Conservation laws, vertex corrections, and screening in Raman spectroscopy

Abstract

We present a microscopic theory for the Raman response of a clean multiband superconductor accounting for the effects of vertex corrections and long-range Coulomb interaction. The measured Raman intensity, $R(\Omega )$, is proportional to the imaginary part of the fully renormalized particle-hole correlator with Raman form-factors $\gamma (\vec{k})$. In a BCS superconductor, a bare Raman bubble is non-zero for any $\gamma (\vec{k})$ and diverges at $\Omega =2\Delta +0$, where $\Delta$ is the largest gap along the Fermi surface. However, for $\gamma (\vec{k})=$ const, the full $R(\Omega )$ is expected to vanish due to particle number conservation. It was long thought that this vanishing is due to the singular screening by long-range Coulomb interaction. We argue that this vanishing actually holds due to vertex corrections from the same short-range interaction that gives rise to superconductivity. We further argue that long-range Coulomb interaction does not affect the Raman signal for $any$ $\gamma (\vec{k})$. We argue that vertex corrections eliminate the divergence at $2\Delta$ and replace it with a maximum at a somewhat larger frequency. We also argue that vertex corrections give rise to sharp peaks in $R(\Omega )$ at $\Omega <2\Delta$, when $\Omega$ coincides with the frequency of one of collective modes in a superconductor, e.g, Leggett mode, Bardasis-Schrieffer mode, or an excitonic mode.

19pp; 8figs; References to more old work added

References in corpus (9)

• Magnetism, superconductivity, and pairing symmetry in Fe-based superconductors
• Inelastic Light Scattering From Correlated Electrons
• Observation of Leggett's collective mode in a multi-band MgB2 superconductor
• Nature and Raman signatures of the Higgs amplitude mode in the coexisting superconducting and charge-density-wave state
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• Probing the pairing interaction and multiple Bardasis-Schrieffer modes using Raman spectroscopy
• Theory of Raman scattering from Leggett's collective mode in a multiband superconductor: Application to MgB${}_2$
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• Contribution of Collective Excitations to Third Harmonic Generation in Multiband Superconductors: the case of MgB${}_2$
• Following the Higgs mode across the BCS-BEC crossover in two dimensions
• Linear optical response from the odd parity Bardasis-Schrieffer mode in locally non-centrosymmetric superconductors
• Fluctuations and pairing in Fe-based superconductors: Light scattering experiments
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• Comment on: Calculation of an Enhanced $A_{1g}$ Symmetry Mode Induced by Higgs Oscillations in the Raman Spectrum of High-Temperature Cuprate Superconductors
• Linear spectroscopy of collective modes and the gap structure in two-dimensional superconductors
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• Quasiparticle scattering in a superconductor near a nematic critical point: resonance mode and multiple attractive channels
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