Raman Spectroscopy of Soft Modes at the Charge-Density-Wave Phase Transition in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>2</mml:mn><mml:mi>H</mml:mi><mml:mo>−</mml:mo><mml:mi mathvariant="normal">Nb</mml:mi><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Se</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>

Tsang, J. C.; Smith, J. E.; Shafer, M. W.

doi:10.1103/physrevlett.37.1407

Cited by 100 publications

(73 citation statements)

References 12 publications

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“…Fig. 2(b) illustrates that the A 1g amplitude mode of Cu x TiSe 2 exhibits temperature-dependent soft mode behavior typical of amplitude modes observed in other CDW systems, [17,18] including: (i) a temperature-dependence (filled squares, Fig. 2(b)) given by the power law form ω o (T) ∼ (1 -T/T CDW ) β with β ∼ 0.15 (solid line, Fig.…”

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confidence: 78%

“…Furthermore, this result suggests that the Cu x TiSe 2 phase diagram is consistent with the T vs. lattice parameter phase diagram plotted by Castro Neto for the layered dichalcogenides, in which there are two quantum critical points as a function of increasing lattice parameter: superconductivity (SC) and CDW order coexist above the lower of the two critical lattice parameters, while SC is present, but CDW order is not, above the higher of the two critical lattice parameters. [20] We note, however, that because the amplitude mode becomes overdamped and unobservable very close to the transition region -due to the breakdown of long-range CDW order and zone-folding [17,18] -we cannot rule out the possibility that other effects, e.g., disorder from Cu intercalation, may lead to different quantum critical behavior (i.e., for T ∼ 0 and near x ∼ 0.07) than that implied by the x-dependent scaling behavior we observe up to x = 0.05 in Fig. 4.…”

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confidence: 88%

“…2(a)) can be made using Rice and collaborators mean-field result for the frequency of a CDW amplitude mode, [12] which has been successfully applied to the analysis of CDW soft mode behavior in other dichalcogenides. [17] In Eq. 1,ω is the unscreened (high temperature) phonon frequency, t = (T CDW -T)/T CDW is the reduced temperature, and λ = N(0)g 2 (0)/ω is the electron-phonon coupling constant associated with the CDW, where g(0) is the electron-phonon coupling matrix element between the soft mode phonon and the electronic states at the Fermi surface involved in the CDW transition, and N(0) is the joint density of states of the electrons and holes involved in the CDW transition.…”

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confidence: 99%

“…1,ω is the unscreened (high temperature) phonon frequency, t = (T CDW -T)/T CDW is the reduced temperature, and λ = N(0)g 2 (0)/ω is the electron-phonon coupling constant associated with the CDW, where g(0) is the electron-phonon coupling matrix element between the soft mode phonon and the electronic states at the Fermi surface involved in the CDW transition, and N(0) is the joint density of states of the electrons and holes involved in the CDW transition. [17] Note that the unscreened frequencyω in Eq. (1) is not expected to have a significant doping dependence between x = 0 and x = 0.06 in Cu x TiSe 2 , which is supported by the fact that the optical phonon frequencies exhibit a negligible change with x (e.g., see 137 cm −1 mode in Fig.…”

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Quantum and Classical Mode Softening Near the Charge-Density-Wave–Superconductor Transition ofCuxTiSe2

et al. 2008

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Temperature-and x-dependent Raman scattering studies of the charge density wave (CDW) amplitude modes in CuxTiSe2 show that the amplitude mode frequency ωo exhibits identical powerlaw scaling with the reduced temperature, T/TCDW, and the reduced Cu content, x/xc, i.e., ωo ∼ (1 -p) 0.15 for p = T/TCDW or x/xc, suggesting that mode softening is independent of the control parameter used to approach the CDW transition. We provide evidence that x-dependent mode softening in CuxTiSe2 is caused by the reduction of the electron-phonon coupling constant λ due to expansion of the lattice, and that x-dependent 'quantum' (T ∼ 0) mode softening reveals a quantum critical point within the superconductor phase of CuxTiSe2. 1T -TiSe 2 is a semimetal or small-gap semiconductor in the normal state, [6,7,8,9] which develops a commensurate CDW with a 2a o ×2a o ×2c o superlattice structure at temperatures below a second-order phase transition at T CDW ∼ 200 K. [6,10] Increasing Cu intercalation in TiSe 2 (increasing x in Cu x TiSe 2 ) results in (i) an expansion of the a-and c-axis lattice parameters, [5] (ii) increased electronic density of states near the L point, [7,8] (iii) a suppression of the CDW transition temperature, [5] and (iv) the emergence near x = 0.04 of a SC phase having a maximum T c of 4.15 K at x = 0.08. [5] The Cu x TiSe 2 system provides an ideal opportunity to investigate the microscopic details of quantum (T ∼ 0) phase transitions between CDW order and SC. It is of particular interest to clarify the nature of the "soft mode" in CDW/SC transitions: the behavior of the soft mode -i.e., the phonon mode whose eigenvector mimics the CDW lattice distortion, and hence whose frequency tends towards zero at the second-order phase transition -is one of the most fundamental and well-studied phenomena associated with classical (thermally driven) displacive phase transitions;[11] on the other hand, soft mode behavior associated with quantum phase transitions is not well understood. In this investigation, we use Raman scattering to study the temperature-and dopingdependent evolution of the CDW 'amplitude' modes in Cu x TiSe 2 . The CDW amplitude mode [12] -which is associated with collective transverse fluctuations of the CDW order parameter -offers detailed information regarding the evolution and stability of the CDW state and the CDW soft mode. In this study, we show that the amplitude mode frequency in Cu x TiSe 2 exhibits identical power-law scaling with the reduced temperature, T/T CDW , and the reduced Cu content, x/x c , indicating that mode softening in Cu x TiSe 2 is independent of the control parameter used to approach the CDW transition. Further, we show that 'quantum' (T ∼ 0) softening of the CDW amplitude mode is consistent with a quantum critical point hidden in the superconductor phase of Cu x TiSe 2 , suggesting a possible connection between quantum criticality and superconductivity.Raman scattering measurements were performed on high quality single-crystal and pressed-pellet samples of Cu x TiSe 2 for x = ...

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Quantum and Classical Mode Softening Near the Charge-Density-Wave–Superconductor Transition ofCuxTiSe2

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“…Typical examples include quasi-one-dimensional (quasi-1D) K 2 Pt(CN) 4 [15], blue bronzes [16], and transition-metal trichalcogenides [17,18], as well as quasi-2D transition-metal dichalcogenides [19,20] and rare-earth tritellurides [21]. In the classical explanation first introduced by Peierls [22], CDW transitions are understood as arising from the presence of a pair of nearly parallel Fermi surfaces, known as Fermi-surface nesting (FSN), which causes the dielectric response of conduction electrons to diverge at the nesting wave vector q n .…”

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confidence: 99%

Charge density waves and phonon-electron coupling inZrTe3

Zheng

Ren

et al. 2015

Phys. Rev. B

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Charge-density-wave (CDW) order has long been interpreted as arising from a Fermi-surface instability in the parent metallic phase. While phonon-electron coupling has been suggested to influence the formation of CDW order in quasi-two-dimensional (quasi-2D) systems, the presumed dominant importance of Fermi-surface nesting remains largely unquestioned in quasi-1D systems.Here we show that phonon-electron coupling is also important for the CDW formation in a model quasi-1D system ZrTe 3 . Our joint experimental and computational study reveals that particular lattice vibrational patterns possess exceedingly strong coupling to the conduction electrons, and are directly linked to the lattice distortions associated with the CDW order. The dependence of the coupling matrix elements on electron momentum further dictates the opening of (partial) electronic gaps in the CDW phase. Since lattice distortions and electronic gaps are the defining signatures of CDW order, our result demonstrates that the conventional wisdom based on Fermisurface geometry needs to be substantially supplemented by phonon-electron coupling even in the simplest quasi-1D case. As prerequisites for the CDW formation, the highly anisotropic electronic structure and strong phonon-electron coupling in ZrTe 3 give rise to a distinct Raman scattering effect, namely, measured phonon linewidths depend on the direction of momentum transfer in the scattering process.

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Terahertz Electrodynamics in Transition Metal Oxides

Prajapati

Dagar

et al. 2019

Advanced Optical Materials

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The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/adom.201900958. 2−y 2 , d z 2 ) levels. [35] The splitting of the d-orbital was successfully explained by the crystal field theory. The ground state properties of these materials are mainly governed by the two interactions; i) the electron correlations (U) and, ii) SOC (λ) in the crystal field split narrow bands. [36] Among d electron systems, electrons in 3d TMOs experiences large electron correlations due to localized nature of 3d orbitals. The idea of electron-electron interaction was given by Sir N. F. Mott in 1949. It originated from the fact that the NiO was expected to be a metal according to the band theory, while the experiments showed insulating behavior. [37][38][39][40][41] This disagreement of experiments with the theory was explained by Hubbard who attributed the insulating state to the splitting

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Raman Spectroscopy of Soft Modes at the Charge-Density-Wave Phase Transition in2H−NbSe2

Cited by 100 publications

References 12 publications

Quantum and Classical Mode Softening Near the Charge-Density-Wave–Superconductor Transition ofCuxTiSe2

Quantum and Classical Mode Softening Near the Charge-Density-Wave–Superconductor Transition ofCuxTiSe2

Charge density waves and phonon-electron coupling inZrTe3

Terahertz Electrodynamics in Transition Metal Oxides

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