Pressure dependence of the charge-density-wave and superconducting states in GdTe$_3$, TbTe$_3$ and DyTe$_3$

We present electrical resistivity and ac-susceptibility measurements of GdTe$_3$, TbTe$_3$ and DyTe$_3$ performed under pressure. An upper charge-density-wave (CDW) is suppressed at a rate of $mathrm{d}T_{mathrm{CDW,1}}/mathrm{d}P$ = $-$85 K/GPa. For TbTe$_3$ and DyTe$_3$, a second CDW below $T_{mathrm{CDW,2}}$ increases with pressure until it reaches the $T_{mathrm{CDW,1}}$($P$) line. For GdTe$_3$, the lower CDW emerges as pressure is increased above $sim$ 1 GPa. As these two CDW states are suppressed with pressure, superconductivity (SC) appears in the three compounds at lower temperatures. Ac-susceptibility experiments performed on TbTe$_3$ provide compelling evidence for bulk SC in the low-pressure region of the phase diagram. We provide measurements of superconducting critical fields and discuss the origin of a high-pressure superconducting phase occurring above 5 GPa.