Holographic Superconductor/Insulator Transition at Zero Temperature

We analyze the five-dimensional AdS gravity coupled to a gauge field and a charged scalar field. Under a Scherk-Schwarz compactification, we show that the system undergoes a superconductor/insulator transition at zero temperature in 2+1 dimensions as we change the chemical potential. By taking into account a confinement/deconfinement transition, the phase diagram turns out to have a rich structure. We will observe that it has a similarity with the RVB (resonating valence bond) approach to high-Tc superconductors via an emergent gauge symmetry.Comment: 25 pages, 23 figures; A new subsection on a concrete string theory embedding added, references added (v2); Typos corrected, references added (v3

Magnetism and its microscopic origin in iron-based high-temperature superconductors

High-temperature superconductivity in the iron-based materials emerges from, or sometimes coexists with, their metallic or insulating parent compound states. This is surprising since these undoped states display dramatically different antiferromagnetic (AF) spin arrangements and N$\rm \acute{e}$el temperatures. Although there is general consensus that magnetic interactions are important for superconductivity, much is still unknown concerning the microscopic origin of the magnetic states. In this review, progress in this area is summarized, focusing on recent experimental and theoretical results and discussing their microscopic implications. It is concluded that the parent compounds are in a state that is more complex than implied by a simple Fermi surface nesting scenario, and a dual description including both itinerant and localized degrees of freedom is needed to properly describe these fascinating materials.Comment: 14 pages, 4 figures, Review article, accepted for publication in Nature 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 In two dimensions in particular, standard methods such as the Random Phase Approximation are no longer valid since they predict a finite temperature antiferromagnetic phase transition prohibited by the Mermin-Wagner theorem.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

Doping dependence of spin excitations and its correlations with high-temperature superconductivity in iron pnictides

In conventional Bardeen-Cooper-Schrieffer (BCS) superconductors, superconductivity occurs when electrons form coherent Cooper pairs below the superconducting transition temperature Tc. Although the kinetic energy of paired electrons increases in the superconducting state relative to the normal state, the reduction in the ion lattice energy is sufficient to give the superconducting condensation energy. For iron pnictide superconductors derived from electron or hole doping of their antiferromagnetic (AF) parent compounds, the microscopic origin for supercnductivity is unclear. Here we use neutron scattering to show that high-Tc superconductivity only occurs for iron pnictides with low-energy itinerant electron-spin excitation coupling and high energy spin excitations. Since our absolute spin susceptibility measurements for optimally hole-doped iron pnictide reveal that the change in magnetic exchange energy below and above Tc can account for the superconducting condensation energy, we conclude that the presence of both high-energy spin excitations giving rise to a large magnetic exchange coupling J and low-energy spin excitations coupled to the itinerant electrons is essential for high-Tc superconductivity in iron pnictides.Comment: 9 pages, 4 figures in the main article; 11 pages, 13 figures in the supplementary material