Optical integral and sum-rule violation in high-Tcsuperconductors

Abstract

The purpose of this work is to investigate the role of the lattice in the optical Kubo sum rule in the cuprates. We compute conductivities, optical integrals W , and ∆W between superconducting and normal states for 2-D systems with lattice dispersion typical of the cuprates for four different models -a dirty BCS model, a single Einstein boson model, a marginal Fermi liquid model, and a collective boson model with a feedback from superconductivity on a collective boson. The goal of the paper is two-fold. First, we analyze the dependence of W on the upper cut-off (ωc) placed on the optical integral because in experiments W is measured up to frequencies of order bandwidth. For a BCS model, the Kubo sum rule is almost fully reproduced at ωc equal to the bandwidth. But for other models only 70%-80% of Kubo sum rule is obtained up to this scale and even less so for ∆W , implying that the Kubo sum rule has to be applied with caution. Second, we analyze the sign of ∆W . In all models we studied ∆W is positive at small ωc, then crosses zero and approaches a negative value at large ωc, i.e. the optical integral in a superconductor is smaller than in a normal state. The point of zero crossing, however, increases with the interaction strength and in a collective boson model becomes comparable to the bandwidth at strong coupling. We argue that this model exhibits the behavior consistent with that in the cuprates.

Effects of the Fermi-surface shrinking on the optical sum rule in pnictides

“…The corresponding variation of the spectral weight W (ω c ) as a function of the temperature is reported in the inset, showing an overall reduction of about 10 %. Note that such a variation is an order of magnitude larger than the one expected in a single-band system for the same coupling value, even when the presence of a finite bandwidth 24,25 and a finite cut-off 26,27 are taken into account. Quite remarkably this temperature variation is as large as the one observed in cuprate superconductors, where it has been interpreted as a consequence of strong correlations.…”

Energetics of superconductivity in the two-dimensional Hubbard model

“…[68][69][70][71][72] Unfortunately, the value of the optical spectral weight depends on the frequency up to which the conductivity is integrated, and the appropriate upper cutoff may be different in the normal and superconducting state; 23,24 also even if the conduction band contribution to the optical sum rule could be determined, the relation between this and the kinetic energy is only approximate, and the errors involved in the approximation may be different in the normal and superconducting state. 25 As can be seen from Fig. 4, the temperature dependent changes are only on the 1% level.…”

“…Another important class of theoretical approaches involves phenomenological spin-fermion models. [19][20][21][22][23][24][25] In these approaches it is assumed that the important physics arises from the interaction of electrons with spin fluctuations (treated as bosons but with boson self-energy effects arising from coupling to fermions playing a crucial role). These models are amenable to semi-analytic treatment.…”

Superconductivity-induced optical anomaly in an iron arsenide

“…In spite of numerous studies (for a comprehensive list of references see ref. 7 ), no modification of interband optical transitions in the superconducting state has been directly identified in the cuprates. Instead, the observed superconductivity-induced anomalies in the optical response of highly conducting CuO 2 planes were found to be confined to the energy range corresponding to transitions within the conduction band below the plasma edge.…”