0428同步年報-2021-全

Physics and Materials Science 009 W hen doped with holes or electrons, cuprates at low temperatures can be tuned from a Mott insulating phase to a superconducting phase and then to a Fermi- liquid phase. In addition, an enigmatic pseudogap phase exists in the underdoped regime of hole-doped cuprates above superconductivity transition temperature T C with crossing temperature T *, which decreases monotonically when the doping is increased. Several symmetry-breaking orders such as charge-density waves (CDW) have also been discovered in cuprates with comparable onset temperatures. Charge fluctuations are among the most fundamental collective excitations in matter. CDW in cuprate superconductors have attracted renewed interest, but their mechanism and competition with superconductivity remain subjects of vigorous discussion. Upon tuning a non-thermal parameter through a critical value, quantum phase transitions occur at the absolute zero of temperature T . The putative quantum-critical point (QCP) in a cuprate holds the key to understanding many profound phenomena related to its superconductivity. In approaching a QCP, two quantum states of the system can exchange their energy ordering. As a result, a CDW state can be intertwined with the superconducting state. Also, because the energy difference is small, switching back and forth between CDW and superconducting ground states is energetically likely, resulting in quantum charge fluctuations. Previous studies proposed that the charge-density fluctuations permeate through a broad region of the cuprate phase diagram, but a crucial task in the scenario of the presence of QCP is to identify the ordered phases that terminate at the QCP. Herein, Atsushi Fujimori (Waseda University, Japan), Chien-Te Chen (NSRRC), and Di-Jing Huang (NSRRC) and their teams presumed the ordered phases to be the CDW order and sought evidence for the QCP associated with the CDW in the superconducting phase. Inelastic X-ray scattering probes charge fluctuations on measuring dynamical structure factor S( q , ω) , which is the space and time Fourier transformation of the density-density correlation function. Because O K-edge resonant inelastic X-ray scattering (RIXS) probes particular characteristics of the dynamical charge fluctuations of CDW, although additionally modulated by the effects of RIXS matrix elements, light polarization and orbital characters, they performed high-resolution O K-edge RIXS measurements and theoretical calculations through a diagrammatic framework to investigate the quantum fluctuations of charge order in superconducting cuprate La 2−x Sr x CuO 4 (LSCO) near the optimal doping. The O K-edge RIXS measurements were conducted with the AGM-AGS spectrometer at TPS 41A of the Taiwan Photon Source. The especially constructed AGM-AGS beamline is based on the energy compensation principle of grating dispersion. The ultra-high energy resolution allows collection of high-resolution RIXS data with energy resolution 16 meV at incident photon energy 530 eV. To unveil the charge instability and the coupling between CDW fluctuations and phonons in LSCO, Fig. 1(a) presents a series of maps of temperature-dependent RIXS intensity distribution in the plane of energy loss vs in-plane momentum transfer q || along (π, 0); Fig. 1(b) shows those maps after the subtraction of elastic scattering. There exists a pronounced excitation feature of energy about 14 meV in the neighborhood of q CDW . This low-energy RIXS excitation appears to shift away from q CDW when the thermal energy approaches the excitation energy. This condition reflects that, at low temperatures, the low-energy RIXS excitation is dominated by charge-density fluctuations and its contribution from the coupling of CDW to acoustic phonons increases with increasing temperature. RIXS measures other phonon excitations in addition to that pronounced low-energy feature. The electron-phonon coupling involved with states near the Fermi level is weak for the apical mode; the contribution of apical phonons to RIXS can be neglected. The RIXS spectra were fitted with three components for high-energy phonons, i.e. , bond-stretching, A 1g buckling, and B 1g buckling phonons, which plot fitted spectra of q || = 0.23 and 0.16 at 24 K, respectively. The observed phonon softening also agreed with the calculation. Their curve-fitting results show that these phonons all exhibit the strongest softening at q || = (0.25, 0) rather than q CDW , supporting the scenario of discommensurate CDW in LSCO at doping level x = 0.15. Although the RIXS measurement was performed only on a sample near optimal doping, quantum-critical scalings of charge fluctuations in the temperature domain were clearly demonstrated. These results are consistent with speculation Evidence for a Quantum-Critical Scaling Associated with Charge Order Elucidating the role of charge order in cuprates provides evidence for quantum-critical scaling and discommensurations associated with charge order.