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Sketch of the electronic structure of 2H-TaSe 2 , 2H-Pd 0.08 TaSe 2 , and 2H-NbSe 2 . Upper row: Sketch of the normal state Fermi surfaces. Lower row: Corresponding band structures. The sketches are the summary of multiple measurements aimed to determine the peaks of the spectral function from raw ARPES data.
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The relationship between charge-density waves (CDWs) and superconductivity is a long-standing debate. Often observed as neighbors in phase diagrams, it is still unclear whether they cooperate, compete, or simply coexist. Using angle-resolved photoemission spectroscopy, we demonstrate here that by tuning the energy position of the van Hove singulari...
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Context 1
... hole-like character of this, perpendicular to Γ-Kdirection dispersion manifests the presence of the van Hove singularity of the saddle-point type in 2H-Pd 0.08 TaSe 2 and this feature is now located at the Fermi level or slightly below it (see Supplementary Fig. 1a, b). Figure 3 schematically summarizes our findings and compares the low-energy electronic structures of three key materials: hightemperature phase of 2H-TaSe 2 , 2H-Pd 0.08 TaSe 2 and 2H-NbSe 2 . As discussed above, in terms of the Fermi surface topology, we observe a gradual transformation of the electron-like "dog-bones" around M points into hole-like Fermi surface sheets around Γ and K points. ...
Context 2
... a gradual transformation of the electron-like "dog-bones" around M points into hole-like Fermi surface sheets around Γ and K points. The reason for this transformation is the change of the energetic location of the van Hove singularity from above the Fermi level in 2H-TaSe 2 to below it in 2H-NbSe 2 , which is illustrated in the lower panels of Fig. 3 by dashed dispersion with red arrow. Remarkably, in optimally intercalated 2H-Pd 0.08 TaSe 2 its bottom nearly coincides with the Fermi level. We have also shown that this singularity is indeed a saddle point (not band edge), since along the cut perpendicular to ΓK, the dispersion is hole like (see cut 4-4 in Fig. 2 and Supplementary ...
Context 3
... result of our stuWelcome@123dy seen in Fig. 3 is the overall bandwidth renormalization of the band structure. While the bands in intercalated sample seem to just shift down, which is natural because of electron doping (and this is the driving mechanism behind the relocation of the singularity), comparison with 2H-NbSe 2 shows that the bandwidth is drastically different 33 . While ...
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Citations
... Superconductivity and charge density wave (CDW) are often found as alternative ground states of metals at low temperatures. In many materials, they tend to accompany each other as close neighbors in the thermodynamic phase diagram [1][2][3][4][5][6][7][8]. This observation has prompted a sustained investigation of their relationship from the condensed-matter community: for example, whether the two orders are competing or cooperative from the macroscopic point of view. ...
... DOI: 10.1103/PhysRevB.108.L100504 Superconductivity and charge density wave (CDW) are often found as alternative ground states of metals at low temperatures. In many materials, they tend to accompany each other as close neighbors in the thermodynamic phase diagram [1][2][3][4][5][6][7][8]. This observation has prompted a sustained investigation of their relationship from the condensed-matter community: for example, whether the two orders are competing or cooperative from the macroscopic point of view. ...
2H-NbSe2 is an archetypal system in which superconductivity and charge density wave (CDW) coexist and compete macroscopically with each other. In particular, this interplay also manifests in their dynamical fluctuations. As a result, the superconducting amplitude fluctuation (i.e., Higgs mode) is pushed below the quasiparticle continuum, allowing it to become a coherent excitation observable by Raman scattering. In the present study, we coherently drive the collective oscillations of the two orders and visualize their interplay in the time domain. We find that both collective modes contribute to terahertz third-harmonic generation (THG) and their THG signals interfere below Tc, leading to an antiresonance of the integrated THG signal. The dynamical Ginzburg-Landau model suggests that around the antiresonance a periodic energy transfer between the driven Higgs oscillations and the driven CDW oscillations is possible. Our results illustrate the roles of collective modes in the terahertz THG process, revealing a close connection of this technique to Raman scattering. In systems where the different collective modes are coupled, our experimental scheme also illustrates a paradigm for realizing coherent control via such couplings.
... Previous research has shown that electron/hole doping into the TaSe 2 can modify its intrinsic electronic properties [53][54][55]. The calculated bulk band structure of the 2H−Pt 0.1 TaSe 2 and 4H b −Pt 0.2 TaSe 2 , as shown in Fig. 3, was calculated using the WANNIER tool to easily distinguish between the compounds bulk and topological surface states, as well as the VHs features modulations. ...
... One of the most critical observations in the Fermi surface map of CDW materials like 2H−TaSe 2 is the presence of Fermi-surface nesting [54]. At the normal phase of 2H−TaSe 2 , its Fermi surface is known to host holelike pockets centered around G and K points, with "dog-bone"-shaped electron pockets around the M point [56,57] as shown in Fig. 3(c). ...
... Moreover, in an angle resolution photoelectron spectroscopy analysis of the CDW state suppression in Pd x TaSe 2 [54], a topological Lifshitz transition is observed from electron-like pockets in the Fermi surfaces as observed in the 2H−TaSe 2 to two holelike pockets [60]. Accompanied by dis-mantling the dog bone, Fermi surfaces are caused by the slight separation between the two holelike pockets. ...
Tantalum diselenide (TaSe 2) has emerged as a promising platform to investigate the interplay between two intriguing quantum electronic states in materials: the charge density wave order (CDW) and superconductivity. In this work, we report the ability to tune these quantum electronic states by intercalating Pt into 2H −TaSe 2. By introducing 20% of Pt into 2H −TaSe 2 , we demonstrate that the structural phase changes from the 2H to the 4H b phase of TaSe 2 with Pt atoms intercalated within the van der Waals spacing. According to the Fermi surface of the 4H b phase, a Lifshitz transition occurred, destroying the Fermi-surface nesting found in the 2H phase. This can be attributed to the structural phase transformation and the influence of donated electrons from Pt, thus tuning the Van Hove singularities into the Fermi-level vicinity, suppressing the CDW state, and enhancing the superconducting temperature (T c) to ∼2.7 K. The resulting superconducting properties of the 4H b −Pt 0.2 TaSe 2 are consistent with those of a BCS type-II superconductor, with a superconducting gap of 3.0 meV. Our results provide insights into the role of electron doping and structural phase changes in fine-tuning quantum electronic-state phenomena in materials. These findings could have significant implications in designing superconducting materials with tailored properties for practical applications.
... We also notice that our results are not at odd with several other situations (e.g. [80][81][82][83]) in which the competition between CDWs and superconductivity has been observed to be detrimental for the critical temperature T c . In fact, as verified by our computations, and already envisaged by the seminal work by Bergmann and Rainer [51], softening does not always lead to an increase of T c . ...
Phonon softening is a ubiquitous phenomenon in condensed matter systems which is usually associated with charge density wave (CDW) instabilities and anharmonicity. The interplay between phonon softening, CDW and superconductivity is a topic of intense debate. In this work, the effects of anomalous soft phonon instabilities on superconductivity are studied based on a recently developed theoretical framework that accounts for phonon damping and softening within the Migdal-Eliashberg theory. Model calculations show that the phonon softening in the form of a sharp dip in the phonon dispersion relation, either acoustic or optical (including the case of Kohn-type anomalies typically associated with CDW), can cause a manifold increase of the electron-phonon coupling constant λ. This, under certain conditions, which are consistent with the concept of optimal frequency introduced by Bergmann and Rainer, can produce a large increase of the superconducting transition temperature T c . In summary, our results suggest the possibility of reaching high-temperature superconductivity by exploiting soft phonon anomalies restricted in momentum space.
... Previous research has shown that electron/hole doping into the TaSe 2 can modify its intrinsic electronic properties [53][54][55]. The calculated bulk band structure of the 2H−Pt 0.1 TaSe 2 and 4H b −Pt 0.2 TaSe 2 , as shown in Fig. 3, was calculated using the WANNIER tool to easily distinguish between the compounds bulk and topological surface states, as well as the VHs features modulations. ...
... One of the most critical observations in the Fermi surface map of CDW materials like 2H−TaSe 2 is the presence of Fermi-surface nesting [54]. At the normal phase of 2H−TaSe 2 , its Fermi surface is known to host holelike pockets centered around G and K points, with "dog-bone"-shaped electron pockets around the M point [56,57] as shown in Fig. 3(c). ...
... Moreover, in an angle resolution photoelectron spectroscopy analysis of the CDW state suppression in Pd x TaSe 2 [54], a topological Lifshitz transition is observed from electron-like pockets in the Fermi surfaces as observed in the 2H−TaSe 2 to two holelike pockets [60]. Accompanied by dis-mantling the dog bone, Fermi surfaces are caused by the slight separation between the two holelike pockets. ...
... The interplay between itinerant magnetism and electron correlations together may be partially responsible for the superconductivity observed in doped samples (Fig. 5) in analogy to superconductivity near correlated magnetism in graphene heterostructures [3,8] and UTe 2 [5]. Other experiments on non-magnetically doped TaSe 2 and disordered TaSe 2 suggest that disorder enhances the electron density of states near the Fermi level by suppressing the charge density wave order present in pure 2H-TaSe 2 [36][37][38], thereby increasing the superconducting transition temperature. In our case, it is possible that reduction of the nickel concentration brings the sharp peaks in the density of states (Fig. 6B) closer to the Fermi level in a similar vein to previous doping studies of TaSe 2 . ...
Metallic ferromagnets with strongly interacting electrons often exhibit remarkable electronic phases such as ferromagnetic superconductivity, complex spin textures, and nontrivial topology. In this report, we discuss the synthesis of a layered magnetic metal NiTa4Se8 (or Ni1/4TaSe2) with a Curie temperature of 58 Kelvin. Magnetization data and density functional theory calculations indicate that the nickel atoms host uniaxial ferromagnetic order of about 0.7μB per atom, while an even smaller moment is generated in the itinerant tantalum conduction electrons. Strong correlations are evident in flat bands near the Fermi level, a high heat capacity coefficient, and a high Kadowaki-Woods ratio. Density functional theory calculations suggest that electron and hole Fermi surfaces in the ferromagnetic phase are associated with opposite spin polarization. When the system is diluted of magnetic ions, the samples become superconducting below about 2 Kelvin. We discuss possible mechanisms for superconductivity in this family.
... In essence, the complete suppression of one of these competing states, i.e., the CDW, can enhance the one, i.e., the superconductivity. Taking advantage of the VHs in 2H-TaSe2 and careful electron doping to tune it into the FS vicinity, the CDW order can be suppressed [27,28]. These will enhance the DOS around the Fermi to facilitate the formation of Cooper pairs therein. ...
... Show a slight shift from the latter to lower binding energy, indicating electron donation from Pt to the TaSe2 and a formation of bonds with the Se atoms. Previous research has shown that electron/hole doping into the TaSe2 modifies intrinsic electronic properties [28][29][30]. The calculated bulk band structure of the PtxTa1-xSe2 (x = 0.1 and 0.2), as shown in Figure 3, was calculated using the Wannier tool to distinguish between the compounds bulk and topological surface states easily, as well as the VHs features modulations. ...
... One of the most critical observations in the Fermi surface map of CDW materials like TaSe2 is the presence of Fermi surface nesting [28]. At the normal phase of TaSe2, its fermi surface is known to host hole-like pockets centered around G and K points, with "dog-bones" shaped electron pockets around the M point, [31,32] as shown in Figure 3(c). ...
Tantalum diselenide (TaSe2) is an exciting material that hosts charge density wave order (CDW) and superconductivity. Thus, providing a playing field for examining the interactions of fundamental electronic quantum states in materials. Recent research has proposed that the intrinsic quantum electronic state in the TaSe2 lattice could be improved by aligning the Van Hove singularity (VHs) with the Fermi level. In this study, we attempt to tune the VHs in TaSe2 to align them within the vicinity of the Fermi level via electron doping by chemically substituting Pt for Ta atoms. On investigating the band structure of Pt0.2Ta0.8Se2, the electron doping brought the VHs closer to the Fermi level vicinity around the K high symmetry point. As a result, the CDW state in pristine TaSe2 is suppressed in the TaSe2 doped system while also hosting an enhanced superconducting temperature (Tc) of ~2.7 K. These observations provide insight into ways to leverage the VHs in materials to tune their electronic properties.
... Here, we provided a simple but concrete verification of this possibility in the context of boson-mediated Eliashberg theory. We also notice that our results are not at odd with several other situations (e.g., [74][75][76][77]) in which the competition between CDWs and superconductivity has been observed to be detrimental for the critical temperature T c . In fact, as verified by our computations, and already envisaged by the seminal work by Bergmann and Rainer [45], softening does not always lead to an increase of T c . ...
Phonon softening is a ubiquitous phenomenon in condensed matter systems which is usually associated with charge density wave (CDW) instabilities and anharmonicity. The interplay between phonon softening, CDW and superconductivity is a topic of intense debate. In this work, the effects of anomalous soft phonon instabilities on superconductivity are studied based on a recently developed theoretical framework that accounts for phonon damping and softening within the Migdal-Eliashberg theory. Model calculations show that the phonon softening in the form of a sharp dip in the phonon dispersion relation, either acoustic or optical (including the case of Kohn-type anomalies typically associated with CDW), can cause a manifold increase of the electron-phonon coupling constant $\lambda$. This, under certain conditions, which are consistent with the concept of optimal frequency introduced by Bergmann and Rainer, can produce a large increase of the superconducting transition temperature Tc. In summary, our results suggest the possibility of reaching high-temperature superconductivity by exploiting soft phonon anomalies restricted in momentum space.
... Superconductivity and charge-density-wave (CDW) are often found as alternative ground states of metals at low temperatures. In many materials, they tend to accompany each other as close neighbors in the thermodynamic phase diagram [1][2][3][4][5][6][7] . This observation has prompted a sustained investigation of their relationship from the condensed matter community: for example, whether the two orders are competing or co-operative from the macroscopic point of view. ...
2H-NbSe2 is an archetypal system in which superconductivity and charge-density-wave (CDW) coexist and compete macroscopically with each other. In particular, this interplay also manifests in their dynamical fluctuations. As a result, the superconducting amplitude fluctuations (i.e. Higgs mode) is pushed below the quasiparticle continuum, allowing it to become a coherent excitation observable by Raman scattering. In the present study, we coherently drive the collective oscillations of the two orders and visualize their interplay in the driven states in the time domain. We find that both collective modes contribute to terahertz third harmonic generation (THG) and the THG signals interfere below Tc, leading to an anti-resonance of the integrated THG signal. The dynamical Ginzburg-Landau model suggests that around the anti-resonance a periodic energy transfer between the driven Higgs oscillations and the driven CDW oscillations is possible. In addition to 2H-NbSe2, we also studied an underdoped La2-xSrxCuO4 (x ~ 0.12) driven beyond the perturbative regime of THG. A similar interference between two sources of THG is observed below Tc. While there might be additional sources of THG in these experiments, our results illustrate the roles of coupled modes in the terahertz THG process and the tantalizing possibility of coherent control via such couplings.
... The TiSe 2 material presents a quasi-2D arrangement, a superconductor state near 4.4K, and a CDW effect. In such CDW model for quasi-2D materials, the Cooper's pair is the wave that creates the high electrical transport without energy dissipation [9]. ...
Superconductivity is one of the most interesting electrical phenomena found in Physical Science. The null electrical resistance provides a unique free displacement for the electrons into the material. TiSe2 is a superconductor material below 4K, creating a charge density wave as electrical propagation. Gaussian basis sets or exchange–correlation functionals poorly described the high interaction distance as van der Waals force because of low exchange–correlation energy. One physical–mathematical tool to indicate long-range distance is the Grimme's or D3 dispersion. In this work, quantum simulations based on DFT using periodic models depicted in CRYSTAL17 code investigated the TiSe2 material regarding PBE0, HSE06, and B3LYP functionals and Grimme's dispersion. In particular, the high covalent feature on the Ti–Se chemical bond is challenging for DFT functionals, while van der Waals interaction between lamellas is essential for crystalline structure. Then, relative errors quantified the functional descriptions to evaluate the influence of hybrid and parameterized hybrid functionals on this critical material's structural, electronic, and vibrational properties.
... where δ c and δ d play the role of the CDW/inCDW order parameters for c-and d-orbitals, respectively, while Q = (Q x , Q y ) is the modulation wave vector [85]. It is worth mentioning that, by incommensurate, we meant a wave vector different from (π, π), with Q α = 2πl L , l = − L 2 , . . . ...
The appearance of an incommensurate charge density wave vector $\vQ = (Q_x,Q_y)$ on multiband intermetallic systems presenting commensurate charge density wave (CDW) and superconductivity (SC) orders is investigated. We consider a two-band model in a square lattice, where the bands have distinct effective masses. The incommensurate CDW (inCDW) and CDW phases arise from an interband Coulomb repulsive interaction, while the SC emerges due to a local intraband attractive interaction. For simplicity, all the interactions, the order parameters and hybridization between bands are considered $\vk$-independent. The multiband systems that we are interested are intermetallic systems with a $d$-band coexisting with a large $c$-band, for which a mean-field approach has proved suitable. We obtain the eigenvalues and eigenvectors of the Hamiltonian numerically and minimize the free energy density with respect to the diverse parameters of the model by means of the Hellmann-Feynman theorem. We investigate the system in real as well as momentum space and we find an inCDW phase with wave vector $\vQ = (\pi, Q_y) = (Q_x, \pi)$. Our numerical results show that the arising of an inCDW state depends on parameters, such as the magnitude of the inCDW and CDW interactions, band filling, hybridization and the relative depth of the bands. In general, inCDW tends to emerge at low temperatures, away from half-filling. We also show that, whether the CDW ordering is commensurate or incommensurate, large values of the relative depth between bands may suppress it. We discuss how each parameter of the model affects the emergence of an inCDW phase.
