The Physics of Correlated Insulators, Metals, and Superconductors

A naive distinction between metals and insulators rests on the single-electron picture: completely filled or empty bands characterize insulators while metals have some partially filled bands. Nature, however, offers a much richer variety of behaviors: Mott insulators would be band metals in the absence of electron correlation while strongly-correlated metals behave quasiparticle-like only in the Fermi-liquid regime. Correlated metals and insulators can be distinguished by the gap in the spectral function. Superconductors form a class of their own, they have a single-electron gap but are not insulators. This year’s school addresses the rich physics of correlated insulators, metals, and superconductors. Insulators show complex ordering phenomena involving charge, spin, and orbital degrees of freedom. Correlated metals exhibit non-Fermi-liquid behavior except right at the Fermi surface. Superconductors are dominated by the delicate interplay of coupling bosons and quasiparticles. Along with the phenomena, the models and methods for understanding and classifying them will be explained. The aim of the school is to introduce advanced graduate students and up to the modern approaches for modeling strongly correlated materials and analyzing their behavior. A school of this size and scope requires support and help from many sources. We are very grateful for all the financial and practical support we have received. The Institute for Advanced Simulation at the Forschungszentrum Jülich and the Jülich Supercomputer Centre provided the major part of the funding and were vital for the organization of the school and the production of this book. The Institute for Complex Adaptive Matter (ICAM) offered travel grants for selected international speakers and participants. The nature of a school makes it desirable to have the lecture notes available when the lectures are given. This way students get the chance to work through the lectures thoroughly while their memory is still fresh. We are therefore extremely grateful to the lecturers that, despite tight deadlines, provided their manuscripts in time for the production of this book. We are confident that the lecture notes collected here will not only serve the participants of the school but will also be useful for other students entering the exciting field of strongly correlated materials. We are grateful to Mrs. H. Lexis of the Verlag des Forschungszentrum Jülich and to Mrs. L.Weidener of the Grafische Betriebe for providing their expert support in producing the present volume on a tight schedule. We heartily thank our students and postdocs who helped with proofreading the manuscripts, often on quite short notice: Julian Mußhoff, Esmaeel Sarvestani, Amin Kiani Sheikhabadi, and Qian Zhang. Finally, our special thanks go to Dipl.-Ing. R. Hölzle for his invaluable advice on the innumerable questions concerning the organization of such an endeavor, and to Mrs. L. Snyders for expertly handling all practical issues