Chiral charge-density-waves

Abstract: We discovered the chirality of charge density waves (CDW) in 1T-TiSe$2$ by using scanning tunnelling microscopy (STM) and optical ellipsometry. We found that the CDW intensity becomes $I{a_1}:I{a_2}:I{a_3} = 1:0.7 \pm 0.1:0.5 \pm 0.1$, where $Ia_i$ (i =1, 2, 3) is the amplitude of the tunnelling current contributed by the CDWs. There were two states, in which the three intensity peaks of the CDW decrease \textit{clockwise} and \textit{anticlockwise} when we index each nesting vector in order of intensity in the Fourier transformation of the STM images. The chirality in CDW results in the three-fold symmetry breaking. Macroscopically, two-fold symmetry was indeed observed in optical measurement. We propose the new generalized CDW chirality $H{CDW} \equiv {\boldmath $q_1$} \cdot ({\boldmath $q_2$}\times {\boldmath $q_3$})$, where ${\boldmath $q_i$}$ are the nesting vectors, which is independent of the symmetry of components. The nonzero $H_{CDW}$ - the triple-${\boldmath $q$}$ vectors do not exist in an identical plane in the reciprocal space - should induce a real-space chirality in CDW system.