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We studied TbTe$_{3}$ using scanning tunneling microscopy (STM) in thetemperature range of 298 - 355 K. As seen in previous STM measurements onRTe$_{3}$ compounds, our measurements detect a unidirectional charge densitywave state (CDW) in the surface Te-layer with a wavevector consistent with thatof the bulk, q$_{cdw}$ = 0.30 $\pm$ 0.01c$^{*}$. However, unlike previous STMmeasurements, and differing from measurements probing the bulk, we detect twoperpendicular orientations for the unidirectional CDWs with no directionalpreference for the in-plane crystal axes (a- or c-axis) and no noticeabledifference in wavevector magnitude. In addition, we find regions in which thebidirectional CDW states coexist. We propose that observation of two CDW statesindicates a decoupling of the surface Te-layer from the rare-earth block layerbelow, and that strain variations in the Te surface layer drive the local CDWdirection to the specific unidirectional or, in rare occurrences, bidirectionalCDW orders observed. This indicates that similar driving mechanisms for CDWformation in the bulk, where anisotropic lattice strain energy is important,are at play at the surface. In our bias-dependent measurements, we find nocontrast inversion for the CDW state between occupied and empty states. Thisfinding differs from other quasi 2-dimensional materials containing a hidden1-dimensional character which leads to a favorable Fermi surface nestingscenario. Our temperature-dependent measurements provide evidence for localizedCDW formation above the bulk transition temperature, T$_{cdw}$.

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