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 formulae 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 formulae 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, w_{+} and w_{-} 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 w_{+-} modes does not have 2pi periodicity along the q_{z}c direction. The w_{+} mode loses spectral weight at inplane momentum q_{||}=(0,0) at q_{z}c=2n pi with n being integer whereas the w_{-} mode has no spectral weight at q_{z}c=0 for any q_{||} but acquires sizable spectral weight at q_{z}c=2n pi with n \ne 0. Both w_{+-} modes are gapped at q_{||}=(0,0). When q_{z}c is away from 2n pi, the w_{+-} modes show striking behavior. When the intrabilayer hopping t_z is relatively small (large), the w_{-} (w_{+}) mode becomes gapless at q_{||}=(0,0) whereas the w_{+} (w_{-}) mode retains the gap. However, when the interbilayer hopping integral t_{z}' is taken into account, the gapless mode acquires a gap at q_{||}=(0,0) and both w_{+-} 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.

arXiv comment50 pages, 18 figures

References in corpus (54)

• A Common Thread: the pairing interaction for the unconventional superconductors
• Long-range incommensurate charge fluctuations in (Y,Nd)Ba2Cu3O(6+x)
• LDA energy bands, low-energy Hamiltonians, t', t'', t_{perp}(k), and J_{perp}
• d-wave superconductivity and Pomeranchuk instability in the two-dimensional Hubbard model
• Charge ordering in the electron-doped superconductor Nd2-xCexCuO4
• Charge-density-wave order with momentum $(2Q,0)$ and $(0,2Q)$ within the spin-fermion model: continuous and discrete symmetry breaking, preemptive composite order, and relation to pseudogap in hole-doped cuprates
• One-band tight-binding model parametrization of the high-$T_c$ cuprates, including the effect of $k_z$-dispersion
• Dynamical charge density fluctuations pervading the phase diagram of a Cu-based high-Tc superconductor
• Instability toward Formation of Quasi-One-Dimensional Fermi Surface in Two-Dimensional t-J Model
• Possible Quasi-One-Dimensional Fermi Surface in La_{2-x}Sr_{x}CuO_4
• Three dimensional collective charge excitations in electron-doped cuprate superconductors
• Dispersive charge density wave excitations and temperature dependent commensuration in Bi2Sr2CaCu2O8+δ
• Asymmetry of collective excitations in electron and hole doped cuprate superconductors
• High-energy spin and charge excitations in electron-doped copper oxide superconductors
• Electronic Collective Modes and Superconductivity in Layered Conductors
• Charge-density-waves and superconductivity as an alternative to phase separation in the infinite-U Hubbard-Holstein model
• Charge Order in the Pseudogap Phase of Cuprate Superconductors
• Doping dependent charge order correlations in electron-doped cuprates
• Bond order instabilities in a correlated two-dimensional metal
• Cascade of phase transitions in the vicinity of a quantum critical point
• Detection of Acoustic Plasmons in Hole-Doped Lanthanum and Bismuth Cuprate Superconductors Using Resonant Inelastic X-Ray Scattering
• Spin-Fluctuation-Driven Nematic Charge-Density-Wave in Cuprate Superconductors: Impact of Aslamazov-Larkin-Type Vertex Correction
• Direct observation of bulk charge modulations in optimally-doped Bi${}_{1.5}$Pb${}_{0.6}$Sr${}_{1.54}$CaCu${}_2$O${}_{8+\delta }$
• Spectroscopic Evidence for Charge Order Melting via Quantum Fluctuations in a Cuprate
• Direct observation of charge order in underdoped and optimally doped Bi${}_2$(Sr,La)${}_2$CuO${}_{6+\delta }$ by resonant inelastic x-ray scattering
• Possible charge instabilities in two-dimensional doped Mott insulators
• Doping Dependence of Bilayer Resonant Spin Excitations in $(\mathbf{Y},\mathbf{Ca})\mathbf{B}{\mathbf{a}}_2\mathbf{C}{\mathbf{u}}_3{\mathbf{O}}_{6+\mathbf{x}}$
• Two resonant magnetic modes in an overdoped high-${\mathbf{T}}_{\mathbf{c}}$ superconductor
• Doping evolution of the charge excitations and electron correlations in electron-doped superconducting La${}_{2-x}$Ce${}_x$CuO${}_4$
• Coupling between dynamic magnetic and charge-order correlations in the cuprate superconductor Nd${}_{2-x}$Ce${}_x$CuO${}_4$
• Plasmon excitations in layered high-Tc cuprates
• Acoustic plasmons and conducting carriers in hole-doped cuprate superconductors
• Signature of quantum criticality in cuprates by charge density fluctuations
• Observation of a dispersive charge mode in hole-doped cuprates using resonant inelastic x-ray scattering at the oxygen K edge
• Temperature-dependent ellipsometry measurements of partial Coulomb energy in superconducting cuprates
• The nature of effective interaction in cuprate superconductors: a sign-problem-free quantum Monte-Carlo study
• Origin of the high-energy charge excitations observed by resonant inelastic x-ray scattering in cuprate superconductors
• Gapped collective charge excitations and interlayer hopping in cuprate superconductors
• Unusual dynamic charge-density-wave correlations in HgBa${}_2$CuO${}_{4+\delta }$
• Evolution of plasmon excitations across the phase diagram of the cuprate superconductor La${}_{2-x}$Sr${}_x$CuO${}_4$
• A strong coupling critique of spin fluctuation driven charge order in underdoped cuprates
• Close inspection of plasmon excitations in cuprate superconductors
• A unified theory of spin and charge excitations in high-$T_c$ cuprates: Quantitative comparison with experiment and interpretation
• Dual structure in the charge excitation spectrum of electron-doped cuprates
• Identification of a Critical Doping for Charge Order Phenomena in Bi-2212 Cuprates via RIXS
• Superconductivity from charge order in cuprates
• Plasmon dispersion in bilayer cuprate superconductors
• $d$-wave bond-order charge excitations in electron-doped cuprates
• Impact of electron correlations on two-particle charge response in electron- and hole-doped cuprates
• Probing the bulk plasmon continuum of layered materials through electron energy loss spectroscopy in a reflection geometry
• Doping dependence of d-wave bond-charge excitations in electron-doped cuprates
• Competition between spin-induced charge instabilities in underdoped cuprates
• Low-energy plasmon excitations in infinite-layer nickelates
• Spin and bond-charge excitation spectra in correlated electron systems near antiferromagnetic phase

Cited by in corpus (8)

• Out-of-phase Plasmon Excitations in the Trilayer Cuprate Bi${}_2$Sr${}_2$Ca${}_2$Cu${}_3$O${}_{10+\delta }$
• Ghost Josephson plasmon in bilayer superconductors
• Strong-coupling theory of bilayer plasmon excitations
• Theoretical perspectives on charge dynamics in high-temperature cuprate superconductors
• Beyond on-site Hubbard interaction in charge dynamics of cuprate superconductors
• Interplay of orbital-selective Mott criticality and flat-band physics in La${}_3$Ni${}_2$O${}_6$
• Strongly correlated model of acousticlike plasmons persisting across the phase diagram of cuprate superconductors
• Observation of correlated plasmons in low-valence nickelates