Experimental Observation of Chiral Order in TiSe$_2$

Recent STM measurements on TiSe$_2$ were interpreted as evidence of chirality in the charge-density-wave order parameter, \textit{i.e.}, a rotation in the phase of the three in-plane components of the CDW order from one layer to the next. Recently, J. van Wezel has shown theoretically how a chiral state can arise from the onset of orbital order of the Ti 3$d$ and Se 4$p$ states in conjunction with the charge order at a temperature at or below the CDW transition temperature [arXiv:1106.1930v1 (2011)]. This theory predicts a lowering of the symmetry of the ordered phase from $P\bar{3}c1$ to $P2$. We present the results of synchrotron x-ray diffraction measurements on a single crystal of TiSe2 that provide evidence of a second structural phase transition 15K below the CDW transition, consistent with the proposed space group.