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

Abstract

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 = ...

77Se and63Cu NMR studies of the electronic correlations in CuxTiSe2(x= 0.05, 0.07)

“…This is corroborated by the temperature-independent Hall coefficient R H observed in heavily Cu-doped samples [11]. Raman scattering measurements as a function of doping suggest that the x-dependent mode softening is associated with the reduction of electron-phonon couplings and the presence of a quantum critical point within the superconducting region [12].…”

Pressure Induced Superconductivity in Pristine1T−TiSe2

“…These features are reminiscent of a quantum critical scenario, signifying the presence of quantum fluctuations around a critical pressure of 3 GPa. This would complement the quantum critical point recently suggested for Cu-intercalated material, Cu x TiSe 2 , near x ¼ 0:07 at ambient pressure [8].…”

“…The parallels with several families of materials where the superconducting dome has been discovered in the vicinity of purely electronic ordered phase, dressing the quantum critical point [16][17][18] strengthen the viewpoint of excitonic superconductivity in 1T-TiSe 2 . On the other hand, the continuous development of the soft phonon mode in the vicinity of the CDW transition, both in Cu-intercalated and pure and pressurized material [8,34,35], suggests that the lattice deformation may not be regarded as a secondary effect that simply follows the electronic ordering. The soft phonon mode, generally regarded as unfavorable for superconductivity within the weak-coupling BCS single-phonon exchange picture, has been identified as helpful in several instances for higher values of the electron-phonon coupling [36][37][38][39].…”

“…The superconductivity in those compounds is thought to be tightly related to neighboring antiferromagnetic ordering, with superconductivity appearing around a (purely electronic) quantum critical point (QCP) [16,18]. On the other hand the case of 1T-TiSe 2 signals the possibility of a novel state, where superconductivity emerges around a new type of quantum critical point, unrelated to magnetic degrees of freedom [4,8].…”

“…The nature in which superconductivity and other types of electronic order combine continues to remain an ongoing puzzle. Recent findings of superconductivity in copper-intercalated 1T-TiSe 2 triggered a great deal of activity [1][2][3][4][5][6][7][8] due to the possible connection between the superconductivity and the charge-density wave (CDW) state [9][10][11], and especially as the latter has been proposed as an example of an exciton condensate [12][13][14]. The superconductivity in Cu x TiSe 2 was found to arise as the CDW state melts with doping, in a region confined around a critical doping [1].…”