Temperature Dependence of the Conductivity Sum Rule in the Normal State due to Inelastic Scattering

Abstract

We examine the temperature dependence of the optical sum rule in the normal state due to interactions. To be concrete we adopt a weak coupling approach which uses an electron-boson exchange model to describe inelastic scattering of the electrons with a boson, in the Migdal approximation. While a number of recent works attribute the temperature dependence in the normal state to that which arises in a Sommerfeld expansion, we show that in a wide parameter regime this contribution can be quite small. Instead, most of the temperature dependence arises from the zeroth order term in the `expansion', through the temperature dependence of the spectral function, and the interaction parameters contained therein. For low boson frequencies this circumstance causes a linear T-dependence in the sum rule. We develop some analytical expressions and understanding of the temperature dependence.

11 pages, 9 figures

References in corpus (6)

• Sum rules and energy scales in the high-temperature superconductor YBa2Cu3O6+x
• Optical-conductivity sum rule in cuprates and unconventional charge density waves: a short review
• Impurity effects on optical response in a finite band electronic system coupled to phonons
• Effect of orbital currents on the restricted optical sum rule
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Cited by in corpus (6)

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• Energetics of superconductivity in the two dimensional Hubbard model
• Robustness of the optical-conductivity sum rule in Bilayer Graphene
• Impact of a finite cut-off for the optical sum rule in the superconducting state
• Observation of the charge density wave collective mode in the infrared optical response of VSe${}_2$
• Optical Sum Rule anomalies in the High-Tc Cuprates