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A number of intriguing phenomena, including exciton condensation, orbital ordering, and emergence of chirality, have been proposed to accompany charge-density-wave (CDW) formation in the layered transition metal dichalcogenide…
The transition metal dichalcogenide 1$T$-TiSe$_2$ is a quasi-two-dimensional layered material undergoing a commensurate 2 $\times$ 2 $\times$ 2 charge density wave (CDW) transition with a weak periodic lattice distortion (PLD) below…
Charge density waves (CDWs) with multi-component order parameters can break unexpected symmetries through the interplay of nearly degenerate instabilities. In the widely investigated material 1T-TiSe$_2$, a central question is whether the…
Superconductivity and charge density wave (CDW) appear in the phase diagram of a variety of materials including the high - $T$$_c$ cuprate family and many transition metal dichalcogenides (TMDs). Their interplay may give rise to exotic…
The interplay between charge-density waves (CDWs), which break translational symmetry, and spatially homogeneous superconductivity, which breaks global U(1) gauge symmetry, can give rise to an intriguing phenomenon: the pair-density wave,…
Two-dimensional (2D) materials have become a fertile playground for the exploration and manipulation of novel collective electronic states. Recent experiments have unveiled a variety of robust 2D orders in highly-crystalline materials…
Charge density waves (CDWs) are periodic modulations of the conduction electron density in solids. They are collective states that arise from intrinsic instabilities often present in low dimensional electronic systems. The layered…
Experimental evidences of spontaneous time-reversal (TR) symmetry breaking have been reported for the superconducting ground state in the transition metal dichalcogenide (TMD) superconductor 4H$_b$-TaS$_2$ or chiral molecule intercalated…
In a vast array of materials, including cuprates, transition metal dichalcogenides (TMDs) and rare earth tritellurides, superconductivity is found in the vicinity of short-range charge density wave (CDW) order. The crossover from long-range…
Layered transition metal dichalcogenides (TMDs) provide an ideal platform for exploring the effects of dimensionality on correlated electronic phases such as charge density wave (CDW) order. When TMDs are reduced in thickness to the 2-D…
The transition metal dichalcogenide $1T$-TiSe$_2$ is a quasi-two-dimensional layered material with a phase transition towards a commensurate charge density wave (CDW) at a critical temperature T$_{c}\approx 200$K. The relationship between…
Transition-metal dichalcogenides (TMDs) $MX_2$ ($M$ = Ti, Nb, Ta; $X$ = S, Se, Te) exhibit a rich set of charge density wave (CDW) orders, which usually coexist and/or compete with superconductivity. The mechanisms of CDWs and…
Recent advancements have established self-intercalation as a powerful technique for manipulating quantum material properties, with precisely controllable intercalation concentrations. Given the inherently rich phase diagrams of transition…
The layered transition metal dichalcogenide, TaSe2, exhibits rich electronic phenomena across its polymorphs, 1T, 2H, and 3R, largely driven by differences in atomic coordination and c-axis stacking. In the 1T phase, octahedral coordination…
Metallic transition metal dichalcogenides (TMDs), consisting of H-NbSe$_2$, H-NbS$_2$, H-TaSe$_2$ and H-TaS$_2$, remain superconducting down to a thickness of a single layer. In these materials, thickness affects a variety of properties,…
The weak van der Waals interlayer interactions in the transition metal dichalcogenide (TMD) materials have created a rich platform to study their exotic electronic properties through chemical doping or physical gating techniques. We…
The semimetallic or semiconducting nature of the transition metal dichalcogenide 1$T$-TiSe$_2$ remains under debate after many decades mainly due to the fluctuating nature of its 2 $\times$ 2 $\times$ 2 charge-density-wave (CDW) phase at…
Recent experimental advances in atomically thin transition metal dichalcogenide (TMD) metals have unveiled a range of interesting phenomena including the coexistence of charge-density-wave (CDW) order and superconductivity down to the…
The exact microscopic origin, symmetry, and thermal melting mechanism of the charge density wave (CDW) phase in TiSe$_{2}$ remain a subject of intense debate, particularly regarding the presence of chiral structural order and a multi-step…
A charge density wave (CDW) of a nonzero ordering vector $\mathbf{q}$ couple electronic states at $\mathbf{k}$ and $\mathbf{k}+\mathbf{q}$ statically, giving rise to a reduced Brillouin zone (RBZ) due to the band folding effect. Its…