Conductivity in Pseudogapped Superconductors: The Role of the Fermi Arcs

TL;DR

This paper calculates the dc conductivity in pseudogapped high-temperature superconductors, emphasizing the importance of the effective carrier number's temperature dependence over lifetime effects, and clarifies the secondary role of Fermi arcs.

Contribution

It introduces a gauge-invariant theoretical calculation of conductivity that includes new terms and highlights the dominant role of carrier number temperature dependence.

Findings

Temperature dependence of effective carrier number is crucial for conductivity behavior.

Fermi arcs play a secondary role in transport properties.

Results align with experimental observations in under- and over-doped regimes.

Abstract

We calculate the dc conductivity $\sigma$ in a pseudogapped high $T_c$ superconductor within a theory which is consistent with gauge invariance. Our results contain additional terms beyond those identified previously. Although it has been thought that lifetime effects dominate the $T$ dependence of transport, here we show (consistent with growing experimental support) that the temperature dependence of the effective carrier number $(n/m(T))_{\rm{eff}}$ plays a critical role and thereby leads to the contrasting behavior between over and under-doped regimes. The role of Fermi arcs is secondary.