The Two Component Optical Conductivity in the Cuprates: A Necessary Consequence of Preformed Pairs

TL;DR

This paper explains the two-component optical conductivity in underdoped cuprates as a natural result of preformed pairs, consistent with experiments and grounded in a robust theoretical framework that extends BCS theory.

Contribution

It demonstrates that the two-component conductivity arises from non-condensed pairs in the pseudogap phase, providing a fundamental explanation consistent with experimental observations.

Findings

Presence of Drude and MIR peaks in conductivity spectra

MIR peak linked to pair-breaking energy

Analytical proof of the f-sum rule validity

Abstract

We address how the finite frequency real conductivity $\sigma(\omega)$ in the underdoped cuprates is affected by the pseudogap, contrasting the behavior above and below $T_c$. The f-sum rule is analytically shown to hold. Here we presume the pseudogap is associated with non-condensed pairs arising from stronger-than-BCS attraction. This leads to both a Drude and a mid infrared (MIR) peak, the latter associated with the energy needed to break pairs. These general characteristics appear consistent with experiment. Importantly, there is no more theoretical flexibility (phenomenology) here than in BCS theory; the origin of the two component conductivity we find is robust.