Incommensurate lattice modulation in CDW compound TbTe$_{3}$

The layered materials $R$Te$_{3}$ ($R=$ rare earth) are simple charge-density wave (CDW) compounds, for which large regions of the original quasi-2D Fermi surface are nested by a single incommensurate wavevector. We use high resolution x-ray diffraction and scanning tunneling microscopy (STM) to study how the lattice responds to the incommensurate ordering. The superlattice of TbTe$_3$ reveals a unidirectional lattice modulation characterized by $q_{CDW}$ = 0.296 c*. Higher harmonics are several orders of magnitude lower in intensity, implying an almost sinusoidal lattice modulation. The CDW is well correlated within and between planes, with correlation lengths in excess of 1000 $\AA$. STM measurements reveal the CDW gap and real-space lattice modulation.