Charge Density Wave Formation Research Articles

Engineering Charge Density Waves by Stackingtronics in Tantalum Disulfide.

In the realm of condensed matter physics and materials science, charge density waves (CDWs) have emerged as a captivating way to modulate correlated electronic phases and electron oscillations in quantum materials. However, collectively and efficiently tuning CDW order is a formidable challenge. Herein, we introduced a novel way to modulate the CDW order in 1T-TaS2 via stacking engineering. By introducing shear strain during the electrochemical exfoliation, the thermodynamically stable AA-stacked TaS2 consecutively transform into metastable ABC stacking, resulting in unique 3a × 1a CDW order. By decoupling atom coordinates, we atomically deciphered the 3D subtle structural variations in trilayer samples. As suggested by density functional theory (DFT) calculations, the origin of CDWs is presumably due to collective excitations and charge modulation. Therefore, our works shed light on a new avenue to collectively modulate the CDW order via stackingtronics and unveiled novel mechanisms for triggering CDW formation via charge modulation.

Anharmonic strong-coupling effects at the origin of the charge density wave in CsV3Sb5

The formation of charge density waves is a long-standing open problem, particularly in dimensions higher than one. Various observations in the vanadium antimonides discovered recently further underpin this notion. Here, we study the Kagome metal CsV3Sb5 using polarized inelastic light scattering and density functional theory calculations. We observe a significant gap anisotropy with 2Δmax/kBTCDW≈20\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2{\\Delta }_{\\max }/{k}_{{{{{{{{\\rm{B}}}}}}}}}{T}_{{{{{{{{\\rm{CDW}}}}}}}}}\\, \\approx \\, 20$$\\end{document}, far beyond the prediction of mean-field theory. The analysis of the A1g and E2g phonons, including those emerging below TCDW, indicates strong phonon-phonon coupling, presumably mediated by a strong electron-phonon interaction. Similarly, the asymmetric Fano-type lineshape of the A1g amplitude mode suggests strong electron-phonon coupling below TCDW. The large electronic gap, the enhanced anharmonic phonon-phonon coupling, and the Fano shape of the amplitude mode combined are more supportive of a strong-coupling phonon-driven charge density wave transition than of a Fermi surface instability or an exotic mechanism in CsV3Sb5.

Atomistic Origin of Diverse Charge Density Wave States in CsV_{3}Sb_{5}.

Kagome metals AV_{3}Sb_{5} (A=K, Rb, or Cs) exhibit intriguing charge density wave (CDW) instabilities, which interplay with superconductivity and band topology. However, despite firm observations, the atomistic origins of the CDW phases, as well as hidden instabilities, remain elusive. Here, we adopt our newly developed symmetry-adapted cluster expansion method to construct a first-principles-based effective Hamiltonian of CsV_{3}Sb_{5}, which not only reproduces the established inverse star of David (ISD) phase, but also predict a series of D_{3h}-n states under mild tensile strains. With such atomistic Hamiltonians, the microscopic origins of different CDW states are revealed as the competition of the second-nearest neighbor V-V pairs versus the first-nearest neighbor V-V and V-Sb couplings. Interestingly, the effective Hamiltonians also reveal the existence of ionic Dzyaloshinskii-Moriya interaction in the high-symmetry phase of CsV_{3}Sb_{5} and drives the formation of noncollinear CDW patterns. Our work thus not only deepens the understanding of the CDW formation in AV_{3}Sb_{5}, but also demonstrates that the effective Hamiltonian is a suitable approach for investigating CDW mechanisms, which can be extended to various CDW systems.

Competing charge-density wave instabilities in the kagome metal ScV6Sn6

Owing to its unique geometry, the kagome lattice hosts various many-body quantum states including frustrated magnetism, superconductivity, and charge-density waves (CDWs). In this work, using inelastic X-ray scattering, we discover a dynamic short-range sqrt{3}times sqrt{3}times 2 CDW that is dominant in the kagome metal ScV6Sn6 above TCDW ≈ 91 K, competing with the sqrt{3}times sqrt{3}times 3 CDW that orders below TCDW. The competing CDW instabilities lead to an unusual CDW formation process, with the most pronounced phonon softening and the static CDW occurring at different wavevectors. First-principles calculations indicate that the sqrt{3}times sqrt{3}times 2 CDW is energetically favored, while a wavevector-dependent electron-phonon coupling (EPC) promotes the sqrt{3}times sqrt{3}times 3 CDW as the ground state, and leads to enhanced electron scattering above TCDW. These findings underscore EPC-driven correlated many-body physics in ScV6Sn6 and motivate studies of emergent quantum phases in the strong EPC regime.

Chiral domain dynamics and transient interferences of mirrored superlattices in nonequilibrium electronic crystals

Mirror symmetry plays a major role in determining the properties of matter and is of particular interest in condensed many-body systems undergoing symmetry breaking transitions under non-equilibrium conditions. Typically, in the aftermath of such transitions, one of the two possible broken symmetry states is emergent. However, synthetic systems and those formed under non-equilibrium conditions may exhibit metastable states comprising of both left (L) and right (R) handed symmetry. Here we explore the formation of chiral charge-density wave (CDW) domains after a laser quench in 1T-TaS2 with scanning tunneling microscopy. Typically, we observed transient domains of both chiralities, separated spatially from each other by domain walls with different structure. In addition, we observe transient density of states modulations consistent with interference of L and R-handed charge density waves within the surface monolayer. Theoretical modeling of the intertwined domain structures using a classical charged lattice gas model reproduces the experimental domain wall structures. The superposition (S) state cannot be understood classically within the correlated electron model but is found to be consistent with interferences of L and R-handed charge-density waves within domains, confined by surrounding domain walls, vividly revealing an interference of Fermi electrons with opposite chirality, which is not a result of inter-layer interference, but due to the interaction between electrons within a single layer, confined by domain wall boundaries.

Tiny Sc Allows the Chains to Rattle: Impact of Lu and Y Doping on the Charge-Density Wave in ScV6Sn6.

The kagome metals display an intriguing variety of electronic and magnetic phases arising from the connectivity of atoms on a kagome lattice. A growing number of these materials with vanadium-kagome nets host charge-density waves (CDWs) at low temperatures, including ScV6Sn6, CsV3Sb5, and V3Sb2. Curiously, only the Sc version of the RV6Sn6 materials with a HfFe6Ge6-type structure hosts a CDW (R = Gd-Lu, Y, Sc). In this study, we investigate the role of rare earth size in CDW formation in the RV6Sn6 compounds. Magnetization measurements on our single crystals of (Sc,Lu)V6Sn6 and (Sc,Y)V6Sn6 establish that the CDW is suppressed by substituting Sc by larger Lu or Y. Single-crystal X-ray diffraction reveals that compressible Sn-Sn bonds accommodate the larger rare earth atoms within loosely packed R-Sn-Sn chains without significantly expanding the lattice. We propose that Sc provides extra room in these chains crucial to CDW formation in ScV6Sn6. Our rattling chain model explains why both physical pressure and substitution by larger rare earth atoms hinder CDW formation despite opposite impacts on lattice size. We emphasize the cooperative effect of pressure and rare earth size by demonstrating that pressure further suppresses the CDW in a Lu-doped ScV6Sn6 crystal. Our model not only addresses why a CDW only forms in the RV6Sn6 materials with tiny Sc but also advances our understanding of why unusual CDWs form in the kagome metals.

Selective Electron-Phonon Coupling in Dimerized 1T-TaS2 Revealed by Resonance Raman Spectroscopy.

The layered transition-metal dichalcogenide material 1T-TaS2 possesses successive phase transitions upon cooling, resulting in strong electron-electron correlation effects and the formation of charge density waves (CDWs). Recently, a dimerized double-layer stacking configuration was shown to form a Peierls-like instability in the electronic structure. To date, no direct evidence for this double-layer stacking configuration using optical techniques has been reported, in particular through Raman spectroscopy. Here, we employ a multiple excitation and polarized Raman spectroscopy to resolve the behavior of phonons and electron-phonon interactions in the commensurate CDW lattice phase of dimerized 1T-TaS2. We observe a distinct behavior from what is predicted for a single layer and probe a richer number of phonon modes that are compatible with the formation of double-layer units (layer dimerization). The multiple-excitation results show a selective coupling of each Raman-active phonon with specific electronic transitions hidden in the optical spectra of 1T-TaS2, suggesting that selectivity in the electron-phonon coupling must also play a role in the CDW order of 1T-TaS2.

Unique Structural Features of NbS3 Ribbon Whiskers

The X-ray diffraction analysis of NbS3 ribbon whiskers has revealed three structural features: (i) a fine-crystalline structure throughout the entire volume with the preferred orientation along the [001] direction perpendicular to the long b axis of the whisker, (ii) the combination of crystalline macroblocks with a length up to 0.5 mm with small crystallites of various orientations, and (iii) the combination of crystalline macroblocks with the left-hand twisting of planes around the b axis with a pitch angle of 1.25° per every 0.2 mm and with the return to the initial orientation in the next block. Structural features (ii) and (iii) of NbS3 whiskers have not yet been observed, and inorganic crystals with such properties are absent to the best of our knowledge. All crystallites have a unit cell with almost right angles and approximately the same lattice constant c (18.130 Å), whereas the lattice constants a and b are noticeably different in a single sample. All crystallites can be referred to phase IV rather than to phase I, as expected. The right angle between the a and c axes can be explained by the twinning of phase I along the c axis. Differences in the lattice constants in macroblocks indicate large stresses in structures. Such stresses near twins (and/or stacking faults) can significantly affect the free electron density and play a key role in the formation of charge density waves in various phases of NbS3.

Periodic Atomic Displacements and Visualization of the Electron-Lattice Interaction in the Cuprate

Traditionally, X-ray scattering techniques have been used to detect the breaking of the structural symmetry of the lattice, which accompanies a periodic displacement of the atoms associated with charge density wave (CDW) formation in the cuprate pseudogap states. Similarly, the Spectroscopic Imaging Scanning Tunneling Microscopy (SI-STM) has visualized the short-range CDW. However, local coupling of electrons to the lattice in the form of a short-range CDW has been a challenge to visualize, thus a link between these measurements has been missing. Here, we introduce a novel STM-based technique to visualize the local bond length variations obtained from topographic imaging with picometer precision. Application of this technique to the high-Tc cuprate superconductor Bi2Sr2CaCu2O8+{\delta} revealed a high-fidelity local lattice distortion of the BiO lattice as large as 2%. In addition, analysis of local breaking of rotational symmetry associated with the bond lengths reveals modulations around four-unit-cell periodicity in both B1 and E representations in the C4v group of the lattice, which coincides with the uni-directional d-symmetry CDW (dCDW) previously identified within the CuO2 planes, thus providing direct evidence of electron-lattice coupling in the pseudogap state and a link between the X-ray scattering and STM measurements. Overall, our results suggest that the periodic lattice displacements in E representations correspond to a locally-frozen version of the soft phonons identified by the X-ray scattering measurements, and a fluctuation of the bond length is reflected by the fluctuation of the dCDW formation near the quantum critical point.

Landau-Ginzburg theory of charge density wave formation accompanying lattice and electronic long-range ordering

We propose an analytical Landau-Ginzburg theory of the charge density waves coupled with lattice and electronic long-range order parameters. Examples of long-range order include electronic wave function of superconducting Cooper pairs, structural distortions, electric polarization, and magnetization. We formulate the Landau-Ginzburg free energy density as power expansion with respect to the charge density and other long-range order parameters, as well as their spatial gradients, and biquadratic coupling terms. We introduced a biquadratic coupling between the charge density gradient and long-range order parameters, as well as nonlinear higher gradients of the long-range order parameters. The biquadratic gradient coupling is critical to the appearance of different spatially-modulated phases in charge-ordered ferroics and high-temperature superconductors. We derived the thermodynamic conditions for the stability of the spatially-modulated phases, which are the intertwined spatial waves of charge density and lattice/electronic long-range order. The analytical expressions for the energies of different phases, corresponding order parameters, charge density waves amplitudes and modulation periods, obtained in this work, can be employed to guide the comprehensive physical explanation, deconvolution and Bayesian analysis of experimental data on quantum materials ranging from charge-ordered ferroics to high-temperature superconductors.

Charge order in the kagome lattice Holstein model: a hybrid Monte Carlo study

The Holstein model is a paradigmatic description of the electron-phonon interaction, in which electrons couple to local dispersionless phonon modes, independent of momentum. The model has been shown to host a variety of ordered ground states such as charge density wave (CDW) order and superconductivity on several geometries, including the square, honeycomb, and Lieb lattices. In this work, we study CDW formation in the Holstein model on the kagome lattice, using a recently developed hybrid Monte Carlo simulation method. We present evidence for sqrt{3}times sqrt{3} CDW order at an average electron filling of 〈n〉 = 2/3 per site, with an ordering wavevector at the K-points of the Brillouin zone. We estimate a phase transition occurring at Tc ≈ t/18, where t is the nearest-neighbor hopping parameter. Our simulations find no signature of CDW order at other electron fillings or ordering momenta for temperatures T ≥ t/20.

Decisive role of electron-phonon coupling for phonon and electron instabilities in transition metal dichalcogenides

The origin of the charge density wave (CDW) in transition metal dichalcogenides has been hotly debated, and no conclusive agreement has been reached. Here, we propose an ab initio framework for an accurate description of both Fermi surface nesting and electron-phonon coupling (EPC) and systematically investigate their roles in the formation of the CDW. Using monolayer $1H\text{\ensuremath{-}}{\mathrm{NbSe}}_{2}$ and $1T\text{\ensuremath{-}}{\mathrm{VTe}}_{2}$ as representative examples, we show that it is the momentum-dependent EPC that softens the phonon frequencies, which become imaginary (phonon instabilities) at CDW vectors (indicating CDW formation). In addition, the distribution of the CDW gap opening (electron instabilities) can be correctly predicted only if EPC is included in the mean-field model. These results emphasize the decisive role of EPC in the CDW formation. Our analytical process is general and can be applied to other CDW systems.

Charge density wave and crystalline electric field effects inTmNiC2

Single crystals of ${\mathrm{TmNiC}}_{2}$ were grown by the optical floating-zone technique and were investigated by x-ray diffraction (XRD), thermal expansion, electrical resistivity, specific heat, and magnetic susceptibility measurements. Single-crystal XRD reveals the formation of a commensurate charge density wave (CDW) characterized by a CDW modulation vector ${\mathbf{q}}_{\mathbf{2}\mathbf{c}}=(0.5,0.5,0.5)$, which is accompanied by a symmetry change from the orthorhombic space group $Amm2$ to the monoclinic space group $Cm$, i.e., to a CDW superstructure which is isostructural with that of ${\mathrm{LuNiC}}_{2}$. For all transport and thermodynamic properties, anomalies related to a second order-type thermodynamic CDW phase transition are observed at around ${T}_{\mathrm{CDW}}\ensuremath{\simeq}375\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. The large specific heat anomaly at ${T}_{\mathrm{CDW}}, \mathrm{\ensuremath{\Delta}}C\ensuremath{\simeq}6.2\phantom{\rule{4pt}{0ex}}\mathrm{J}\phantom{\rule{0.16em}{0ex}}{\mathrm{mol}}^{\ensuremath{-}1}{\mathrm{K}}^{\ensuremath{-}1}$, together with noticeable changes in entropy and enthalpy related to the CDW transition, suggests that this point group symmetry breaking CDW phase transition affects more significant parts of the Fermi surface as compared to the incommensurate CDW transition of, e.g., ${\mathrm{SmNiC}}_{2}$ with no change in point group symmetry. The results on the antiferromagnetic and paramagnetic state of ${\mathrm{TmNiC}}_{2}$ obtained by the above macroscopic techniques were complemented by microscopic studies via inelastic neutron scattering. A crystalline electric field modeling of macroscopic susceptibility and magnetic specific heat and entropy contributions as well as microscopic neutron scattering data, reveal crystal field eigenstates and eigenvalues with a ground-state doublet of the Tm-$4f$ electrons, which is well separated by about 25 meV from exited states of the $J=6$ ground-state multiplet.

Hole doping dependent electronic instability and electron-phonon coupling in infinite-layer nickelates

Recently, charge density waves (CDWs) have been observed in $\mathrm{CaCu}{\mathrm{O}}_{2}\text{\ensuremath{-}}\mathrm{analogous}$ infinite-layer nickelates $R\mathrm{Ni}{\mathrm{O}}_{2}$ ($R=\mathrm{La}$, Nd) but exhibit very different hole doping dependent behaviors compared to that in cuprates, raising a challenging question on its origin. In this paper, employing density functional theory, many-body dynamic mean field theory, and determinant quantum Monte Carlo calculations, we propose a synergetic contribution from both electronic instability (EI) and moment-dependent electron-phonon coupling (MEPC). Unexpectedly, the EI and MEPC are mainly contributed by Ni $3{d}_{x2\ensuremath{-}y2}$ and $R 5{d}_{z2}$, highlighting the unique multiorbital feature. Interestingly, a strong Fermi surface nesting (FSN) induced by the unique feature of van Hove singularity (VHS) across the Fermi level exists in $R\mathrm{Ni}{\mathrm{O}}_{2}$, which is sensitive to hole doping. The hole doping can rapidly reduce FSN of Ni $3{d}_{x2\ensuremath{-}y2}$ by shifting VHS and decrease the occupation of $R 5{d}_{z2}$, which can largely weaken EI and MEPC in $R\mathrm{Ni}{\mathrm{O}}_{2}$. Remarkably, the temperature-insensitive feature of EI and MEPC could be a hint for rather high-temperature CDWs observed in undoped $R\mathrm{Ni}{\mathrm{O}}_{2}$. Our theory may offer one possible explanation to the experimentally observed CDW formation and its hole-doping dependence in nickelates, and also establishes a unified understanding of the hole doping dependent EI and MEPC in nickelates and cuprates.

Field direction dependent quantum-limit magnetoresistance of correlated Dirac electrons in perovskite CaIrO3

Correlated-electron perovskite ${\mathrm{CaIrO}}_{3}$ shows the topologically protected line node near the Fermi level, wherein the high-mobility Dirac electrons reach the quantum limit (QL) with the one-dimensionally (1D) dispersive $n=0$ Landau level (LL) state at a moderate magnetic field. In the QL, the longitudinal magnetoresistance (MR) shows an extreme anisotropy against the field $(B)$ direction in spite of nearly isotropic Dirac band dispersions. The resistivity for $B\ensuremath{\parallel}a$ shows an insulating behavior with the MR ratio exceeding $2000%$ around 18 T, whereas the $B\ensuremath{\parallel}c$ MR always remains metallic. This is accounted for in terms of the large difference of Fermi velocity of the $n=0$ LL between $B\ensuremath{\parallel}a$ and $B\ensuremath{\parallel}c$ due to the $B$ direction dependent $5d$ orbital electron hopping, which triggers the different instability toward the charge density wave formation for the 1D $(\ensuremath{\parallel}B)$ dispersive $n=0$ LL.

Interplay of charge ordering and superconductivity in two-dimensional 2H group V transition-metal dichalcogenides

Layered $2H\text{\ensuremath{-}}T{X}_{2}$ with $T=\mathrm{Nb}$, Ta and $X=\mathrm{S}$, Se exhibit rich dimensionality effects on charge density wave (CDW) order and superconductivity, but comprehensive understanding of these correlated quantum phases in the two-dimensional limit of $2H\text{\ensuremath{-}}T{X}_{2}$ is still lacking, hindering their practical applications. Here, I calculate from first principles the phonon linewidth and bare susceptibility to study the origin of CDW formation in ${\mathrm{NbSe}}_{2}$, ${\mathrm{TaS}}_{2}$, ${\mathrm{TaSe}}_{2}$, and ${\mathrm{NbS}}_{2}$ monolayers, analyze their relative CDW strength, and evaluate electron-phonon superconductivity within the fully anisotropic Migdal-Eliashberg theory. A peaked linewidth of the longitudinal acoustic branch and no Fermi-surface nesting around ${\mathbf{q}}_{\mathrm{CDW}}$ indicate CDW instability driven by the wave-vector-dependent electron-phonon coupling. The $3\ifmmode\times\else\texttimes\fi{}3$ CDW ground state favors a distinct hollow-centered clustering of transition-metal atoms, with larger distortion amplitude in ${\mathrm{NbSe}}_{2}$ and ${\mathrm{TaSe}}_{2}$ than in ${\mathrm{TaS}}_{2}$ and ${\mathrm{NbS}}_{2}$. Superconducting results of the monolayer CDW phase prove that strong spin-orbit coupling effects are dominant in determining the critical temperature ${T}_{\mathrm{c}}$ of each system via modifying both the strength and anisotropic extent of electron-phonon interactions. I also recapitulate measured opposite thickness dependencies of ${T}_{\mathrm{c}}$ in $\mathrm{Nb}{X}_{2}$ and $\mathrm{Ta}{X}_{2}$, and show that whether superconductivity is weakened or enhanced in monolayer limit relies on specific evolution of CDW-modulated Fermi-level density of states and electron-phonon matrix elements under reduced dimensionality. This work lays the foundation for applications of $2H$ group V transition-metal dichalcogenides in versatile nanoscale quantum devices.

Charge order with unusual star-of-David lattice in monolayer NbTe2

Interplay between fermiology and electron correlation is crucial for realizing exotic quantum phases. Transition-metal dichalcogenide (TMD) 1T-TaS2 has sparked a tremendous attention owing to its unique Mott-insulating phase coexisting with the charge-density wave (CDW). However, how the fermiology and electron correlation are associated with such properties has yet to be claried. Here we demonstrate that monolayer 1T-NbTe2 is a new class of two-dimensional TMD which has the star-of-David lattice similarly to bulk TaS2 and isostructural monolayer NbSe2, but exhibits a metallic ground state with an unusual lattice periodicity root19xroot19 characterized by the sparsely occupied star-of-David lattice. By using angle-resolved photoemission and scanning-tunneling spectroscopies in combination with first-principles band-structure calculations, we found that the hidden Fermi-surface nesting and associated CDW formation are a primary cause to realize this unique correlated metallic state with no signature of Mott gap. The present result points to a vital role of underlying fermiology to characterize the Mott phase of TMDs.

Unveiling the selenium content effect on the properties of TiSe2±α

We systematically examined the properties of the polycrystalline 1T-TiSe2±α series synthesized by solid-state method, combined chemical analysis and physical property characterization, including Energy-dispersive X-ray spectroscopy (EDXS), x-ray photoelectron spectroscopy (XPS) x-ray diffraction (XRD), resistivity, hall effect and magnetization measurement have been employed to study how Ti/Se ratio influences the charge density wave (CDW) formation, the crystal structure, and the electrical characteristics. The electrical resistivity of Se-rich -TiSe2 (Ti/Se ​= ​0.484) is found to be a metallic behavior with decreased CDW transition temperature. This study emphasizes how sensitive 1T-TiSe2 characteristics are to defects and stoichiometry.

Structural phase transitions and superconductivity in the Heusler intermetallics XPd2Sn ( X = Ti, Zr, Hf)

We report the discovery of structural phase transitions and superconductivity in the full Heusler compounds $X{\mathrm{Pd}}_{2}\mathrm{Sn}$ ($X=\text{Ti}$, Zr, Hf), by means of electrical transport, magnetic susceptibility, specific heat, and x-ray diffraction measurements. $\mathrm{Ti}{\mathrm{Pd}}_{2}\mathrm{Sn}$, $\mathrm{Zr}{\mathrm{Pd}}_{2}\mathrm{Sn}$, and $\mathrm{Hf}{\mathrm{Pd}}_{2}\mathrm{Sn}$ undergo structural phase transitions from the room-temperature cubic $\mathrm{Mn}{\mathrm{Cu}}_{2}\mathrm{Al}$-type structure (space group $Fm\overline{3}m$) to a low-temperature tetragonal structure at around 160, 110, and 90 K, respectively, which are likely related to charge density wave (CDW) instabilities. Low-temperature single-crystal x-ray diffraction measurements of $\mathrm{Zr}{\mathrm{Pd}}_{2}\mathrm{Sn}$ demonstrate the emergence of a superstructure with multiple commensurate modulations below ${T}_{s}$. $\mathrm{Zr}{\mathrm{Pd}}_{2}\mathrm{Sn}$ and $\mathrm{Hf}{\mathrm{Pd}}_{2}\mathrm{Sn}$ have bulk superconductivity with transition temperatures ${T}_{c}\ensuremath{\sim}1.2$ and 1.3 K, respectively. Density functional theory calculations reveal evidence for structural and electronic instabilities which can give rise to CDW formation, suggesting that these $X{\mathrm{Pd}}_{2}\mathrm{Sn}$ systems are good candidates for examining the interplay between CDW and superconductivity.

Observation of superconductivity and its enhancement at the charge density wave critical point in LaAgSb2

We discover superconductivity (SC) in LaAgSb$_2$ at ambient pressure and its close correlation with a charge density wave (CDW) under pressure. The superconducting transition temperature ($T_c$) exhibits a sharp peak at the CDW critical pressure of 3.2 GPa. We demonstrate that the carriers inhabiting the Sb-square net is crucial not only in the formation of CDW but also in SC for their relatively strong electron-phonon coupling (EPC). Furthermore, theoretical EPC strength in pristine LaAgSb$_2$ cannot explain the observed peak with $T_c\sim 1$ K, which indicates that an additional mechanism reinforces SC only around the CDW critical pressure.