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Book Description
This proposal is for theoretical work on strongly correlated electron systems, which are at the center of experimental and theoretical activities in condensed-matter physics. The interest to this field is driven fascinating variety of observed effects, universality of underlying theoretical ideas, and practical applications. I propose to do research on Iron-based superconductors (FeSCs), which currently attract high attention in the physics community. My goal is to understand superconductivity and magnetism in these materials at various dopings, the interplay between the two, and the physics in the phase in which magnetism and superconductivity co-exist. A related goal is to understand the origin of the observed pseudogap-like behavior in the normal state. My research explores the idea that superconductivity is of electronic origin and is caused by the exchange of spin-fluctuations, enhanced due to close proximity to antiferromagnetism. The multi-orbital/multi-band nature of FeSCs opens routes for qualitatively new superconducting states, particularly the ones which break time-reversal symmetry. By all accounts, the coupling in pnictdes is below the threshold for Mott physics and I intend to analyze these systems within the itinerant approach. My plan is to do research in two stages. I first plan to address several problems within weak-coupling approach. Among them: (i) what sets stripe magnetic order at small doping, (ii) is there a preemptive instability into a spin-nematic state, and how stripe order affects fermions; (iii) is there a co-existence between magnetism and superconductivity and what are the system properties in the co-existence state; (iv) how superconductivity emerges despite strong Coulomb repulsion and can the gap be s-wave but with nodes along electron FSs, (v) are there complex superconducting states, like s+id, which break time reversal symmetry. My second goal is to go beyond weak coupling and derive spin-mediated, dynamic interaction between fermions, understand what sets the upper scale for attractive interaction, compute T_c, and then obtain and solve matrix non-linear gap equation for spin-mediated pairing and study various feedbacks from the pairing on fermions on ARPES spectra, optical and thermal conductivity, and other observables, The problems I have chosen are quite generic, and the understanding of magnetically-mediated superconductivity in the strong-coupling regime will not only advance the theory of superconductivity in FeSCs, but will contribute to a generic understanding of the pairing of fermions near quantum-critical points -- the problems ranging from s-wave pairing by soft optical phonons to to color superconductivity of quarks mediated by a gluon exchange.