M. R. Norman

Quantum spin liquids form a novel class of matter where, despite the existence of strong exchange interactions, spins do not order down to the lowest measured temperature. Typically, these occur in lattices that act to frustrate the appearance of magnetism. In two dimensions, the classic example is the kagome lattice composed of corner sharing triangles. There are a variety of minerals whose transition metal ions form such a lattice. Hence, a number of them have been studied and were then subsequently synthesized in order to obtain more pristine samples. Of particular note was the report in 2005 by Dan Nocera's group of the synthesis of herbertsmithite, composed of a lattice of copper ions sitting on a kagome lattice, which indeed does not order down to the lowest measured temperature despite the existence of a large exchange interaction of 17 meV. Over the past decade, this material has been extensively studied, yielding a number of intriguing surprises that have in turn motivated a resurgence of interest in the theoretical study of the spin $1/2$ Heisenberg model on a kagome lattice. This Colloquium reviews these developments and then discusses potential future directions, both experimental and theoretical, as well as the challenge of doping these materials with the hope that this could lead to the discovery of novel topological and superconducting phases.

Although nineteen years have passed since the discovery of high temperature cuprate superconductivity 1 Bednorz, JG and Müller, KA. 1986. Z. Phys. B, 64: 189[Crossref] , [Google Scholar], there is still no consensus on its physical origin. This is in large part because of a lack of understanding of the state of matter out of which the superconductivity arises. In optimally and underdoped materials, this state exhibits a pseudogap at temperatures large compared to the superconducting transition temperature 2 Warren, WW Jr., Walstedt, RE, Brennert, GF, Cava, RJ, Tycko, R, Bell, R and Dabbagh, G. 1989. Phys. Rev. Lett., 62: 1193[Crossref], [PubMed], [Web of Science ®] , [Google Scholar], 3 Alloul, H, Ohno, T and Mendels, P. 1989. Phys. Rev. Lett., 63: 1700[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]. Although discovered only three years after the pioneering work of Bednorz and Müller, the physical origin of this pseudogap behavior and whether it constitutes a distinct phase of matter is still shrouded in mystery. In the summer of 2004, a band of physicists gathered for five weeks at the Aspen Center for Physics to discuss the pseudogap. In this perspective, we would like to summarize some of the results presented there and discuss the importance of the pseudogap phase in the context of strongly correlated electron systems. The pseudogap: friend or foe of high T c ?All authorsM. R. Norman, D. Pines & C. Kallinhttps://doi.org/10.1080/00018730500459906Published online:19 February 2007Table Download CSVDisplay Table