Unique Charge-density-wave Order and Fluctuation-induced Phonon Softening in the Optimally-doped Trilayer Cuprate Bi${}_2$Sr${}_2$Ca${}_2$Cu${}_3$O${}_{10+\delta }$

S. Nakata, K. Yamamoto, J. Okamoto +11

Charge-density-wave (CDW) order is a ubiquitous feature of cuprate superconductors that competes with superconductivity. However, its behavior remains poorly understood in trilayer…