The idea has emerged in recent years that the physical properties of several strongly correlated electron systems emerge from a competition between different types of states, usually including various types of charge and spin density order on several length scales. Many materials of much current interest are inhomogeneous at the nanoscale as a consequence of this competition. The inhomogeneities appear to be intrinsic, but intentionally adding impurities can lead to a better understanding of their ground state properties. A qualitatively new phenomenon, static or slowly fluctuating nanoscale inhomogeneities driven by interactions, arises in these compounds and its study is emerging as a fundamental new research area called "Complexity in Strongly Correlated Electronic Systems".
COLOSSAL MAGNETORESISTANCE MANGANITES:
The study of manganites is an exciting area of research in the transition metal oxide field. The reasons for this excitement are(i) the colossal magnetoresistance(CMR) effect which could lead to applications,(ii) the complex phase diagram, with spin/charge/orbital ordered in exotic arrangements, and(iii) the presence of inhomogeneities even in the best available crystals predicted by theory to be the cause of the CMR effect. The evidence for inhomogeneous states has been documented in books and reviews, and on the experimental side it is simply overwhelming. Jahn-Teller distortions and polaron formation play a key role, leading to the formation of large structures near the metal-insulator transitions where the CMR is the largest. Many workshops have been organized in the area of manganites, yet its relation with inhomogeneities in other compounds has not been addressed. On the theory front, models of mobile eg-electrons interacting with localized t(2g)-spins and with Jahn-Teller phonons, have been widely used to analyze manganite properties using many approximations. Electronic phase separation in combination with quenched disorder have been proposed as the origin of the curious magnetotransport properties of these compounds. Computational studies have played an important role in the development of these ideas. Percolative effects have been discussed extensively.
HIGH TEMPERATURE SUPERCONDUCTORS:
Shortly after the discovery of high temperature superconductivity in ceramic samples of the cuprates, many suggestions were made that the new materials were intrinsically inhomogeneous, and even that superconductivity itself depended on the existence of unusual defect structures. Most of these ideas were laid aside when single crystals, particularly of YBCO, were produced. More recently, however, new experiments probing local microscopic order have revealed, at least in some materials, nanoscale inhomogeneities in both spin and charge sectors. It is important to recognize that these states are probably not present simply because of the usual difficulties of preparing high quality samples of complex materials, but may represent a fundamentally new type of quantum-mechanical ordering driven by the competition between spin exchange, kinetic energy, and long-range Coulomb interactions.
Recently, inhomogeneous nanoscale structures have been identified using STM techniques on optimally doped BSCCO, with a superconducting gap that fluctuates spatially following an approximate bimodal distribution. These STM results represent a challenge to the theory community since it is necessary to understand how disorder and interactions conspire to produce different types of inhomogeneities. Some fascinating open questions to be addressed at the miniprogram include:(1) Are inhomogeneities intrinsic to the cuprates? (2) In what general circumstances do stripe-like or patchy structures form? (3) Are the current microscopic models for transition metal oxides sufficient to explain the observed phenomena?(4) Is there a relationship between the anisotropy of the pairing in momentum space and the observed inhomogeneity in real space?
WHY A KITP PROGRAM IS NEEDED:
Theorists that have been working on several distinct and complex materials systems(cuprate high-Tc superconductors and colossal magnetoresistivity manganites in particular) have been grappling with related issues, but working largely independently. Cross fertilization between these areas has been slow, in part because each has a complex phenomenology that is usually fully appreciated only be experts. We believe that only a KITP program in which experts in these areas have opportunities to confront different conceptual frameworks and approximation schemes in detailed discussions, will enable these barriers to be surmounted.
The miniprogram will bring together theorists and experimentalists working in all aspects of this area of investigations. The theorists must stay for the three weeks of the miniprogram, while the experimentalists will rotate every week with approximately 5 visiting per week. The entire size of the miniprogram will approximately be 20-25 people every week. For miniprograms of this short length, the KITP does not provide funding for a conference. However, seminars will be frequent(hopefully at the rate of two 1-hour talks every day). Of course, interactions outside the lecture room in the relaxed KITP environment will be the main goal of the program.
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