Observation of a third, previously unknown charge-density-wave order in RTe$_3$ by optical spectroscopy

The occurrences of collective quantum states, such as superconductivity and charge- or spin-density-waves (CDWs or SDWs), are among the most fascinating phenomena in solids. Rare-earth tri-telluride RTe$_3$ (R being an element of the lanthanide family) represents an interesting and well-known CDW family in which the CDW phase transition temperature could be tuned by changing the size of the rare earth element. Previously it was known that the light rare-earth element R based compounds have only one CDW order or phase transition, while for the four heavy rare-earth RTe$_3$ (R=Tm, Er, Ho, Dy) compounds, a second CDW order with the wave vector $\textbf{q}_2$$\sim$1/3 $\textbf{a}^{\ast}$ perpendicular to the first one developed at lower temperature. Here we report the observation of a third CDW order in the series by optical spectroscopy probe. This third CDW order also evolves systematically with the size of R element. With increased chemical pressure, the first and third CDW orders are both substantially suppressed and compete with the second one by depleting the low energy spectral weight. A complete phase diagram for the multiple CDW orders in this series is established. We acknowledge B. Cheng and R. H. Yuan for their help in the experiments.