  Transition metal dichalcogenides (TMDs) are a class of two-dimensional (2D)
layered materials that exhibit a diverse range of electronic structures,
including charge density waves (CDWs) that can lead to insulating,
semiconducting, metallic, and even superconducting phases. While the formation
of CDWs in these systems has been recognized in early research [Phys. Rev.
Lett. 129, 156401 (2022); Nat. Phys. 11, 328 (2015)], the underlying mechanisms
driving the commensurate CDW (CCDW) phase remain largely unexplored. CCDWs
typically originate from factors such as perfect Fermi surface nesting and/or
electron-phonon coupling, causing the divergence of the chiral electronic
structure. However, in the case of layered 2D TMD materials with CCDW phases,
the significance of reconstructed electronic structures resulting from periodic
lattice distortions (PLD) and photoemission matrix element effects in the CCDW
instability needs to be visualized. This study focuses on computationally
accessible CCDW phases in 1T-Ta$S_2$, a prototypical TMD with a rich CDW phase
diagram, aiming to understand the origins of CCDW phases. The insights gained
from this investigation have the potential to advance the application of 2D
materials in next-generation electronics, quantum sensing and information
science.
