  Generally, lattice distortions play a key role in determining the ground
states of materials. Although it is well known that trigonal distortions are
generic to most two-dimensional transition metal dichalcogenides, the impact of
this structural distortion on the electronic structure has not been understood
conclusively. Here, by using a combination of polarization dependent X-ray
absorption spectroscopy (XAS), X-ray photoelectron spectroscopy (XPS) and
atomic multiplet cluster calculations, we have investigated the electronic
structure of titanium dichalcogenides TiX2 (X=S, Se, Te), where the magnitude
of the trigonal distortion increase monotonically from S to Se and Te. Our
results reveal the presence of an anomalous and large crystal filed splitting.
This unusual kind of crystal field splitting is likely responsible for the
unconventional electronic structure of TiX2 compounds. Our results also
indicate the drawback of the distorted crystal field picture in explaining the
observed electronic ground state of these materials and emphasize the key
importance of metal-ligand hybridization and electronic correlation in defining
the electronic structures near Fermi energy.
