Single layers of transition metal dichalcogenides are of interest for emergent properties; an often-neglected issue is substrate effects. Our experiments show that the charge density wave in a single-layer TiTe_{2} grown on PtTe_{2} films is strongly suppressed by increasing the PtTe_{2} substrate thickness. Given that the interfacial bonding remains of the weak incommensurate van der Waals type, the observed changes are correlated with a thickness-dependent metallicity transformation in the PtTe_{2} substrate. The results illustrate the crucial role of the substrate in single-layer physics.

Collective phenomena in solids can be sensitive to the dimensionality of the system; a case of special interest is VSe2, which shows a (7×3) charge density wave (CDW) in the single layer with threefold symmetry in the normal phase spontaneously broken, in contrast to the (4×4) in-plane CDW in the bulk. Angle-resolved photoemission spectroscopy (ARPES) from VSe2 ranging from a single layer to the bulk reveals the evolution of the electronic structure including the Fermi surface contours and the CDW gap. At a thickness of two layers, the ARPES maps are already nearly bulklike, but the transition temperature TC for the (4×4) CDW is much higher than the bulk value of 110 K. These results can be understood as due to dimensional crossover of phonon instability driven by a competition of nesting vectors. In this letter, we provide key insights into the CDW mechanisms and offer a perspective in the search and control of emergent phases in quantum materials.

Single layers of transition metal dichalcogenides (TMDCs) are excellent candidates for electronic applications beyond the graphene platform; many of them exhibit novel properties including charge density waves (CDWs) and magnetic ordering. CDWs in these single layers are generally a planar projection of the corresponding bulk CDWs because of the quasi-two-dimensional nature of TMDCs; a different CDW symmetry is unexpected. We report herein the successful creation of pristine single-layer VSe_{2}, which shows a (sqrt[7]×sqrt[3]) CDW in contrast to the (4×4) CDW for the layers in bulk VSe_{2}. Angle-resolved photoemission spectroscopy from the single layer shows a sizable (sqrt[7]×sqrt[3]) CDW gap of ∼100  meV at the zone boundary, a 220 K CDW transition temperature twice the bulk value, and no ferromagnetic exchange splitting as predicted by theory. This robust CDW with an exotic broken symmetry as the ground state is explained via a first-principles analysis. The results illustrate a unique CDW phenomenon in the two-dimensional limit.

A van der Waals bonded moiré bilayer formed by sequential growth of TiSe₂ and TiTe₂ monolayers exhibits emergent electronic structure as evidenced by angle-resolved photoemission band mapping. The two monolayers adopt the same lattice orientation but incommensurate lattice constants. Despite the lack of translational symmetry, sharp dispersive bands are observed. The dispersion relations appear distinct from those for the component monolayers alone. Theoretical calculations illustrate the formation of composite bands by coherent electronic coupling despite the weak interlayer bonding, which leads to band renormalization and energy shifts.

Charge density wave (CDW) formation, a key physics issue for materials, arises from interactions among electrons and phonons that can also lead to superconductivity and other competing or entangled phases. The prototypical system TiSe₂, with a particularly simple (2 × 2 × 2) transition and no Kohn anomalies caused by electron-phonon coupling, is a fascinating but unsolved case after decades of research. Our angle-resolved photoemission measurements of the band structure as a function of temperature, aided by first-principles calculations, reveal a hitherto undetected but crucial feature: a (2 × 2) electronic order in each layer sets in at ~232 K before the widely recognized three-dimensional structural order at ~205 K. The dimensional crossover, likely a generic feature of such layered materials, involves renormalization of different band gaps in two stages.

Charge density wave (CDW) formation in solids is a critical phenomenon involving the collective reorganization of the electrons and atoms in the system into a wave structure, and it is expected to be sensitive to the geometric constraint of the system at the nanoscale. Here, we study the CDW transition in TiSe₂, a quasi-two-dimensional layered material, to determine the effects of quantum confinement and changing dimensions in films ranging from a single layer to multilayers. Of key interest is the characteristic length scale for the transformation from a two-dimensional case to the three-dimensional limit. Angle-resolved photoemission spectroscopy (ARPES) measurements of films with thicknesses up to six layers reveal substantial variations in the energy structure of discrete quantum well states; however, the temperature-dependent band gap renormalization converges at just three layers. The results indicate a layer-dependent mixture of two transition temperatures and a very-short-range CDW interaction within a three-dimensional framework.

A single molecular layer of titanium diselenide (TiSe2) is a promising material for advanced electronics beyond graphene-a strong focus of current research. Such molecular layers are at the quantum limit of device miniaturization and can show enhanced electronic effects not realizable in thick films. We show that single-layer TiSe2 exhibits a charge density wave (CDW) transition at critical temperature TC=232±5 K, which is higher than the bulk TC=200±5 K. Angle-resolved photoemission spectroscopy measurements reveal a small absolute bandgap at room temperature, which grows wider with decreasing temperature T below TC in conjunction with the emergence of (2 × 2) ordering. The results are rationalized in terms of first-principles calculations, symmetry breaking and phonon entropy effects. The observed Bardeen-Cooper-Schrieffer (BCS) behaviour of the gap implies a mean-field CDW order in the single layer and an anisotropic CDW order in the bulk.

Two-dimensional (2D) topological insulators (TIs) are promising platforms for low-dissipation spintronic devices based on the quantum-spin-Hall (QSH) effect, but experimental realization of such systems with a large band gap suitable for room-temperature applications has proven difficult. Here, we report the successful growth on bilayer graphene of a quasi-freestanding WSe₂ single layer with the 1T' structure that does not exist in the bulk form of WSe₂. Using angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy/spectroscopy (STM/STS), we observe a gap of 129 meV in the 1T' layer and an in-gap edge state located near the layer boundary. The system's 2D TI characters are confirmed by first-principles calculations. The observed gap diminishes with doping by Rb adsorption, ultimately leading to an insulator-semimetal transition. The discovery of this large-gap 2D TI with a tunable band gap opens up opportunities for developing advanced nanoscale systems and quantum devices.

Platinum ditelluride (PtTe_{2}), a type-II Dirac semimetal, remains semimetallic in ultrathin films down to just two triatomic layers (TLs) with a negative gap of -0.36  eV. Further reduction of the film thickness to a single TL induces a Lifshitz electronic transition to a semiconductor with a large positive gap of +0.79  eV. This transition is evidenced by experimental band structure mapping of films prepared by layer-resolved molecular beam epitaxy, and by comparing the data to first-principles calculations using a hybrid functional. The results demonstrate a novel electronic transition at the two-dimensional limit through film thickness control.

Nickel ditelluride (NiTe2), a recently discovered Type-II Dirac semimetal with topological Dirac fermions near the Fermi energy, is expected to exhibit strong thickness-mediated electronic tunability and intrinsic two-gap superconductivity in the single-layer limit. Realizing such intriguing phenomena requires the fabrication of ultrathin NiTe2 films and an understanding of the underlying physics that is still under debate. By conducting experimental band mappings of ultrathin films prepared with molecular beam epitaxy, we reveal spectroscopic evidence for the dimensionality crossover of single-crystalline ultrathin NiTe2 films as a function of film thickness. As the film thickness increases from one to five layers, the gap in the conical topological surface states closes. Comparisons of experimental to first-principles results also highlight difficulties in fabricating atomically smooth single-layer NiTe2 films. Our results not only provide further impetus for studying emergent phenomena in NiTe2 but also underscore the limitations of fabricating NiTe2 films for device applications.