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Charge-density-waves (CDW) which occur mainly in low-dimensional systems havea macroscopic wave function similar to superfluids and superconductors.Kosterlitz-Thouless (KT) transition is observed in superfluids andsuperconductors, but the presence of KT transition in ultra-thin CDW systemshas been an open problem. We report the direct real-space observation of CDWswith new order states in mono-, bi-, and tri-layer 1T-TaS_2 crystal by using alow voltage scanning-transmission-electron-microscope (STEM) without asubstrate. This method is ideal to observe local atomic structures and possibledefects. We clearly observed that the mono-layer crystal has a new triclinicstripe CDW order without the triple q condition q_1 + q_2 + q_3 = 0. A strongelectron-phonon interaction gives rise to new crevasse (line) type defectsinstead of disclination (point) type defects due to the KT transition. Theseresults reaffirm the importance of the electron-phonon interaction inmono-layer nanophysics.

Direct Observation of Mono-, Bi-, and Tri-layer Charge Density Waves in 1T-TaS_2 by Transmission Electron Microscopy without a Substrate