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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 metal dichalcogenides (TMDCs), studying the self-intercalated TMDCs can offer promising candidates for investigating the interplay between various orderings. This work focuses on fully intercalated bilayer TaSe$_2$ (Ta$_3$Se$_4$), which has recently been fabricated experimentally. By performing first-principles calculations, we demonstrate the suppression of an intrinsic $3\times3$ charge density wave (CDW) in parent TaSe$_2$ layers, and the emergence of $2\times 2$, $\sqrt{3} \times \sqrt{3}$, or the absence of a CDW in the intercalated layers, depending on the interlayer stacking orders and intercalation sites being occupied. Particularly, the $2\times 2$ CDW shows an increase in electronic states at the Fermi level compared to its non-CDW phase. This unusual behavior contrasts with that of typical CDW materials in TMDCs. Furthermore, superconductivity is preserved in these Ta$_3$Se$_4$ structures, with superconducting transition temperatures comparable to or substantially smaller than those of TaSe$_2$. Spin-orbit coupling is found to enhance the density of states at Fermi levels while simultaneously reducing the electron-phonon coupling matrix elements. These two competing effects result in varying impacts on superconductivity across different Ta$_3$Se$_4$ structures. Moreover, our calculations indicate that magnetic order is absent. Our study deepens the understanding of underlying physics in Ta$_3$Se$_4$, and provides experimentally feasible candidates for studying CDW, superconductivity, and their interplay., Comment: 10 pages, 7 figures

Recently, two-dimensional Nb$_2$C has garnered increasing attention due to its functional-group-dependent superconductivity, both experimentally and theoretically. In contrast to the halogen and chalcogen additives that have been the main focus of previous studies, we study the effect of lithium adsorption, which can also be incorporated during the synthesis of Nb$_2$C. Our computational analysis reveals a metal-to-superconductor transition in monolayer Nb$_2$C with a critical temperature ($T_{\mathrm{c}}$) of 22.1 K and a strong anisotropic superconducting gap distribution following the adsorption of lithium atoms. This emergent superconductivity is attributed to the increased electronic states at the Fermi energy, resulting from the contribution of Nb-$d$ orbitals and electron gas states induced by the low electronegativity of lithium. Furthermore, the application of tensile strain raises the $T_{\mathrm{c}}$ to 24 K, which is higher than that of most functional-group-modified Nb$_2$C systems. Our work deepens the understanding of electron-phonon coupling in layered Nb$_2$C, and provides new insights into achieving high critical temperature superconductivity with a strong anisotropic superconducting gap distribution in this system., Comment: 9 pages, 5 figures

Interlayer coupling can significantly influence the physical properties of layered transition metal compounds. The superconductivity in layered Mo$_2$C systems, belonging to the emergent family of MXene, has garnered considerable attention. However, the impact of interlayer coupling on superconductivity, and the anisotropic superconducting properties in these systems are not yet clear. By performing first-principles calculations of electron-phonon coupling and anisotropic superconducting properties, we show that the interlayer coupling in bilayer 1$T$-Mo$_2$C suppresses superconductivity, resulting in a significant drop in superconducting transition temperature ($T_{\mathrm{c}}$) from 4.2 $K$ in its monolayer form to nearly 0 $K$. By introducing lithium atoms into the interlayer space of the bilayer, the interlayer coupling can be effectively weakened, transforming the system into a two-gap superconductor with a $T_{\mathrm{c}}$ above 10 $K$. A 3\% tensile strain can further transform the system into a three-gap superconductor with a significantly enhanced $T_{\mathrm{c}}$ of approximately 24.7 $K$, which is very high in the Mo$_2$C related systems. The enhancement of the superconductivity induced by the strain is mainly due to the downshift of an energy band with a flat dispersion to the energy near the Fermi level. The in-plane vibrations of Mo atoms and the $d$-orbital electrons of Mo atoms are most important for the formation of the superconductivity. Our method can also be applied to multilayer Mo$_2$C systems. Given the successful synthesis of layered Mo$_2$C systems and the experimental realization of alkaline metal atom depositions, our work presents a practically feasible strategy for achieving high $T_{\mathrm{c}}$ and multigap superconductivity in layered Mo$_2$C., Comment: 9 pages, 7 figures

Recently, intercalation emerges as an effective way to manipulate ground-state properties and enrich quantum phase diagrams of layered transition metal dichalcogenides (TMDCs). In this work, we focus on fully Ta-intercalated bilayer 2$H$-TaS$_{2}$ with a stoichiometry of Ta$_{3}$S$_{4}$, which has recently been experimentally synthesized. Based on first-principles calculations, we computationally show the suppression of an intrinsic $3\times3$ charge-density wave (CDW) in the TaS$_{2}$ layer, and the emergence of a $2\times1$ CDW in intercalated Ta layer. The formation of the CDW in Ta$_{3}$S$_{4}$ is triggered by strong electron-phonon coupling (EPC) between the $d$-like orbitals of intercalated Ta atoms via the imaginary phonon modes at M point. A 2$\times$1 CDW structure is identified, featuring quasi-one-dimensional Ta chains, attributable to the competition between the CDW displacements associated with potential CDW vectors ($\boldsymbol{q}_{\text{CDW}}$s). Superconductivity is found to coexist with the 2$\times$1 CDW in Ta$_{3}$S$_{4}$, with an estimated superconducting transition temperature ($T_{\mathrm{c}}$) of 3.0 K, slightly higher than that of bilayer TaS$_{2}$. The Ta$_{3}$S$_{4}$ structures of non-CDW, 2$\times$1 CDW, and $2\times$2 CDW can be switched by strain. Our work enriches the phase diagram of TaS$_{2}$, offers a candidate material for studying the interplay between CDW and superconductivity, and highlights intercalation as an effective way to tune the physical properties of layered materials., Comment: 7 pages, 5 figures. Published as a Letter in PRB

Layered platinum tellurium (PtTe2) was recently synthesized with controllable layer numbers down to a monolayer limit. Using ab initio calculations based on anisotropic Midgal-Eliashberg formalism, we show that by rubidium (Rb) intercalation, weak superconductivity in bilayer PtTe2 can be significantly boosted with superconducting Tc = 8 K in the presence of spin-orbit coupling (SOC). The intercalant on one hand mediates the interlayer coupling and serves as an electron donor, leading to large density of states at Fermi energy. On the other hand, it increases the mass-enhancement parameter with electron-phonon coupling strength comparable to that of Pt. The potassium intercalated bilayer PtTe2 has a comparable Tc to the case of Rb intercalation. The relatively high Tc with SOC combined with experimental accessible crystal structures suggest that these superconductors are promising platforms to study the novel quantum physics associated with two-dimensional superconductivity, such as the recently proposed type-II Ising superconductivity., Comment: 7 pafges, 4 figures. Accepted by PRB(2021)

Despite growing interest in them, highly crystalline two-dimensional superconductors derived from exfoliated layered materials are few. Employing the anisotropic Migdal-Eliashberg formalism based on {\it ab initio} calculations, we find monolayer NiTe$_{2}$ to be an intrinsic superconductor with a $T_{\text c}\sim$5.7~K, although the bulk crystal is not known to superconduct. Remarkably, bilayer NiTe$_{2}$ intercalated with lithium is found to display two-gap superconductivity with a critical temperature $T_{\text{c}}\sim 11.3$~K and superconducting gap of $\sim$3.1~meV, arising from a synergy of electronic and phononic effects. The comparatively high $T_\text{c}$, substrate independence and proximity tunability will make these superconductors ideal platforms for exploring intriguing correlation effects and quantum criticality associated two-dimensional superconductivity.

Experimental signatures of charge density waves (CDW) in high-temperature superconductors have evoked much recent interest, yet an alternative interpretation has been theoretically raised based on electronic standing waves resulting from quasiparticles scattering off impurities or defects, also known as Friedel oscillations (FO). Indeed the two phenomena are similar and related, posing a challenge to their experimental differentiation. Here we report a resonant X-ray diffraction study of ZrTe$_3$, a model CDW material. Near the CDW transition, we observe two independent diffraction signatures that arise concomitantly, only to become clearly separated in momentum while developing very different correlation lengths in the well-ordered state. Anomalously slow dynamics of mesoscopic ordered nanoregions are further found near the transition temperature, in spite of the expected strong thermal fluctuations. These observations reveal that a spatially-modulated CDW phase emerges out of a uniform electronic fluid via a process that is promoted by self-amplifying FO, and identify a viable experimental route to distinguish CDW and FO., Comment: 6 pages, 4 figures; supplementary information available upon request

Monolayer 2H-NbSe2 has recently been shown to be a 2-dimensional superconductor, with a coexisting charge-density wave (CDW). As both phenomena are intimately related to electron-lattice interaction, a natural question is how superconductivity and CDW are interrelated through electron-phonon coupling (EPC), which is important to the understanding of 2-dimensional superconductivity. This work investigates the superconductivity of monolayer NbSe2 in CDW phase using the anisotropic Migdal-Eliashberg formalism based on first principles calculations. The mechanism of the competition between and coexistence of the superconductivity and CDW is studied in detail by analyzing EPC. It is found that the intra-pocket scattering is related to superconductivity, leading to almost constant value of superconducting gaps on parts of the Fermi surface. The inter-pocket scattering is found to be responsible for CDW, leading to partial or full bandgap on the remaining Fermi surface. Recent experiment indicates that there is transitioning from regular superconductivity in thin-film NbSe2 to two-gap superconductivity in the bulk, which is shown here to have its origin in the extent of Fermi surface gapping of K and K' pockets induced by CDW. Overall blue shifts of the phonons and sharp decrease of Eliashberg spectrum are found when the CDW forms., Comment: 12 pages, 13 figures in total. Accepted, Physical Review B (Rapid Communication) (2019)

Monolayer NbSe$_2$ has recently been shown to be a 2-dimensional superconductor, with a competing charge-density wave (CDW) order. This work investigates the electronic structure of monolayer NbSe$_2$ based on first principles calculations, focusing on charge and magnetic orders in connection to the superconductivity. It is found that decreased screening in the monolayer NbSe$_2$ with a perfect lattice exhibits magnetic instability, which is removed by the formation of CDW. Two energetically competitive but distinct $3\times3$ CDW structures are revealed computationally, which have a significant impact on the Fermi surface. The relations of the potential CDW phases with experimental structure and the coexisting superconductivity are discussed., Comment: 10 pages, 9 figures, 2 tables including supplemental materials

Two-dimensional (2D) transition metal dichalcogenides (TMDs) have a range of unique physics properties and could be used in the development of electronics, photonics, spintronics and quantum computing devices. The mechanical exfoliation technique of micro-size TMD flakes has attracted particular interest due to its simplicity and cost effectiveness. However, for most applications, large area and high quality films are preferred. Furthermore, when the thickness of crystalline films is down to the 2D limit (monolayer), exotic properties can be expected due to the quantum confinement and symmetry breaking. In this paper, we have successfully prepared macro-size atomically flat monolayer NbSe2 films on bilayer graphene terminated surface of 6H-SiC(0001) substrates by molecular beam epitaxy (MBE) method. The films exhibit an onset superconducting critical transition temperature above 6 K, 2 times higher than that of mechanical exfoliated NbSe2 flakes. Simultaneously, the transport measurements at high magnetic fields reveal that the parallel characteristic field Bc// is at least 4.5 times higher than the paramagnetic limiting field, consistent with Zeeman-protected Ising superconductivity mechanism. Besides, by ultralow temperature electrical transport measurements, the monolayer NbSe2 film shows the signature of quantum Griffiths singularity when approaching the zero-temperature quantum critical point.

Quantum spin Hall (QSH) materials are two-dimensional systems exhibiting insulating bulk and helical edge states simultaneously. A QSH insulator processes topologically non-trivial edge states protected by time-reversal symmetry, so that electrons can propagate unscattered. Realization of such topological phases enables promising applications in spintronics, dissipationless transport and quantum computations. Presently, realization of such QSH-based devices are limited to complicated heterostructures. Monolayer 1T'-WTe2 was predicted to be semimetallic QSH materials, though with a negative band gap. The quasi-particle spectrum obtained using hybrid functional approach shows directly that the quantum spin Hall gap is positive for monolayer 1T'-WTe2. Optical measurement shows a systematic increase in the interband relaxation time with decreasing number of layers, whereas transport measurement reveals Schottcky barrier in ultrathin samples, which is absent for thicker samples. These three independent pieces of evidence indicate that monolayer 1T'-WTe2 is likely a truly 2-dimensional quantum spin Hall insulator., Comment: 21 pages, 6 figures; Has been published online by Advanced Materials (2016)

Charge-density-wave (CDW) order has long been interpreted as arising from a Fermi-surface instability in the parent metallic phase. While phonon-electron coupling has been suggested to influence the formation of CDW order in quasi-two-dimensional (quasi-2D) systems, the presumed dominant importance of Fermi-surface nesting remains largely unquestioned in quasi-1D systems. Here we show that phonon-electron coupling is also important for the CDW formation in a model quasi-1D system ZrTe$_3$. Our joint experimental and computational study reveals that particular lattice vibrational patterns possess exceedingly strong coupling to the conduction electrons, and are directly linked to the lattice distortions associated with the CDW order. The dependence of the coupling matrix elements on electron momentum further dictates the opening of (partial) electronic gaps in the CDW phase. Since lattice distortions and electronic gaps are the defining signatures of CDW order, our result demonstrates that the conventional wisdom based on Fermi-surface geometry needs to be substantially supplemented by phonon-electron coupling even in the simplest quasi-1D case. As prerequisites for the CDW formation, the highly anisotropic electronic structure and strong phonon-electron coupling in ZrTe$_3$ give rise to a distinct Raman scattering effect, namely, measured phonon linewidths depend on the direction of momentum transfer in the scattering process., Comment: 23 pages, 9 figures