Direct observation without a substrate

Charge-density-waves (CDW), which occur 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 [1,2] the direct realspace observation of CDW in mono-layer, bi-layer, and tri-layer 1T-TaS₂ crystals using a low voltage scanning-transmission-electron-microscopy (STEM) without a substrate, i.e., free-standing. 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 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 KT transition.
Bilayer crystal clearly shows nearly-commensurate CDW structure. In trilayer crystals, commensurate structure has been observed to be more robust than in the bulk crystal, being stable even at room temperature.

[1] D. Sakabe, Z. Liu, K. Suenaga, K. Nakatsugawa and S. Tanda, npj Quantum Materials, 2, Article number: 22 (2017)
[2] J. Ishioka et. al., Chiral CDW, PRL 105, 176401 (2010)