Direct observation of mono-layer, bi-layer, and tri-layer charge density waves in 1T-TaS₂ by transmission electron microscopy without a substrate

Charge-density-waves, which occur mainly in low-dimensional systems, have a macroscopic wave function similar to superfluids and superconductors. Kosterlitz-Thouless transition is observed in superfluids and superconductors, but the presence of Kosterlitz-Thouless transition in ultra-thin charge-density-waves systems has been an open problem. We report the direct real-space observation of charge-density-waves with new order states in mono-layer, bi-layer, and tri-layer 1T-TaS₂ crystals using a low voltage scanning-transmission-electron-microscopy without a substrate. This method is ideal to observe local atomic structures and possible defects. We clearly observed that the mono-layer crystal has a new triclinic stripe charge-density-waves order without satisfying the triple q condition q₁ + q₂ + q₃ = 0. A strong electron-phonon interaction gives rise to new crevasse (line) type defects instead of disclination (point) type defects due to the Kosterlitz-Thouless transition. These results reaffirm the importance of the electron-phonon interaction in mono-layer nanophysics.