J. Ishioka, 1 Y. H. Liu, 2 K. Shimatake, 1 T. Kurosawa, 2 

K. Ichimura, 1, 3 Y. Toda, 1, 3 M. Oda, 2, 3 and S. Tanda 1, 3,$_{∗}$ 

# Chiral charge-density-waves 

$^{1}$Department of Applied Physics, Hokkaido University, Sapporo 060-8628, Japan 

$^{2}$Department of Physics, Hokkaido University, Sapporo 060-0810, Japan 

$^{3}$Center of Education and Research for Topological Science and Technology, 

Hokkaido University, Sapporo 060-8628, Japan 

(Dated: October 31, 2018) 

## 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 Ia$_{1}$ : Ia$_{2}$ : Ia$_{3}$ = 1 : 0 . 7 ± 0 . 1 : 0 . 5 ± 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 clockwise and 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$_{CDW}$ ≡ q 1 · ( q 2 × q 3 ), where q i are the nesting vectors, which is independent of the symmetry of components. The nonzero H$_{CDW}$ - the triple- q vectors do not exist in an identical plane in the reciprocal space - should induce a real-space chirality in CDW system. 

PACS numbers: 71.45.Lr, 68.37.Ef, 72.80.Ga, 73.22.Gk, 78.47.J- 

