Charge order from orbital-dependent coupling evidenced by NbSe2

Charge density waves in two-dimensional transition metal dichalcogenides

Charge density wave (CDW is one of the most ubiquitous electronic orders in quantum materials. While the essential ingredients of CDW order have been extensively studied, a comprehensive microscopic understanding is yet to be reached. Recent research efforts on the CDW phenomena in two-dimensional (2D) materials provide a new pathway toward a deeper understanding of its complexity. This review provides an overview of the CDW orders in 2D with atomically thin transition metal dichalcogenides (TMDCs) as the materials platform. We mainly focus on the electronic structure investigations on the epitaxially grown TMDC samples with angle-resolved photoemission spectroscopy and scanning tunneling microscopy/spectroscopy as complementary experimental tools. We discuss the possible origins of the 2D CDW, novel quantum states coexisting with them, and exotic types of charge orders that can only be realized in the 2D limit.

Structural approach to charge density waves in low-dimensional systems: electronic instability and chemical bonding

The charge density wave (CDW) instability, usually occurring in low-dimensional metals, has been a topic of interest for longtime. However, some very fundamental aspects of the mechanism remain unclear. Recently, a plethora of new CDW materials, a substantial fraction of which is two-dimensional or even three-dimensional, has been prepared and characterised as bulk and/or single-layers. As a result, the need for revisiting the primary mechanism of the instability, based on the electron-hole instability established more than 50 years ago for quasi-one-dimensional (quasi-1D) conductors, has clearly emerged. In this work, we consider a large number of CDW materials to revisit the main concepts used in understanding the CDW instability, and emphasise the key role of the momentum dependent electron-phonon coupling in linking electronic and structural degrees of freedom. We argue that for quasi-1D systems, earlier weak coupling theories work appropriately and the energy gain due to the CDW and the concomitant periodic lattice distortion (PLD) remains primarily due to a Fermi surface nesting mechanism. However, for materials with higher dimensionality, intermediate and strong coupling regimes are generally at work and the modification of the chemical bonding network by the PLD is at the heart of the instability. We emphasise the need for a microscopic approach blending condensed matter physics concepts and state-of-the-art first-principles calculations with quite fundamental chemical bonding ideas in understanding the CDW phenomenon in these materials.

Precursor region with full phonon softening above the charge-density-wave phase transition in 2H-TaSe2

Research on charge-density-wave (CDW) ordered transition-metal dichalcogenides continues to unravel new states of quantum matter correlated to the intertwined lattice and electronic degrees of freedom. Here, we report an inelastic x-ray scattering investigation of the lattice dynamics of the canonical CDW compound 2H-TaSe2 complemented by angle-resolved photoemission spectroscopy and density functional perturbation theory. Our results rule out the formation of a central-peak without full phonon softening for the CDW transition in 2H-TaSe2 and provide evidence for a novel precursor region above the CDW transition temperature TCDW, which is characterized by an overdamped phonon mode and not detectable in our photoemission experiments. Thus, 2H-TaSe2 exhibits structural before electronic static order and emphasizes the important lattice contribution to CDW transitions. Our ab-initio calculations explain the interplay of electron-phonon coupling and Fermi surface topology triggering the CDW phase transition and predict that the CDW soft phonon mode promotes emergent superconductivity near the pressure-driven CDW quantum critical point.

Softening of a flat phonon mode in the kagome ScV6Sn6

Geometrically frustrated kagome lattices are raising as novel platforms to engineer correlated topological electron flat bands that are prominent to electronic instabilities. Here, we demonstrate a phonon softening at the kz = π plane in ScV6Sn6. The low energy longitudinal phonon collapses at ~98 K and q = [Formula: see text] due to the electron-phonon interaction, without the emergence of long-range charge order which sets in at a different propagation vector qCDW = [Formula: see text]. Theoretical calculations corroborate the experimental finding to indicate that the leading instability is located at [Formula: see text] of a rather flat mode. We relate the phonon renormalization to the orbital-resolved susceptibility of the trigonal Sn atoms and explain the approximately flat phonon dispersion. Our data report the first example of the collapse of a kagome bosonic mode and promote the 166 compounds of kagomes as primary candidates to explore correlated flat phonon-topological flat electron physics.

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.

Soft-Phonon and Charge-Density-Wave Formation in Nematic BaNi_{2}As_{2}

We use diffuse and inelastic x-ray scattering to study the formation of an incommensurate charge-density-wave (I-CDW) in BaNi_{2}As_{2}, a candidate system for charge-driven electronic nematicity. Intense diffuse scattering is observed around the modulation vector of the I-CDW, Q_{I-CDW}. It is already visible at room temperature and collapses into superstructure reflections in the long-range ordered state where a small orthorhombic distortion occurs. A clear dip in the dispersion of a low-energy transverse optical phonon mode is observed around Q_{I-CDW}. The phonon continuously softens upon cooling, ultimately driving the transition to the I-CDW state. The transverse character of the soft-phonon branch elucidates the complex pattern of the I-CDW satellites observed in the current and earlier studies and settles the debated unidirectional nature of the I-CDW. The phonon instability and its reciprocal space position are well captured by our ab initio calculations. These, however, indicate that neither Fermi surface nesting, nor enhanced momentum-dependent electron-phonon coupling can account for the I-CDW formation, demonstrating its unconventional nature.

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.

Electron-momentum dependence of electron-phonon coupling underlies dramatic phonon renormalization in YNi2B2C

Electron-phonon coupling, i.e., the scattering of lattice vibrations by electrons and vice versa, is ubiquitous in solids and can lead to emergent ground states such as superconductivity and charge-density wave order. A broad spectral phonon line shape is often interpreted as a marker of strong electron-phonon coupling associated with Fermi surface nesting, i.e., parallel sections of the Fermi surface connected by the phonon momentum. Alternatively broad phonons are known to arise from strong atomic lattice anharmonicity. Here, we show that strong phonon broadening can occur in the absence of both Fermi surface nesting and lattice anharmonicity, if electron-phonon coupling is strongly enhanced for specific values of electron-momentum, k. We use inelastic neutron scattering, soft x-ray angle-resolved photoemission spectroscopy measurements and ab-initio lattice dynamical and electronic band structure calculations to demonstrate this scenario in the highly anisotropic tetragonal electron-phonon superconductor YNi2B2C. This new scenario likely applies to a wide range of compounds.

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.

Basic aspects of the charge density wave instability of transition metal trichalcogenides NbSe3and monoclinic-TaS3

NbSe₃and monoclinic-TaS₃(m-TaS₃) are quasi-1D metals containing three different types of chains and undergoing two different charge density wave Peierls transitions atTP1andTP2associated with type III and type I chains, respectively. The nature of these transitions is discussed on the basis of first-principles DFT calculation of their Fermi surface (FS) and electron-hole response function. Because of the stronger inter-chain interactions, the FS and electron-hole response function are considerably more complex for NbSe₃thanm-TaS₃; however a common scenario can be put forward to rationalize the results. The intra-chain inter-band nesting processes dominate the strongest response for both type I and type III chains of the two compounds. Two well-defined maxima of the electron-hole response for NbSe₃are found with the (0a^*, 0c^*) and (1/2a^*, 1/2c^*) transverse components atTP1andTP2, respectively, whereas the second maximum is not observed form-TaS₃atTP2. Analysis of the different inter-chain coupling mechanisms leads to the conclusion that FS nesting effects are only relevant to set the transversea^*components in NbSe₃. The strongest inter-chain Coulomb coupling mechanism must be taken into account for the transverse coupling alongc^*in NbSe₃and along botha^*andc^*form-TaS₃. Phonon spectrum calculations reveal the formation of a giant 2k_FKohn anomaly form-TaS₃. All these results support a weak coupling scenario for the Peierls transition of transition metal trichalcogenides.

Angle, Spin, and Depth Resolved Photoelectron Spectroscopy on Quantum Materials

The role of X-ray based electron spectroscopies in determining chemical, electronic, and magnetic properties of solids has been well-known for several decades. A powerful approach is angle-resolved photoelectron spectroscopy, whereby the kinetic energy and angle of photoelectrons emitted from a sample surface are measured. This provides a direct measurement of the electronic band structure of crystalline solids. Moreover, it yields powerful insights into the electronic interactions at play within a material and into the control of spin, charge, and orbital degrees of freedom, central pillars of future solid state science. With strong recent focus on research of lower-dimensional materials and modified electronic behavior at surfaces and interfaces, angle-resolved photoelectron spectroscopy has become a core technique in the study of quantum materials. In this review, we provide an introduction to the technique. Through examples from several topical materials systems, including topological insulators, transition metal dichalcogenides, and transition metal oxides, we highlight the types of information which can be obtained. We show how the combination of angle, spin, time, and depth-resolved experiments are able to reveal "hidden" spectral features, connected to semiconducting, metallic and magnetic properties of solids, as well as underlining the importance of dimensional effects in quantum materials.

Electric field gradients in 2H-NbSe2:93Nb NMR measurements and first-principles calculations

Accurate atomic scale structure is of importance for revealing the still mysterious electronic phase transitions in a famous 2D metal, 2H-NbSe₂. In this work, the electric field gradients (EFGs) of 2H-NbSe₂at Nb sites in the normal state were investigated by⁹³Nb nuclear magnetic resonance spectroscopy in combination with first-principles computations. The previousT^3/2and linearTmodels for describing the temperature dependent EFGs were tested and discussed according to our measured and theoretically computed EFG data in this two-dimensional metal.

Straintronic effect for superconductivity enhancement in Li-intercalated bilayer MoS2

In this study, ab initio calculations were performed to show that the superconductivity in Li-intercalated bilayer MoS2 could be enhanced by applying either compressive or tensile strain. Moreover, the mechanism for superconductivity enhancement for the tensile strain case was found to be different than that of the compressive strain case. Enhanced electron phonon coupling (EPC) under tensile strain could be explained by an increase in the nesting function involved with the change in the Fermi surface topology in a wide range of Brillouin zones. The superconducting transition temperature T c of 0.46 K at zero strain increased up to 9.12 K under a 6.0% tensile strain. Meanwhile, the enhancement in compressive strain was attributed to the increase in intrinsic electron phonon matrix elements. Furthermore, the contribution from interband scattering was large, which suggested the importance of electron pockets on the Fermi surface. Finally, 80% of the total EPC (λ = 0.98) originated from these pockets and the estimated T c was 13.50 K.

Inelastic Electron Tunneling in 2H-Ta_{x}Nb_{1-x}Se_{2} Evidenced by Scanning Tunneling Spectroscopy

We report a detailed study of tunneling spectra measured on 2H-Ta_{x}Nb_{1-x}Se_{2} (x=0∼0.1) single crystals using a low-temperature scanning tunneling microscope. The prominent gaplike feature, which has not been understood for a long time, was found to be accompanied by some "in-gap" fine structures. By investigating the second-derivative spectra and their temperature and magnetic field dependencies, we were able to prove that inelastic electron tunneling is the origin of these features and obtain the Eliashberg function of 2H-Ta_{x}Nb_{1-x}Se_{2} at an atomic scale, providing a potential way to study the local Eliashberg function and the phonon spectra of the related transition-metal dichalcogenides.

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.

Dielectric Properties of NbxW1-xSe2 Alloys

The growth of transition metal dichalcogenide (TMDC) alloys provides an opportunity to experimentally access information elucidating how optical properties change with gradual substitutions in the lattice compared with their pure compositions. In this work, we performed growths of alloyed crystals with stoichiometric compositions between pure forms of NbSe₂ and WSe₂, followed by an optical analysis of those alloys by utilizing Raman spectroscopy and spectroscopic ellipsometry.

Using controlled disorder to probe the interplay between charge order and superconductivity in NbSe2

The interplay between superconductivity and charge-density wave (CDW) in 2H-NbSe₂ is not fully understood despite decades of study. Artificially introduced disorder can tip the delicate balance between two competing long-range orders, and reveal the underlying interactions that give rise to them. Here we introduce disorder by electron irradiation and measure in-plane resistivity, Hall resistivity, X-ray scattering, and London penetration depth. With increasing disorder, the superconducting transition temperature, T_c, varies non-monotonically, whereas the CDW transition temperature, T_CDW, monotonically decreases and becomes unresolvable above a critical irradiation dose where T_c drops sharply. Our results imply that the CDW order initially competes with superconductivity, but eventually assists it. We argue that at the transition where the long-range CDW order disappears, the cooperation with superconductivity is dramatically suppressed. X-ray scattering and Hall resistivity measurements reveal that the short-range CDW survives above the transition. Superconductivity persists to much higher dose levels, consistent with fully gapped superconductivity and moderate interband pairing.

Atomic-scale strain manipulation of a charge density wave

Charge density waves (CDWs) are simple periodic reorganizations of charge in a crystal, and yet they are still poorly understood and continue to bear surprises. External perturbations, such as strain or pressure, can in principle push a CDW phase into a different ordering geometry. However, engineering this type of quantum criticality has been experimentally challenging. Here, we implement a simple method for straining bulk materials. By applying it to 2H-NbSe₂, a prototypical CDW system studied for decades, we discover two dramatic strain-induced CDW phase transitions. Our atomic-scale spectroscopic imaging measurements, combined with theory, reveal the distinct roles of electrons and phonons in forming these emergent states, thus opening a window into the rich phenomenology of CDWs.

A charge density wave (CDW) is one of the fundamental instabilities of the Fermi surface occurring in a wide range of quantum materials. In dimensions higher than one, where Fermi surface nesting can play only a limited role, the selection of the particular wavevector and geometry of an emerging CDW should in principle be susceptible to controllable manipulation. In this work, we implement a simple method for straining materials compatible with low-temperature scanning tunneling microscopy/spectroscopy (STM/S), and use it to strain-engineer CDWs in 2H-NbSe₂. Our STM/S measurements, combined with theory, reveal how small strain-induced changes in the electronic band structure and phonon dispersion lead to dramatic changes in the CDW ordering wavevector and geometry. Our work unveils the microscopic mechanism of a CDW formation in this system, and can serve as a general tool compatible with a range of spectroscopic techniques to engineer electronic states in any material where local strain or lattice symmetry breaking plays a role.

Comprehensive optical characterization of atomically thin NbSe2

Transition-metal dichalcogenides (TMDCs) have offered experimental access to quantum confinement in one dimension. In recent years, metallic TMDCs like NbSe₂ have taken center stage with many of them exhibiting interesting temperature-dependent properties such as charge density waves and superconductivity. In this paper, we perform a comprehensive optical analysis of NbSe₂ by utilizing Raman spectroscopy, differential reflectance contrast, and spectroscopic ellipsometry. These analyses, when coupled with Kramers-Kronig analysis, allow us to extract the dielectric functions of bulk and atomically thin NbSe₂ and relate them to the resonant behavior of the Raman spectra.

Quantum Phase Transition in Few-Layer NbSe_{2} Probed through Quantized Conductance Fluctuations

We present the first observation of dynamically modulated quantum phase transition between two distinct charge density wave (CDW) phases in two-dimensional 2H-NbSe_{2}. There is recent spectroscopic evidence for the presence of these two quantum phases, but its evidence in bulk measurements remained elusive. We studied suspended, ultrathin 2H-NbSe_{2} devices fabricated on piezoelectric substrates-with tunable flakes thickness, disorder level, and strain. We find a surprising evolution of the conductance fluctuation spectra across the CDW temperature: the conductance fluctuates between two precise values, separated by a quantum of conductance. These quantized fluctuations disappear for disordered and on-substrate devices. With the help of mean-field calculations, these observations can be explained as to arise from dynamical phase transition between the two CDW states. To affirm this idea, we vary the lateral strain across the device via piezoelectric medium and map out the phase diagram near the quantum critical point. The results resolve a long-standing mystery of the anomalously large spectroscopic gap in NbSe_{2}.

Vibrational contributions to intrinsic friction in charged transition metal dichalcogenides

Vibrational contributions to intrinsic friction in layered transition metal dichalcogenides (TMDs) have been studied at different charge contents. We find that any deviation from charge neutrality produces complex rearrangements of atomic positions and electronic distributions, and consequent phase transitions. Upon charge injection, cell volume expansion is observed, due to charge accumulation along an axis orthogonal to the layer planes. Such accumulation is accounted for by the d_3z²-r² orbital of the transition metal and it is regulated by the P_t2g,eg orbital polarization. The latter, in turn, determines the frequency of the phonon modes related to the intrinsic friction through non-trivial electro-vibrational coupling. The bond covalency and atom pair cophonicity can be exploited as a knob to control such coupling, ruling subtle charge flows through atomic orbitals hence determining vibrational frequencies at a specific charge content. The results can be exploited to finely tune vibrational contributions to intrinsic friction in TMD structures, in order to facilitate assembly and operation of nanoelectromechanical systems and, ultimately, to govern electronic charge distribution in TMD-based devices for applications beyond nanoscale tribology.

Unexpected coordination number and phase diagram of niobium diselenide under compression

We discovered several new high-pressure structures of NbSe₂ with unexpected coordination number and constructed its high pressure and temperature phase diagram based on quasi-harmonic approximation.

Superconducting ferecrystals: turbostratically disordered atomic-scale layered (PbSe)1.14(NbSe2)n thin films

Hybrid electronic heterostructure films of semi- and superconducting layers possess very different properties from their bulk counterparts. Here, we demonstrate superconductivity in ferecrystals: turbostratically disordered atomic-scale layered structures of single-, bi- and trilayers of NbSe2 separated by PbSe layers. The turbostratic (orientation) disorder between individual layers does not destroy superconductivity. Our method of fabricating artificial sequences of atomic-scale 2D layers, structurally independent of their neighbours in the growth direction, opens up new possibilities of stacking arbitrary numbers of hybrid layers which are not available otherwise, because epitaxial strain is avoided. The observation of superconductivity and systematic Tc changes with nanostructure make this synthesis approach of particular interest for realizing hybrid systems in the search of 2D superconductivity and the design of novel electronic heterostructures.

Coherent optical phonon oscillation and possible electronic softening in WTe2 crystals

A rapidly-growing interest in WTe2 has been triggered by the giant magnetoresistance effect discovered in this unique system. While many efforts have been made towards uncovering the electron- and spin-relevant mechanisms, the role of lattice vibration remains poorly understood. Here, we study the coherent vibrational dynamics in WTe2 crystals by using ultrafast pump-probe spectroscopy. The oscillation signal in time domain in WTe2 has been ascribed as due to the coherent dynamics of the lowest energy A1 optical phonons with polarization- and wavelength-dependent measurements. With increasing temperature, the phonon energy decreases due to anharmonic decay of the optical phonons into acoustic phonons. Moreover, a significant drop (15%) of the phonon energy with increasing pump power is observed which is possibly caused by the lattice anharmonicity induced by electronic excitation and phonon-phonon interaction.

Spin-valley locking in the normal state of a transition-metal dichalcogenide superconductor

Metallic transition-metal dichalcogenides (TMDCs) are benchmark systems for studying and controlling intertwined electronic orders in solids, with superconductivity developing from a charge-density wave state. The interplay between such phases is thought to play a critical role in the unconventional superconductivity of cuprates, Fe-based and heavy-fermion systems, yet even for the more moderately-correlated TMDCs, their nature and origins have proved controversial. Here, we study a prototypical example, 2H-NbSe₂, by spin- and angle-resolved photoemission and first-principles theory. We find that the normal state, from which its hallmark collective phases emerge, is characterized by quasiparticles whose spin is locked to their valley pseudospin. This results from a combination of strong spin–orbit interactions and local inversion symmetry breaking, while interlayer coupling further drives a rich three-dimensional momentum dependence of the underlying Fermi-surface spin texture. These findings necessitate a re-investigation of the nature of charge order and superconducting pairing in NbSe₂ and related TMDCs.

The origin of intertwined electronic orders in transition-metal dichalcogenides has long been debated. Here, Bawden et al. report that the normal state, from which these phases emerge, is unexpectedly spin-polarized, with spins locked to both valley and layer pseudospins.

One-Dimensional Quasicrystals from Incommensurate Charge Order

Artificial quasicrystals are nowadays routinely manufactured, yet only two naturally occurring examples are known. We present a class of systems with the potential to be realized both artificially and in nature, in which the lowest energy state is a one-dimensional quasicrystal. These systems are based on incommensurately charge-ordered materials, in which the quasicrystalline phase competes with the formation of a regular array of discommensurations as a way of interpolating between incommensurate charge order at high temperatures and commensurate order at low temperatures. The nonlocal correlations characteristic of the quasicrystalline state emerge from a free-energy contribution localized in reciprocal space. We present a theoretical phase diagram showing that the required material properties for the appearance of such a ground state allow for one-dimensional quasicrystals to form in real materials. The result is a potentially wide class of one-dimensional quasicrystals.

Electro-vibrational coupling effects on “intrinsic friction” in transition metal dichalcogenides

M–X pair cophonicity is an intrinsic property exploitable to tune the electro-vibrational coupling determining the intrinsic friction.