Theory Of Metal Insulator Transition In Strongly Correlated Electron Systems

Proceedings of the NATO Advanced Research Workshop, Bled, Slovenia, 26-30 April 2000

The properties of strongly correlated electrons confined in two dimensions are a forefront area of modern condensed matter physics. In the past two or three decades, strongly correlated electron systems have garnered a great deal of scientific interest due to their unique and often unpredictable behavior. Two of many examples are the metallic state and the metal–insulator transition discovered in 2D semiconductors: phenomena that cannot occur in noninteracting systems. Tremendous efforts have been made, in both theory and experiment, to create an adequate understanding of the situation; however, a consensus has still not been reached. Strongly Correlated Electrons in Two Dimensions compiles and details cutting-edge research in experimental and theoretical physics of strongly correlated electron systems by leading scientists in the field. The book covers recent theoretical work exploring the quantum criticality of Mott and Wigner–Mott transitions, experiments on the metal–insulator transition and related phenomena in clean and dilute systems, the effect of spin and isospin degrees of freedom on low-temperature transport in two dimensions, electron transport near the 2D Mott transition, experimentally observed temperature and magnetic field dependencies of resistivity in silicon-based systems with different levels of disorder, and microscopic theory of the interacting electrons in two dimensions. Edited by Sergey Kravchenko, a prominent experimentalist, this book will appeal to advanced graduate-level students and researchers specializing in condensed matter physics, nanophysics, and low-temperature physics, especially those involved in the science of strong correlations, 2D semiconductors, and conductor–insulator transitions.

The physics of materials with strongly correlated electrons is one of the most exciting topics of present-day theoretical and experimental solid-state research. A wide variety of interesting phenomena, among them metal-insulator transitions, the giant and colossal magnetoresistance effect and heavy-fermion behavior, can be attributed to electronic correlations. One focus of current research is on transition metals and especially transition metal oxides due to the diversity of correlation phenomena found in these systems. In this thesis, the physics of strongly correlated transition metal oxide systems is investigated with the LDA+DMFT approach. This method combines the advantages of the local density approximation (LDA), which provides a realistic ab initio description for many materials, with the correct treatment of the local correlations within dynamical mean-field theory (DMFT). The self-consistent equations of the DMFT are solved with an auxiliary-field quantum Monte Carlo algorithm. In particular, the metallic and insulating phase of V2O3 and the peculiarities of its metal-insulator transition are explored. Furthermore, the strongly correlated metals SrVO3 and CaVO3 are studied, as well as LiV2O4 which is the first d-electron system found to exhibit heavy-fermion behavior. Where possible, the theoretical results are compared with recent experimental data.

This is the second in a series of miniworkshops and Adriatico conferences devoted to the exciting field of strongly correlated electron systems including quantum Hall effect, metal insulator transition, heavy fermions and high Tc superconductivity. In spite of enormous efforts made by physicists worldwide to solve these difficult problems, many important issues are still widely open and this topic remains the most active field in condensed matter physics. The review talks and reports on original research given by the experts in the field represent a state-of-the-art summary of this fast-moving field.

Since the discovery of high Tc superconductivity, the role of electron correlation on superconductivity has been an important issue in condensed matter physics. Here the role of electron correlation in metals is explained in detail on the basis of the Fermi liquid theory. The book, originally published in 2004, discusses the following issues: enhancements of electronic specific heat and magnetic susceptibility, effects of electron correlation on transport phenomena such as electric resistivity and Hall coefficient, magnetism, Mott transition and unconventional superconductivity. These originate commonly from the Coulomb repulsion between electrons. In particular, superconductivity in strongly correlated electron systems is discussed with a unified point of view. This book is written to explain interesting physics in metals for undergraduate and graduate students and researchers in condensed matter physics.

I study the Mott metal-insulator transition within the dynamical mean-field theory in two schematic Hamiltonians widely used to describe the strongly correlated electron systems : the Hubbard model and the periodic Anderson model. The scenario for the transition in the Hubbard model is reviewed and the analysis of the photoemission spectra near the transition is presented in detail. The doping driven Mott transition in the periodic Anderson model is discussed with respect to the one realized in the Hubbard model. The main finding is a qualitatively different scenario for electron or hole driven transitions. In the former case the transition is expectedly similar to the first order transition of the Hubbard model. However, in the latter case, a second order transition is found. Thus I demonstrate that the transition scenario of the Hubbard model is not generic for the periodic Anderson model.

The volume contains the lectures delivered at the XIV Training Course in the Physics of Strongly Correlated Systems, held in Vietri sul Mare (Salerno) Italy, in October 2009. The project of the meeting was to promote the formation of young scientists by means of training through research. These features are reflected in the book: the lectures are up-to-date monographs of relevant subjects in the field of Condensed Matter Physics. Contributions include: Electronic Structure of Strongly Correlated Materials (Electronic structure calculations in one-electron approximation; Hubbard model in Dynamical Mean-Field Theory (DMFT); Electronic structure calculations for real materials by LDA+DMFT method); Computational Studies of Quantum Spin Systems (Quantum spin models, their ground states and quantum phase transitions; Classical phase transitions, Monte Carlo simulations, and finite-size scaling; Exact diagonalization methods; Quantum Monte Carlo simulations and the Stochastic Series Expansion method; Survey of related computational methods); Dynamical Mean-Field Theory of Electronic Correlations in Models and Materials (Mean-field theories for many-body systems; Lattice fermions in the limit of high dimensions; Dynamical mean-field theory for correlated lattice fermions; The Mott-Hubbard Metal-Insulator Transition; Electronic correlations and disorder; Theory of electronic correlations in materials; Kinks in the dispersion of strongly correlated electron systems).

When many particles come together how do they organize themselves? And what destroys this organization? Combining experiments and theory, this book describes intriguing quantum phases - metals, superconductors and insulators - and transitions between them. It captures the excitement and the controversies on topics at the forefront of research.