Out-of-phase Plasmon Excitations in the Trilayer Cuprate Bi$_2$Sr$_2$Ca$_2$Cu$_3$O$_{10+\delta}$

TL;DR

This study uses resonant inelastic x-ray scattering to investigate out-of-phase plasmon excitations in a trilayer cuprate superconductor, revealing layer-dependent charge dynamics and a nearly $q_z$-independent plasmon mode.

Contribution

It provides the first detailed characterization of out-of-phase plasmon modes in a trilayer cuprate, showing how layer stacking influences collective charge excitations.

Findings

Identified a nearly $q_z$-independent plasmon mode with a 300 meV gap.

Observed the $ ext{omega}_-$ mode where outer layers oscillate out of phase.

Found the acoustic mode's intensity diminishes near zero momentum.

Abstract

Within a homologous series of cuprate superconductors, variations in the stacking of CuO$_2$ layers influence the collective charge dynamics through the long-range Coulomb interactions. We use O $K$-edge resonant inelastic x-ray scattering to reveal plasmon excitations in the optimally-doped trilayer Bi$_2$Sr$_2$Ca$_2$Cu$_3$O$_{10+\delta}$. The observed plasmon exhibits nearly $q_z$-independent dispersion and a large excitation gap of approximately 300 meV. This mode is primarily ascribed to the $\omega_{-}$ mode, where the charge density on the outer CuO$_2$ sheets oscillates out of phase while the density in the inner sheet remains unaltered at $q_z=0$. The intensity of the acoustic $\omega_3$ mode is relatively weak and becomes vanishingly small near $(q_x, q_y)=(0, 0)$. This result highlights a qualitative change in the eigenmode of the dominant low-energy plasmon with the number of CuO$_2$ layers.