Theory of charge dynamics in bilayer electron system with long-range Coulomb interaction

Abstract

We perform a comprehensive study of charge excitations in a bilayer electron system in the presence of the long-range Coulomb interaction (LRC). Our major point is to derive formulas of the LRC that fully respect the bilayer lattice structure. This is an extension of the LRC obtained by Fetter in the electron-gas model 50 years ago and can now be applicable to any electron density. We then provide general formulas of the charge susceptibility in the random phase approximation and study them numerically. The charge ordering tendency is not found and instead we find two plasmon modes: ${\ensuremath{\omega}}_{+}$ and ${\ensuremath{\omega}}_{\ensuremath{-}}$ modes. Our second major point is to elucidate their spectral weight distribution and the effect of electron tunneling between the layers. The spectral weight of the ${\ensuremath{\omega}}_{\ifmmode\pm\else\textpm\fi{}}$ modes does not have $2\ensuremath{\pi}$ periodicity along the ${q}_{z}c$ direction; ${q}_{z}$ and $c$ are momentum and the lattice constant along the $z$ direction, respectively. The ${\ensuremath{\omega}}_{+}$ mode loses spectral weight at in-plane momentum ${\mathbf{q}}_{\ensuremath{\parallel}}=(0,0)$ at ${q}_{z}c=2n\ensuremath{\pi}$ with $n$ being integer whereas the ${\ensuremath{\omega}}_{\ensuremath{-}}$ mode has no spectral weight at ${q}_{z}c=0$ for any ${\mathbf{q}}_{\ensuremath{\parallel}}$ but acquires sizable spectral weight at ${q}_{z}c=2n\ensuremath{\pi}$ with $n\ensuremath{\ne}0$. Both ${\ensuremath{\omega}}_{\ifmmode\pm\else\textpm\fi{}}$ modes are gapped at ${\mathbf{q}}_{\ensuremath{\parallel}}=(0,0)$. When ${q}_{z}c$ is away from $2n\ensuremath{\pi}$, the ${\ensuremath{\omega}}_{\ifmmode\pm\else\textpm\fi{}}$ modes show striking behavior. When the intrabilayer hopping ${t}_{z}$ is relatively small (large), the ${\ensuremath{\omega}}_{\ensuremath{-}}$ (${\ensuremath{\omega}}_{+}$) mode becomes gapless at ${\mathbf{q}}_{\ensuremath{\parallel}}=(0,0)$ whereas the ${\ensuremath{\omega}}_{+}$ (${\ensuremath{\omega}}_{\ensuremath{-}}$) mode retains the gap. However, when the interbilayer hopping integral ${t}_{z}^{\ensuremath{'}}$ is taken into account, the gapless mode acquires a gap at ${\mathbf{q}}_{\ensuremath{\parallel}}=(0,0)$ and both ${\ensuremath{\omega}}_{\ifmmode\pm\else\textpm\fi{}}$ modes are gapped at any ${q}_{z}c$. To highlight the special feature of the LRC, we also clarify a difference to the case of a short-range interaction. While the strong electron correlation effects are not included, the present theory captures available data of the charge excitations observed by resonant inelastic x-ray scattering for Y-based cuprate superconductors.

Topics & Concepts