  Charge-density-waves (CDW) which occur mainly in low-dimensional systems have
a macroscopic wave function similar to superfluids and superconductors.
Kosterlitz-Thouless (KT) transition is observed in superfluids and
superconductors, but the presence of KT transition in ultra-thin CDW systems
has been an open problem. We report the direct real-space observation of CDWs
with new order states in mono-, bi-, and tri-layer 1T-TaS_2 crystal by using a
low voltage scanning-transmission-electron-microscope (STEM) 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 CDW order without the triple q condition q_1 + q_2 + q_3 = 0. A strong
electron-phonon interaction gives rise to new crevasse (line) type defects
instead of disclination (point) type defects due to the KT transition. These
results reaffirm the importance of the electron-phonon interaction in
mono-layer nanophysics.
