The pseudogap: friend or foe of high Tc?

Although nineteen years have passed since the discovery of high temperature superconductivity, 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. Although discovered only three years after the pioneering work of Bednorz and Muller, 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 its importance in the context of strongly correlated electron systems.Comment: expanded version, 20 pages, 11 figures, to be published, Advances in Physic

Two-Particle-Self-Consistent Approach for the Hubbard Model

Even at weak to intermediate coupling, the Hubbard model poses a formidable challenge. In two dimensions in particular, standard methods such as the Random Phase Approximation are no longer valid since they predict a finite temperature antiferromagnetic phase transition prohibited by the Mermin-Wagner theorem. The Two-Particle-Self-Consistent (TPSC) approach satisfies that theorem as well as particle conservation, the Pauli principle, the local moment and local charge sum rules. The self-energy formula does not assume a Migdal theorem. There is consistency between one- and two-particle quantities. Internal accuracy checks allow one to test the limits of validity of TPSC. Here I present a pedagogical review of TPSC along with a short summary of existing results and two case studies: a) the opening of a pseudogap in two dimensions when the correlation length is larger than the thermal de Broglie wavelength, and b) the conditions for the appearance of d-wave superconductivity in the two-dimensional Hubbard model.Comment: Chapter in "Theoretical methods for Strongly Correlated Systems", Edited by A. Avella and F. Mancini, Springer Verlag, (2011) 55 pages. Misprint in Eq.(23) corrected (thanks D. Bergeron

DNA barcoding in pencilfishes (lebiasinidae: nannostomus) reveals cryptic diversity across the brazilian Amazon

Nannostomus is comprised of 20 species. Popularly known as pencilfishes the vast majority of these species lives in the flooded forests of the Amazon basin and are popular in the ornamental trade. Among the lebiasinids, it is the only genus to have undergone more than one taxonomic revision. Even so, it still possesses poorly defined species. Here, we report the results of an application of DNA barcoding to the identification of pencilfishes and highlight the deeply divergent clades within four nominal species. We surveyed the sequence variation in the mtDNA cytochrome c oxidase subunit I gene among 110 individuals representing 14 nominal species that were collected from several rivers along the Amazon basin. The mean Kimura-2-parameter distances within species and genus were 2% and 19,0%, respectively. The deep lineage divergences detected in N. digrammus, N. trifasciatus, N. unifasciatus and N. eques suggest the existence of hidden diversity in Nannostomus species. For N. digrammus and N. trifasciatus, in particular, the estimated divergences in some lineages were so high that doubt about their conspecific status is raised.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES