Multiband Electronic Raman Scattering in Bilayer Superconductors

Abstract

A theory of electronic Raman scattering in the presence of several energy bands crossing the Fermi surface is developed. The contributions to the light scattering cross section are calculated for each band and it is shown that the cross section can be written in terms of the sum of the single band contributions and a mixing term which only contributes to the fully symmetric channels $(A_{1g})$. Particular emphasis is placed on screening in bilayer superconductors. Since any charge fluctuation with long range character in real space is screened by the Coulomb interaction, the relevant fluctuations in a single layer case are induced between different parts of the Fermi surface. In a single band $d$-wave superconductor the scattering at energy transfer twice the maximum gap ${\Delta }_{max}$ is dominated by those parts of the Fermi surface where ${\Delta }^2(\mathbf{k})$ is largest. As a consequence, the fully symmetric ($A_{1g}$) scattering is screened. In the case of a bilayer superconductor however, the charge transfer is possible between layers inside the unit cell. Therefore a formalism is considered which is valid for general band structure, superconducting energy gaps, and inter-layer hopping matrix elements. The spectra is calculated for La 2:1:4 and Y 1:2:3 as representative single and bilayer superconductors. The mixing term is found to be negligible and thus the response is well approximated by the sum of the contributions from the individual bands. The theory imposes strong constraints on both the magnitude and symmetry of the energy gap for the bilayer cuprates, and indicates that a nearly identical energy gap of $d_{x^2-y^2}$ symmetry provides a best fit to the data. However, the $A_{1g}$ part of the spectrum depends sensitively on many parameters.

Previous version has been changed to include a more general discussion of the role of band structure, energy gap, and Raman vertex harmonics on the resulting Raman spectra in unconventional superconducting bilayers. A previous numerical error for the A1g spectra is remedied and readdressed. Two additional figures are included. 14 pages Revtex + 8 Figures.

References in corpus (2)

• LDA energy bands, low-energy Hamiltonians, t', t'', t_{perp}(k), and J_{perp}
• Antiferromagnetic Excitations and Van Hove Singularities in YBa${}_2$Cu${}_3$O${}_{6+x}$

Cited by in corpus (23)

• Inelastic Light Scattering From Correlated Electrons
• Evolution of Magnetic and Superconducting Fluctuations with Doping of High-Tc Superconductors
• Directly characterizing the relative strength and momentum dependence of electron-phonon coupling using resonant inelastic x-ray scattering
• Evolution of Superconductivity in Electron-Doped Cuprates: Magneto-Raman Spectroscopy
• Pinpointing Gap Minima in Ba(Fe${}_{0.94}$Co${}_{0.06}{)}_2$As${}_2$ \textit{via} Band Structure Calculations and Electronic Raman Scattering
• c-axis Raman Scattering in MgB2: Observation of a Dirty-Limit Gap in the pi-bands
• A balancing act: Evidence for a strong subdominant d-wave pairing channel in $\mathrm{B}{\mathrm{a}}_{0.6}{\mathrm{K}}_{0.4}\mathrm{F}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2$
• Anisotropic quasiparticle lifetimes in Fe-based superconductors
• Collective $d-$wave Excitonic Modes in the Fe-Superconductors
• Evolution of Magnetic and Superconducting Fluctuations with Doping of High-Tc Superconductors (An electronic Raman scattering study)
• Probing the pairing symmetry of the iron pnictides with electronic Raman scattering
• Conservation laws, vertex corrections, and screening in Raman spectroscopy
• Electronic Raman Scattering in Superconducting Cuprates
• Electronic Raman scattering in a multiband model for cuprate superconductors
• Fluctuations and pairing in Fe-based superconductors: Light scattering experiments
• Signatures of a momentum independent pseudogap in the electronic density of states and Raman spectroscopy of the underdoped cuprates
• Many-body physics-induced selection rules: application to Raman spectroscopy
• The effect of disorder on electronic Raman scattering in the superconducting state of iron pnictides
• Low energy inelastic response in the superconducting phases of $PrO{s}_{4}S{b}_{12}$
• Electronic Raman Scattering in Nearly Antiferromagnetic Fermi Liquids
• Collective Modes and Electronic Raman Scattering in the Cuprates
• Raman response in superconducting multiorbital systems with application to nickelates
• Raman response of collective modes in multicomponent superconductors