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Multiple Charge Density Wave States at the Surface of TbTe$_3$

We studied TbTe$_{3}$ using scanning tunneling microscopy (STM) in the temperature range of 298 - 355 K. As seen in previous STM measurements on RTe$_{3}$ compounds, our measurements detect a unidirectional charge density wave state (CDW) in the surface Te-layer with a wavevector consistent with that of the bulk, q$_{cdw}$ = 0.30 $\pm$ 0.01c$^{*}$. However, unlike previous STM measurements, and differing from measurements probing the bulk, we detect two perpendicular orientations for the unidirectional CDWs with no directional preference for the in-plane crystal axes (a- or c-axis) and no noticeable difference in wavevector magnitude. In addition, we find regions in which the bidirectional CDW states coexist. We propose that observation of two CDW states indicates a decoupling of the surface Te-layer from the rare-earth block layer below, and that strain variations in the Te surface layer drive the local CDW direction to the specific unidirectional or, in rare occurrences, bidirectional CDW orders observed. This indicates that similar driving mechanisms for CDW formation in the bulk, where anisotropic lattice strain energy is important, are at play at the surface. In our bias-dependent measurements, we find no contrast inversion for the CDW state between occupied and empty states. This finding differs from other quasi 2-dimensional materials containing a hidden 1-dimensional character which leads to a favorable Fermi surface nesting scenario. Our temperature-dependent measurements provide evidence for localized CDW formation above the bulk transition temperature, T$_{cdw}$.