High-precision measurement of the Ferrell-Glover-Tinkham sum rule in a cuprate high-temperature superconductor

The Ferrell-Glover-Tinkham (FGT) sum rule in superconductors defines the superfluid density, rho s, as the optical conductivity spectral weight (SW) that transfers into a delta function at omega = 0 due to the opening of the energy gap below Tc. In high-Tc superconductors, strong electron-boson coupling, self-energy effects, and intertwining of energy scales can link rho s to various high-energy processes, making the question of whether or not the FGT sum rule is valid in cuprates, and at what energy scale, central to a full understanding of the pairing mechanism. Here, we report high-precision measurements of the FGT sum rule in near-optimally doped DyBa2Cu3O7-delta thin films. We resolve the low-energy balance of SW by combining submillimeter-microwave interferometry, terahertz time-domain spectroscopy, and infrared ellipsometry to independently obtain the real and imaginary parts of the complex dielectric function between 0.8 meV and 1.1 eV (6-9000 cm-1). By applying a Kramers-Kronig consistency analysis to the measured spectra we find that the FGT sum rule is obeyed, and the total intraband SW is conserved to within +/- 0.2% below an energy scale similar to 0.6 eV. We attribute specific anomalies observed in the conductivity spectra below similar to 0.6 eV to coupling of charge carriers to the spectrum of collective antiferromagnetic spin fluctuations. The procedure presented here, applied to near-optimally doped DyBa2Cu3O7-delta, lays out a protocol for how the FGT sum rule should be studied in other doping levels and compounds.