Lattice, spin, and charge excitations in cuprates

Tracking doping evolution of elementary excitations is a crucial approach to understand the complex phenomena exhibited in cuprates. In the first part of my talk, I will discuss the role of the lattice in the quasi-one-dimensional edge-sharing cuprate Y$_{\mathrm{2+x}}$Ca$_{\mathrm{2-x}}$Cu$_{5}$O$_{10}$ [1]. Using O K-edge RIXS, we resolve site-dependent harmonic phonon excitations of a 70 meV mode. Coupled with theory, this provides a direct measurement of electron-lattice coupling strength. We show that such electron-lattice coupling causes doping-dependent distortions of the Cu-O-Cu bond angle, which sets the intra-chain spin exchange interactions. In the second part of my talk, I will discuss collective excitations in the electron-doped superconducting cuprate, Nd$_{\mathrm{2-x}}$Ce$_{\mathrm{x}}$CuO$_{4}$ [2] observed using Cu L-edge RIXS. Surprisingly, despite the fact that the spin stiffness is zero and the AFM correlations are short-ranged, magnetic excitations harden significantly across the AFM-HTSC phase boundary, in stark contrast with the hole-doped cuprates. Furthermore, we found an unexpected and highly dispersive mode emanating from the zone center in superconducting NCCO that is undetected in the hole-doped compounds. This may signal a quantum phase distinct from superconductivity. Thus, our results indicate an asymmetry of the collective excitations in electron- and hole-doped cuprates, providing a new perspective on the doping evolution of the cuprate ground state. \\[4pt] [1] W. S. Lee \textit{et al., }Phys. Rev. Lett. \textbf{110}, 265502 (2013).\\[0pt] [2] W. S. Lee \textit{et al., }arXiv: 1308. 4740.