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

Physics – Condensed Matter – Strongly Correlated Electrons

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11 pages, 9 figures

Scientific paper

10.1103/PhysRevB.74.155115

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.

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