Atomic-scale strain manipulation of a charge density wave

Possible charge ordering and anomalous transport in graphene/graphene quantum dot heterostructure

Observations of superconductivity and charge density waves (CDW) in graphene have been elusive thus far due to weak electron-phonon coupling (EPC) interactions. Here, we report a unique observation of anomalous transport and multiple charge ordering phases at high temperatures (T1∼213K,T2∼325K) in a 0D-2D van der Waals (vdW) heterostructure comprising of single layer graphene (SLG) and functionalized (amine) graphene quantum dots (GQD). The presence of functionalized GQD contributed to charge transfer with shifting of the Dirac point ∼ 0.05 eV above the Fermi level (ab initio   simulations) and carrier densityn∼-0.3×1012 cm-2confirming p-doping in SLG and two-fold increase in EPC interaction was achieved. Moreover, we elucidate the interplay between electron-electron and electron-phonon interactions to substantiate high temperature EPC driven charge ordering in the heterostructure through analyses of magnetotransport and weak anti-localization (WAL) framework. Our results provide impetus to investigate strongly correlated phenomena such as CDW and superconducting phase transitions in novel graphene based heterostructures.

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.

Charge instability of topological Fermi arcs in chiral crystal CoSi

Topological boundary states emerged at the spatial boundary between topological non-trivial and trivial phases, are usually gapless, or commonly referred as metallic states. For example, the surface state of a topological insulator is a gapless Dirac state. These metallic topological boundary states are typically well described by non-interacting fermions. However, the behavior of topological boundary states with significant electron-electron interactions, which could turn the gapless boundary states into gapped ordered states, e.g., density wave states or superconducting states, is of great interest theoretically, but is still lacking evidence experimentally. Here, we report the observation of incommensurable charge density wave (CDW) formed on the topological boundary states driven by the electron-electron interactions on the (001) surface of CoSi. The wavevector of CDW varies as the temperature changes, which coincides with the evolution of topological surface Fermi arcs with temperature. The orientation of the CDW phase is determined by the chirality of the Fermi arcs, which indicates a direct association between CDW and Fermi arcs. Our finding will stimulate the search of more interactions-driven ordered states, such as superconductivity and magnetism, on the boundaries of topological materials.

Tunable biaxial strain device for low-dimensional materials

Strain is attracting much interest as a mean to tune the properties of thin exfoliated two-dimensional materials and their heterostructures. Numerous devices to apply tunable uniaxial strain are proposed in the literature, but only few for biaxial strain, often with a trade-off between maximum strain and uniformity, reversibility, and device size. We present a compact device that allows for the controlled application of uniform in-plane biaxial strain, with maximum deformation and uniformity comparable to those found in much larger devices. Its performance and strain uniformity over the sample area are modeled using finite element analysis and demonstrated by measuring the response of exfoliated 2H-MoS₂ to strain by Raman spectroscopy.

Moiré modulation of charge density waves

Here we investigate how charge density waves (CDWs), inherent to a monolayer, are effected by creating twisted van der Waals structures. Homobilayers of metallic transition metal dichalcogenides (TMDs), at small twist angles where there is significant atomic reconstruction, are utilised as an example to investigate the interplay between the moiré domain structure and CDWs of different periods. For3×3CDWs, there is no geometric constraint to prevent the CDWs from propagating throughout the moiré structure. Whereas for2×2CDWs, to ensure the CDWs in each layer have the most favourable interactions in the domains, the CDW phase must be destroyed in the connecting domain walls. For3×3CDWs with twist angles close to 180^∘, moiré-scale triangular structures can form; while close to 0^∘, moiré-scale dimer domains occur. The star-of-David CDW (13×13) is found to host CDWs in the domains only, since there is one low energy stacking configuration, similar to the2×2CDWs. These predictions are offered for experimental verification in twisted bilayer metallic TMDs which host CDWs, and we hope this will stimulate further research on the interplay between the moiré superlattice and CDW phases intrinsic to the comprising 2D materials.

Chirality locking charge density waves in a chiral crystal

In Weyl semimetals, charge density wave (CDW) order can spontaneously break the chiral symmetry, gap out the Weyl nodes, and drive the material into the axion insulating phase. Investigations have however been limited since CDWs are rarely seen in Weyl semimetals. Here, using scanning tunneling microscopy/spectroscopy (STM/S), we report the discovery of a novel unidirectional CDW order on the (001) surface of chiral crystal CoSi - a unique Weyl semimetal with unconventional chiral fermions. The CDW is incommensurate with both lattice momentum and crystalline symmetry directions, and exhibits an intra unit cell π phase shift in the layer stacking direction. The tunneling spectrum shows a particle-hole asymmetric V-shaped energy gap around the Fermi level that modulates spatially with the CDW wave vector. Combined with first-principle calculations, we identify that the CDW is locked to the crystal chirality and is related by a mirror reflection between the two enantiomers of the chiral crystal. Our findings reveal a novel correlated topological quantum state in chiral CoSi crystals and raise the potential for exploring the unprecedented physical behaviors of unconventional chiral fermions.

Coexisting Charge-Ordered States with Distinct Driving Mechanisms in Monolayer VSe2

Thinning crystalline materials to two dimensions (2D) creates a rich playground for electronic phases, including charge, spin, superconducting, and topological order. Bulk materials hosting charge density waves (CDWs), when reduced to ultrathin films, have shown CDW enhancement and tunability. However, charge order confined to only 2D remains elusive. Here we report a distinct charge ordered state emerging in the monolayer limit of 1T-VSe₂. Systematic scanning tunneling microscopy experiments reveal that bilayer VSe₂ largely retains the bulk electronic structure, hosting a tridirectional CDW. However, monolayer VSe₂ ─consistently across distinct substrates─exhibits a dimensional crossover, hosting two CDWs with distinct wavelengths and transition temperatures. Electronic structure calculations reveal that while one CDW is bulk-like and arises from the well-known Peierls mechanism, the other is decidedly unconventional. The observed CDW-lattice decoupling and the emergence of a flat band suggest that the second CDW could arise from enhanced electron-electron interactions in the 2D limit. These findings establish monolayer-VSe₂ as a host of coexisting charge orders with distinct origins, and enable the tailoring of electronic phenomena via emergent interactions in 2D materials.

Proximity Effects on the Charge Density Wave Order and Superconductivity in Single-Layer NbSe2

Collective electronic states such as the charge density wave (CDW) order and superconductivity (SC) respond sensitively to external perturbations. Such sensitivity is dramatically enhanced in two dimensions (2D), where 2D materials hosting such electronic states are largely exposed to the environment. In this regard, the ineludible presence of supporting substrates triggers various proximity effects on 2D materials that may ultimately compromise the stability and properties of the electronic ground state. In this work, we investigate the impact of proximity effects on the CDW and superconducting states in single-layer (SL) NbSe₂ on four substrates of diverse nature, namely, bilayer graphene (BLG), SL-boron nitride (h-BN), Au(111), and bulk WSe₂. By combining low-temperature (340 mK) scanning tunneling microscopy/spectroscopy and angle-resolved photoemission spectroscopy, we compare the electronic structure of this prototypical 2D superconductor on each substrate. We find that, even when the electronic band structure of SL-NbSe₂ remains largely unaffected by the substrate except when placed on Au(111), where a charge transfer occurs, both the CDW and SC show disparate behaviors. On the insulating h-BN/Ir(111) substrate and the metallic BLG/SiC(0001) substrate, both the 3 × 3 CDW and superconducting phases persist in SL-NbSe₂ with very similar properties, which reveals the negligible impact of graphene on these electronic phases. In contrast, these collective electronic phases are severely weakened and even absent on the bulk insulating WSe₂ substrate and the metallic single-crystal Au(111) substrate. Our results provide valuable insights into the fragile stability of such electronic ground states in 2D materials.

Experimental and Theoretical Study of Possible Collective Electronic States in Exfoliable Re-Doped NbS2

Metallic transition-metal dichalcogenides (TMDs) are rich material systems in which the interplay between strong electron-electron and electron-phonon interactions often results in a variety of collective electronic states, such as charge density waves (CDWs) and superconductivity. While most metallic group V TMDs exhibit coexisting superconducting and CDW phases, 2H-NbS₂ stands out with no charge ordering. Further, due to strong interlayer interaction, the preparation of ultrathin samples of 2H-NbS₂ has been challenging, limiting the exploration of presumably rich quantum phenomena in reduced dimensionality. Here, we demonstrate experimentally and theoretically that light substitutional doping of NbS₂ with heavy atoms is an effective approach to modify both interlayer interaction and collective electronic states in NbS₂. Very low concentrations of Re dopants (<1%) make NbS₂ exfoliable (down to monolayer) while maintaining its 2H crystal structure and superconducting behavior. In addition, first-principles calculations suggest that Re dopants can stabilize some native CDW patterns that are not stable in pristine NbS₂.

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.

Topical review: recent progress of charge density waves in 2D transition metal dichalcogenide-based heterojunctions and their applications

Charge density wave (CDW) is an intriguing physical phenomenon especially found in two-dimensional (2D) layered systems such as transition-metal dichalcogenides (TMDs). The study of CDW is vital for understanding lattice modification, strongly correlated electronic behaviors, and other related physical properties. This paper gives a review of the recent studies on CDW emerging in 2D TMDs. First, a brief introduction and the main mechanisms of CDW are given. Second, the interplay between CDW patterns and the related unique electronic phenomena (superconductivity, spin, and Mottness) is elucidated. Then various manipulation methods such as doping, applying strain, local voltage pulse to induce the CDW change are discussed. Finally, examples of the potential application of devices based on CDW materials are given. We also discuss the current challenge and opportunities at the frontier in this research field.

Discovery of a Cooper-pair density wave state in a transition-metal dichalcogenide

Among the most intriguing of the many phases of cuprate superconductors is the so-called pair density wave (PDW) state. PDW is characterized by a spatially modulated density of Cooper pairs and can be detected with a scanning tunneling microscope equipped with a superconducting tip. Liu et al. used Josephson tunneling microscopy, modified for the task, to detect PDW in niobium diselenide, a superconductor with a layered hexagonal structure. The PDW state is expected to appear in other transition metal dichalcogenides as well.

Science , abd4607, this issue p. 1447

Tuning Molecular Superlattice by Charge-Density-Wave Patterns in Two-Dimensional Monolayer Crystals

Charge density wave (CDW) in two-dimensional (2D) crystals plays a vital role in tuning the interface structures and properties. However, how the CDW tunes the self-assembled molecular superlattice still remains unclear. In this study, we investigated the self-assembled manganese phthalocyanine (MnPc) molecular superlattice on single-layered 1T- and 2H-NbSe₂ crystals under regulation by distinct CDW patterns. We observe that, in low coverage, MnPc molecules preferentially adsorb on 2H-NbSe₂ compared to 1T-NbSe₂. With increasing coverage, MnPc can form a highly ordered superlattice on 2H-NbSe₂; however, it is randomly distributed on 1T-NbSe₂. We reveal a perfect geometric commensurability between the molecular superlattice and intrinsic CDW pattern in 2H-NbSe₂ and a poor commensurability for that of 1T-NbSe₂. We believe that the subtly different geometric commensurability dominates the different adsorption and arrangement of the molecular superlattices on 2D CDW patterns. Our study provides a pioneering approach for tuning the molecular superlattices using the CDW patterns.

Nanoscale decoupling of electronic nematicity and structural anisotropy in FeSe thin films

In a material prone to a nematic instability, anisotropic strain in principle provides a preferred symmetry-breaking direction for the electronic nematic state to follow. This is consistent with experimental observations, where electronic nematicity and structural anisotropy typically appear hand-in-hand. In this work, we discover that electronic nematicity can be locally decoupled from the underlying structural anisotropy in strain-engineered iron-selenide (FeSe) thin films. We use heteroepitaxial molecular beam epitaxy to grow FeSe with a nanoscale network of modulations that give rise to spatially varying strain. We map local anisotropic strain by analyzing scanning tunneling microscopy topographs, and visualize electronic nematic domains from concomitant spectroscopic maps. While the domains form so that the energy of nemato-elastic coupling is minimized, we observe distinct regions where electronic nematic ordering fails to flip direction, even though the underlying structural anisotropy is locally reversed. The findings point towards a nanometer-scale stiffness of the nematic order parameter.

Experimental observations and density functional simulations on the structural transition behavior of a two-dimensional transition-metal dichalcogenide

In this work, we show an obvious evidence of nondestructive Raman spectra for the structural transition, i.e., the existence of a charge density wave (CDW) in monolayer 2H-TaS₂, which can exhibit a much higher transition temperature than bulk and results in additional vibrational modes, indicating strong interactions with light. Furthermore, we reveal that the degenerate breath and wiggle modes of 2H-TaS₂ originated from the periodic lattice distortion can be probed using the optical methods. Since recently several light-tunable devices have been proposed based on the CDW phase transition of 1 T-TaS₂, our study and in particular, the theoretical results will be very helpful for understanding and designing electronic devices based on the CDW of 2H-TaS₂.

Charge density waves and degenerate modes in exfoliated monolayer 2H-TaS2

Charge density waves spontaneously breaking lattice symmetry through periodic lattice distortion, and electron-electron and electron-phonon inter-actions, can lead to a new type of electronic band structure. Bulk 2H-TaS2 is an archetypal transition metal dichalcogenide supporting charge density waves with a phase transition at 75 K. Here, it is shown that charge density waves can exist in exfoliated monolayer 2H-TaS2 and the transition temperature can reach 140 K, which is much higher than that in the bulk. The degenerate breathing and wiggle modes of 2H-TaS2 originating from the periodic lattice distortion are probed by optical methods. The results open an avenue to investigating charge density wave phases in two-dimensional transition metal dichalcogenides and will be helpful for understanding and designing devices based on charge density waves.

Exchange Interactions and Curie Temperature of Ce-Substituted SmCo5

A partial substitution such as Ce in SmCo 5 could be a brilliant way to improve the magnetic performance, because it will introduce strain in the structure and breaks the lattice symmetry in a way that enhances the contribution of the Co atoms to magnetocrystalline anisotropy. However, Ce substitutions, which are benefit to improve the magnetocrystalline anisotropy, are detrimental to enhance the Curie temperature ( T C ). With the requirements of wide operating temperature range of magnetic devices, it is important to quantitatively explore the relationship between the T C and ferromagnetic exchange energy. In this paper we show, based on mean-field approximation, artificial tensile strain in SmCo 5 induced by substitution leads to enhanced effective ferromagnetic exchange energy and T C , even though Ce atom itself reduces T C .