The discovery in 1986 of superconductivity at high critical temperatures (Tc’s above the boiling point of liquid nitrogen, 77 K) in the cuprate materials [1] came as something of a surprise in a field where the successful theory of superconductivity by Bardeen, Cooper and Schrieffer (BCS) predicted an upper limit for Tc of about 30 K. The purity of a superconductor allows it to be described as in either the dirty or clean limit – here the clean limit is where the mean free path of the free carriers in the normal state is much larger than the superconducting coherence length (size of the superconducting pairs); the opposite is true in the dirty limit. Despite their untidy nature, the high-temperature superconductors are described as being in the clean limit; however, from an optics point of view, they look like they are in the dirty limit. With only a single band at the Fermi level, strong frequency renormalization is necessary to describe the optical properties. The recent discovery of superconductivity at elevated temperatures in the iron-based materials [2] offers some insight: these are multiband materials with a minimum of two bands at the Fermi level – one with a large mean free path, while the other mean free path is relatively short, allowing this material to simultaneously exist in both the clean and dirty limits [3]. The superconducting energy gaps in the iron-based materials are mostly isotropic. However, the superconducting energy gap in the cuprates is momentum dependent, with nodes at the Fermi level, implying the coherence length is also momentum dependent. The possibility of multiple length scales allows the cuprates to appear as if they are also in both the clean and dirty limit.

The talk will begin with a general introduction to superconductivity and the key elements of the BCS theory, followed by a discussion of the optical properties of metals and superconductors, including the definition of the clean and dirty limit. The experimental details for determining the optical properties of solids will be described; examples for the cuprate Bi2Sr2CaCu2O8+ and the iron-based material FeTe0.55Se0.45 will be presented. Common elements, such as scaling behavior [4], will be discussed in terms of the clean and dirty limit response, with implications for a mechanism.

References:
[1] J. G. Bednorz and K. A. Müller, Z. Phys. B 64, 189 (1986).
[2] Y. Kamihara, T. Watanabe, M. Hirano, and H. Hosono, J. Am. Chem. Soc. 130, 3296 (2008).
[3] C. C. Homes et al., Phys. Rev. B 91, 144503 (2015).
[4] C. C. Homes et al., Nature 430, 539 (2004).