We discovered the chirality of charge density waves (CDW) in 1T-TiSe2 by
using scanning tunnelling microscopy (STM) and optical ellipsometry. We found
that the CDW intensity becomes Ia1:Ia2:Ia3=1:0.7±0.1:0.5±0.1, where Iai (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 HCDW - 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.Comment: 12 pages, 4 figure