Direct spectroscopic evidence of 2x2x2 CDW order and its evolution with temperature in 1T-TiSe₂

1T-TiSe₂ is a canonical charge density wave (CDW) material, in which a commensurate CDW order with three-dimensional 2a_ox2a_ox2c_o superstructure appears at around 200K. This leads to the backfolding of energy bands at high symmetry points of the Brillouin zone, which has indeed been observed by Angle Resolved Photoemission Spectroscopy (ARPES) experiments predominantly at L and M points. Even though these experiments clearly evidence the existence of CDW order in 1T-TiSe₂, they can’t categorically establish the three-dimensional aspect of the CDW order as majority of the experimental data can qualitatively be explained via 2x2x1 type CDW spanning as well. We have conducted detailed photon energy and temperature-dependent ARPES studies on 1T-TiSe₂ samples focusing on Γ and A points. Our data show evidence for the presence of Γ-derived valence bands in the CDW state at A points and vice versa, which is a straightforward spectroscopic signature of the three-dimensional nature of the CDW order in 1T-TiSe₂. This three-dimensional nature of the CDW order persists even at room temperature. This is counterintuitive as the recent structural measurements showed a two-step process in the CDW transition of 1T-TiSe₂, where the CDW-related lattice distortions initiate in individual TiSe₂ planes first at around 240K and then become fully three-dimensional at around 200K. This apparent inconsistency between spectroscopic and structural studies most likely imply additional ordering in the sample.