Strong-coupling theory of bilayer plasmon excitations

TL;DR

This work develops a strong-coupling, large-$N$ theory for bilayer plasmon excitations in cuprates by applying a bilayer $t$-$J$-$V$ model with lattice long-range Coulomb interactions. The authors compute the charge-response function $\chi({\bf q},\omega)$ via a 14-component bosonic field and show that two plasmon branches $\omega_{+}$ and $\omega_{-}$ emerge, with their dispersions and spectral weights highly dependent on interlayer hopping $t_z$, interbilayer hopping $t_z^{\prime}$, and Coulomb strength $V_c$. Despite the fundamentally different theoretical framework from weak-coupling RPA, the plasmon dispersions and intensity maps closely resemble those obtained in prior studies, with the notable distinction that strong correlations suppress particle-hole continua and stabilize the modes over wider momentum ranges. The work also identifies a rich dependence of the mode structure on $V_c$, including a transition toward zero-sound behavior in the $V_c\to 0$ limit and an inverted energy ordering of the two modes for large $t_z$, offering a potential interpretation for Y-based cuprate RIXS data and guiding future experiments to map ${\bf q}$-space in bilayer cuprates.

Abstract

Recently plasmon excitations in bilayer lattice systems were studied extensively in the weak-coupling regime. Unlike single-layer systems, these bilayers exhibit two distinct modes, $ω_{\pm}$, which show characteristic dependences upon the momentum and hopping integrals along the $z$ direction. To apply them to cuprates, strong correlation effects should be considered, but a comprehensive analysis has not yet been investigated. In this work, we present a strong-coupling theory to analyze the charge dynamics of a bilayer system, utilizing the $t$-$J$-$V$ model, which includes the long-range Coulomb interaction, $V$, on a lattice. Although our theoretical framework is fundamentally different from the weak-coupling approach, we find that resulting plasmon excitations are similar to those of a weak-coupling theory. A key distinction is that our strong-coupling framework reveals a noticeable suppression of particle-hole excitations, which allows the plasmon modes to remain well-defined over a wider region of momentum. We suggest that the experimentally reported plasmon excitations in Y-based cuprates can be described by the $ω_{-}$ mode, although we call for more systematic experiments to verify this.

Figures (15)

• Figure 1: Schematic of the bilayer lattice and corresponding hopping integrals. Each layer forms a square lattice with lattice constant $a$; $d$ is the intrabilayer distance and $c$ is the lattice constant along the $z$ direction.
• Figure 2: (a) Bare fermionic $G^{(0)}_{\alpha \beta}$ and bosonic $D^{(0)}_{ab}$ propagators, solid and dashed lines, respectively. (b) $\Lambda_{\alpha\beta,a}$ and $\Lambda_{\alpha\beta,ab}$ are the three- and four-legs vertices, respectively. (c) $\Pi_{ab}$ is the bosonic self-energy. (d) Double dashed line is the dressed bosonic propagator $D_{ab}$.
• Figure 3: Intensity map of charge excitation spectrum $\log_{10} | {\rm Im}\chi({\bf q}, \omega)|$ in the plane of in-plane momentum ${\bf q}_{\parallel}$ and energy transfer $\omega$. The white dotted curve represents the upper boundary of the particle-hole continuum excitations. The strong intensity corresponds to plasmon modes.
• Figure 4: Intensity maps of $\log_{10} | {\rm Im}\chi({\bf q}, \omega)|$ for a sequence of $q_{z}$ around a region of ${\bf q}_{\parallel}=(0,0)$ for $t_{z}=0.1t$: (a) $q_{z}=0$, (b) $q_{z}=0.5\pi$, (c) $q_{z}=\pi$, (d) $q_{z}=1.5\pi$, and (e) $q_{z}=2\pi$. The white dotted curve denotes the upper boundary of the particle-hole continuum. It goes to zero at ${\bf q}_{\parallel} =(0,0)$ and $q_{z}=0$ in (a).
• Figure 5: $q_{z}$ dependence of $\omega_{+}$ mode (higher energy) and $\omega_{-}$ mode (lower energy) at (a) ${\bf q}_{\parallel}=(0.02\pi, 0)$ and (b) ${\bf q}_{\parallel}=(0.05\pi, 0)$ for $t_{z}=0.1t$. The white dotted line is the upper boundary of the continuum spectrum and exhibits a sharp drop at $q_{z}=0$ because of the vanishing of the $\omega_{-}$ mode there.