Abstract
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.
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