# Colloquia

**Colloquium**

Friday, April 29, 2016

3:30 PM

Physics Building, Room 204

## "30 years of high Tc: Superfluid and normal-fluid densities in the cuprate superconductors"

**David Tanner , University of Florida**

[Host: Seunghun Lee]

It was in April 1986 when Bednorz and Mueller of the IBM Zürich laboratories sent a paper about “possible high-Tc superconductivity” to *Zeitschrift für Physik* B. The resulting bombshell changed condensed-matter physics forever. Experimenters and theorists developed methods to measure and calculate in ways that were much improved over prior years. However, despite 30 years of intense study, the description of these materials remains incomplete. I’ll discuss the discovery of the high Tc cuprates from the perspective of a participant. I’ll then turn to what infrared spectroscopy can tell us about their properties. Measurements for a number of cuprate families of optical reflectance over a wide spectral range (far-infrared to ultraviolet) have been analyzed using Kramers-Kronig analysis to obtain the optical conductivity, *s*(*w*), and (by integration of the real part of the conductivity) the spectral weight of low- and mid-energy excitations. For the Kramers-Kronig analysis to give reliable results, accurate high-frequency extrapolations, based on x-ray atomic scattering functions, were used. When the optical conductivities of the normal and superconducting states are compared, a transfer of spectral weight from finite frequencies to the zero-frequency delta-function conductivity of the superconductor is seen. The strength of this delta function gives the superfluid density, *r**s*. There are two ways to measure *r**s*, using either the low energy spectral weight or by examination of the imaginary part, *s*2(*w*); both estimates show that 98% of the *ab*-plane superfluid density comes from low energy scales, below about 0.15 eV. Moreover, there is a notable difference between clean metallic superconductors and the cuprates. In the former, the superfluid density is essentially equal to the conduction electron density. The cuprates, in contrast, have only about 20% of the *ab*-plane low-energy spectral weight in the superfluid. The rest remains in finite-frequency, midinfrared absorption. In underdoped materials the superfluid fraction is even smaller. The consequences of this observation for the electronic structure will be addressed.

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