the whole pressure range studied, 0 < P < 4 kbar. However, the character of the transition drastically changes with suppressing the charge-density wave state.