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Two-dimensional (2D) materials that exhibit charge density waves (CDWs)—spontaneous reorganization of their electrons into a periodic modulation—have generated many research endeavors in the hopes of employing their exotic properties for various quantum-based technologies. Early investigations surrounding CDWs were mostly focused on bulk materials. However, applications for quantum devices require few-layer materials to fully utilize the emergent phenomena. The CDW field has greatly expanded over the decades, warranting a focus on the computational efforts surrounding them specifically in 2D materials. In this review, we cover ground in the following relevant theory-driven subtopics for TaS2 and TaSe2: summary of general computational techniques and methods, resulting atomic structures, the effect of electron–phonon interaction of the Raman scattering modes, the effects of confinement and dimensionality on the CDW, and we end with a future outlook. Through understanding how the computational methods have enabled incredible advancements in quantum materials, one may anticipate the ever-expanding directions available for continued pursuit as the field brings us through the 21st century. 

Abstract Alloyed transition metal dichalcogenides provide an opportunity for coupling band engineering with valleytronic phenomena in an atomically-thin platform. However, valley properties in alloys remain largely unexplored. We investigate the valley degree of freedom in monolayer alloys of the phase change candidate material WSe 2(1-x) Te 2x . Low temperature Raman measurements track the alloy-induced transition from the semiconducting 1H phase of WSe 2 to the semimetallic 1T d phase of WTe 2 . We correlate these observations with density functional theory calculations and identify new Raman modes from W-Te vibrations in the 1H-phase alloy. Photoluminescence measurements show ultra-low energy emission features that highlight alloy disorder arising from the large W-Te bond lengths. Interestingly, valley polarization and coherence in alloys survive at high Te compositions and are more robust against temperature than in WSe 2 . These findings illustrate the persistence of valley properties in alloys with highly dissimilar parent compounds and suggest band engineering can be utilized for valleytronic devices. 

ZrS2, ZrSe2 and mixed alloy ZrSxSe2−x materials were achieved through chemical vapor transport. The incongruent melting system of Zr-S-Se formed crystalline layered flakes as a transport product that grew up to 2 cm in lateral size with cm-scale flakes consistently obtained for the entire compositional range exhibiting visible hexagonal features. Bulk flakes of the series ZrSxSe2−x (x=0, 0.15, 0.3, 0.6, 1.05, 1.14, 1.51, 1.8 and 2) were analyzed through Raman spectroscopy revealing significant convolution of primary bonding modes and shifting of Raman features as a function of increasing sulfur composition. Additionally, activation of new modes not present in the pure compounds are observed as effects which result from disorder introduced into the crystal due to the random mixing of S-Se in the alloying process. Further structural characterization was performed via x-ray diffraction (XRD) on the layered flakes to evaluate the progression of layer spacing function of alloy composition which was found to range between 6.24 Å for ZrSe2 and 5.85 Å for ZrS2. Estimation of the compositional ratios of the alloy flakes through energy dispersive spectroscopy (EDS) large-area mapping verified the relation of the targeted source stoichiometry represented in the layered flakes. Atomic-resolution high angle annular dark field (HAADF)-scanning transmission electron microscopy (STEM) imaging was performed on the representative Zr (S0.5Se0.5)2 alloy to validate the 1T atomic structure and observe the arrangement of the chalcogenide columns stacks. Additionally, selected area diffraction pattern generated from the [0 0 0 1] zone axis revealed the in-plane lattice parameter to be approximately 3.715 Å.