Journal
PHYSICAL REVIEW B
Volume 74, Issue 15, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.74.155115
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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 that 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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