Topological Landscape of Competing Charge Density Waves in 2H-NbSe_{2}

Visualization of Alternating Triangular Domains of Charge Density Waves in 2H-NbSe_{2} by Scanning Tunneling Microscopy

The charge density wave (CDW) state of 2H-NbSe_{2} features commensurate domains separated by domain boundaries accompanied by phase slips known as discommensurations. We have unambiguously visualized the structure of CDW domains using a displacement-field measurement algorithm on a scanning tunneling microscopy image. Each CDW domain is delimited by three vertices and three edges of discommensurations and is designated by a triplet of integers whose sum identifies the types of commensurate structure. The observed structure is consistent with the alternating triangular tiling pattern predicted by a phenomenological Landau theory. The domain shape is affected by crystal defects and also by topological defects in the CDW phase factor. Our results provide a foundation for a complete understanding of the CDW state and its relation to the superconducting state.

Dual Higgs modes entangled into a soliton lattice in CuTe

Recently discovered Higgs particle is a key element in the standard model of elementary particles and its analogue in materials, massive Higgs mode, has elucidated intriguing collective phenomena in a wide range of materials with spontaneous symmetry breaking such as antiferromagnets, cold atoms, superconductors, superfluids, and charge density waves (CDW). As a straightforward extension beyond the standard model, multiple Higgs particles have been considered theoretically but not yet for Higgs modes. Here, we report the real-space observations, which suggest two Higgs modes coupled together with a soliton lattice in a solid. Our scanning tunneling microscopy reveals the 1D CDW state of an anisotropic transition metal monochalcogenide crystal CuTe is composed of two distinct but degenerate CDW structures by the layer inversion symmetry broken. More importantly, the amplitudes of each CDW structure oscillate in an out-of-phase fashion to result in a regular array of alternating domains with repeating phase-shift domain walls. This unusual finding is explained by the extra degeneracy in CDWs within the standard Landau theory of the free energy. The multiple and entangled Higgs modes demonstrate how novel collective modes can emerge in systems with distinct symmetries broken simultaneously.

Interplay of the charge density wave transition with topological and superconducting properties

Exotic phenomena due to the interplay of different quantum orders have been observed and the study of these phenomena has emerged as a new frontier in condensed matter research, especially in the two-dimensional limit. Here, we report the coexistence of charge density waves (CDWs), superconductivity, and nontrivial topology in monolayer 1H-MSe2 (M = Nb, Ta) triggered by momentum-dependent electron-phonon coupling through electron doping. At a critical electron doping concentration, new 2 × 2 CDW phases emerge with nontrivial topology, Dirac cones, and van Hove singularities. Interestingly, these 2 × 2 CDW phases are also superconducting. Our findings not only reveal a route towards realizing nontrivial electronic characters by CDW engineering, but also provide an exciting platform to modulate different quantum states at the confluence of CDWs, superconductivity, nontrivial topology, and electron-phonon coupling.

Alternative Structure Model of Correlated Charge Density Wave in Monolayer 1T-Nb(Ta)Se2

The putative Mott charge density wave (CDW) phases of monolayer 1T-NbSe2 and 1T-TaSe2 have attracted a lot of recent interest due to the unexpected orbital texture of their Mott-Hubbard states and the superstructure related to an exotic possibility of a quantum spin liquid with a spinon Fermi surface. The origins of the orbital texture and the superstructure have been, however, elusive. We find by using density functional theory calculations that these CDW phases can have an alternative metastable structure, an anion (Se) centered cluster, in contrast to the prevailing model of a cation (Nb or Ta) centered David star cluster. This structure can be stabilized by the charge transfer from the bilayer graphene/SiC substrate used commonly in the experiments. The anion-centered structure has a similar electronic band structure of a charge transfer insulator to that of DS clusters but naturally explains the orbital texture of the upper Hubbard band from simply its atomic structure. Moreover, this band structure exhibits a Fermi surface nesting to possibly break the symmetry spontaneously into a 3 × 3 -R30° superstructure observed experimentally. The resulting ground state of the superstructure is shown to be a trivial band insulator, in contrast to exotic proposals. This result emphasizes the huge structural flexibility of these heteroexpitaxial monolayers, for which careful studies on atomic structures and interactions with substrates are highly requested.

Nuclear Quantum Effects on the Charge-Density Wave Transition in NbX2 (X = S, Se)

Understanding the origin of charge-density wave (CDW) instability is important for manipulating novel collective electronic states. Many layered transition metal dichalcogenides (TMDs) share similarity in the structural and electronic instability, giving rise to diverse CDW phases and superconductivity. It is still puzzling that even isostructural and isoelectronic TMDs show distinct CDW features. For instance, bulk NbSe₂ exhibits CDW order at low temperature, while bulk NbS₂ displays no CDW instability. The CDW transitions in single-layer NbS₂ and NbSe₂ are also different. In the classic limit, we investigate the electron correlation effects on the dimensionality dependence of the CDW ordering. By performing ab initio path integral molecular dynamics simulations and comparative analyses, we further revealed significant nuclear quantum effects in these systems. Specifically, the quantum motion of sulfur anions significantly reduces the CDW transition temperature in both bulk and single-layer NbS₂, resulting in distinct CDW features in the NbS₂ and NbSe₂ systems.

Confinement-Engineered Superconductor to Correlated-Insulator Transition in a van der Waals Monolayer

Transition metal dichalcogenides (TMDC) are a rich family of two-dimensional materials displaying a multitude of different quantum ground states. In particular, d³ TMDCs are paradigmatic materials hosting a variety of symmetry broken states, including charge density waves, superconductivity, and magnetism. Among this family, NbSe₂ is one of the best-studied superconducting materials down to the monolayer limit. Despite its superconducting nature, a variety of results point toward strong electronic repulsions in NbSe₂. Here, we control the strength of the interactions experimentally via quantum confinement and use low-temperature scanning tunneling microscopy (STM) and spectroscopy (STS) to demonstrate that NbSe₂ is in close proximity to a correlated insulating state. This reveals the coexistence of competing interactions in NbSe₂, creating a transition from a superconducting to an insulating quantum correlated state by confinement-controlled interactions. Our results demonstrate the dramatic role of interactions in NbSe₂, establishing NbSe₂ as a correlated superconductor with competing interactions.

Multiband charge density wave exposed in a transition metal dichalcogenide

In the presence of multiple bands, well-known electronic instabilities may acquire new complexity. While multiband superconductivity is the subject of extensive studies, the possibility of multiband charge density waves (CDWs) has been largely ignored so far. Here, combining energy dependent scanning tunnelling microscopy (STM) topography with a simple model of the charge modulations and a self-consistent calculation of the CDW gap, we find evidence for a multiband CDW in 2H-NbSe₂. This CDW not only involves the opening of a gap on the inner band around the K-point, but also on the outer band. This leads to spatially out-of-phase charge modulations from electrons on these two bands, which we detect through a characteristic energy dependence of the CDW contrast in STM images.

While multiband superconductivity is the subject of extensive studies, the possibility of multiband charge density waves (CDW) remains elusive. Here, the authors report evidence of gap opening on both inner and outer bands by a CDW state in 2H-NbSe₂, suggesting a possible multiband CDW.

Machine-Intelligence-Driven High-Throughput Prediction of 2D Charge Density Wave Phases

Charge density wave (CDW) materials are an important subclass of two-dimensional materials exhibiting significant resistivity switching with the application of external energy. However, the scarcity of such materials impedes their practical applications in nanoelectronics. Here we combine a first-principles-based structure-searching technique and unsupervised machine learning to develop a fully automated high-throughput computational framework, which identifies CDW phases from a unit cell with inherited Kohn anomaly. The proposed methodology not only rediscovers the known CDW phases but also predicts a host of easily exfoliable CDW materials (30 materials and 114 phases) along with associated electronic structures. Among many promising candidates, we pay special attention to ZrTiSe₄ and conduct a comprehensive analysis to gain insight into the Fermi surface nesting, which causes significant semiconducting gap opening in its CDW phase. Our findings could provide useful guidelines for experimentalists.

Negative resistance state in superconducting NbSe2 induced by surface acoustic waves

We report a negative resistance, namely, a voltage drop along the opposite direction of a current flow, in the superconducting gap of NbSe₂ thin films under the irradiation of surface acoustic waves (SAWs). The amplitude of the negative resistance becomes larger by increasing the SAW power and decreasing temperature. As one possible scenario, we propose that soliton-antisoliton pairs in the charge density wave of NbSe₂ modulated by the SAW serve as a time-dependent capacitance in the superconducting state, leading to the dc negative resistance. The present experimental result would provide a previously unexplored way to examine nonequilibrium manipulation of the superconductivity.

Defect-Selective Charge-Density-Wave Condensation in 2H-NbSe_{2}

Defects have been known to substantially affect quantum states of materials including charge density wave (CDW). However, the microscopic mechanism of the influence of defects is often elusive due partly to the lack of atomic scale characterization of defects themselves. We investigate native defects of a prototypical CDW material 2H-NbSe_{2} and their microscopic interaction with CDW. Three prevailing types of atomic scale defects are classified by scanning tunneling microscope, and their atomic structures are identified by density functional theory calculations as Se vacancies and Nb intercalants. Above the transition temperature, two distinct CDW structures are found to be induced selectively by different types of defects. This intriguing phenomenon is explained by competing CDW ground states and local lattice strain fields induced by defects, providing a clear microscopic mechanism of the defect-CDW interaction.

Atomic-Scale Observation of Topological Vortices in the Incommensurate Charge Density Wave of 2H-TaSe2

It has been only recently realized that topological vortices associated with structural distortions or ordered spins are rather common in numerous materials where long-range interactions are not dominant. Incommensurate modulations that frequently occur in charge density wave (CDW) materials are often understood in terms of discommensurations with a periodic phase shift. The accumulation of a one-dimensional (1D) phase shift can result in, for example, CDW dislocations in 2H-TaSe₂ with incommensurate CDW (I-CDW). Since any atomic-scale experimental investigation of CDW dislocations in 2H-TaSe₂ has been lacking, we have performed the atomic-scale observation of 2H-TaSe₂ with I-CDW, stabilized with Pd intercalation or strain, with scanning probe microscopy, and unveiled the existence of topological Z₆ or Z₄ vortices with topologically protected 2D winding movements of atomic displacement vectors. The discovery opens the ubiquitous nature of topological vortex domains and a new avenue to explore new facets of various incommensurate modulations or discommensurations.

Coupled Sublattice Melting and Charge-Order Transition in Two Dimensions

Two-dimensional melting is one of the most fascinating and poorly understood phase transitions in nature. Theoretical investigations often point to a two-step melting scenario involving unbinding of topological defects at two distinct temperatures. Here, we report on a novel melting transition of a charge-ordered K-Sn alloy monolayer on a silicon substrate. Melting starts with short-range positional fluctuations in the K sublattice while maintaining long-range order, followed by longer-range K diffusion over small domains, and ultimately resulting in a molten sublattice. Concomitantly, the charge order of the Sn host lattice collapses in a multistep process with both displacive and order-disorder transition characteristics. Our combined experimental and theoretical analysis provides a rare insight into the atomistic processes of a multistep melting transition of a two-dimensional materials system.

Yu-Shiba-Rusinov States in the Charge-Density Modulated Superconductor NbSe2

NbSe₂ is a remarkable superconductor in which charge-density order coexists with pairing correlations at low temperatures. Here, we study the interplay of magnetic adatoms and their Yu-Shiba-Rusinov (YSR) bound states with the charge density order. Exploiting the incommensurate nature of the charge-density wave (CDW), our measurements provide a thorough picture of how the CDW affects both the energies and the wave functions of the YSR states. Key features of the dependence of the YSR states on adsorption site relative to the CDW are explained by model calculations. Several properties make NbSe₂ a promising substrate for realizing topological nanostructures. Our results will be important in designing such systems.