Metal Insulator Transition In Two Dimensional Electron Systems

The interplay between strong electron-electron interactions and disorder has been a long-standing question in condensed matter physics. The discovery of the metal-insulator transition (MIT) in two-dimensional (2D) electron systems challenged one of the most influential theories of the last century which stated that "there is no true metallic state in 2D". However, the scaling theory of localization did not account for interactions between electrons. This book provides recent thermodynamic and transport experimental findings which indicate that MIT in 2D can be considered as a quantum phase transition. In the ballistic regime, strong interactions between carriers lead to Pauli spin susceptibility growing critically at low electron densities. Such behavior is characteristic in the close vicinity of a phase transition. In the immediate vicinity of the MIT, both the resistance and the effective interactions exhibit a fan-like spread as the MIT is crossed. A resistance-interaction flow diagram clearly reveals a quantum critical point. The book should be especially useful to graduate students, postdoctoral researches, or scientists working in the field of mesoscopic physics.

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.

Metal-insulator transitions (MITs) remain one of the unresolved science problems of condensed-matter physics, which are rather general and of fundamental importance. In the vicinity of the MITs, the behavior is found to be unconventional and exotic. This complexity makes it difficult to recognize the dominant degrees of freedom, resulting in a plethora of theoretical viewpoints based on very different ideas. First we study the transport behavior and the dielectric response near Mott Metal-Insulator transition (MIT) using the Iterative Perturbation Theory (IPT), which is exact at the atomic limit at half-filling, for the single-band Hubbard model supplemented by percolation theory. We successfully interpret the experimental observation of a colossal peak of the dielectric function near the Mott MIT in organic material $\\\\kappa\\\\text{-(BEDT-TTF)}_2\\\\text{Cu}_2\\\\text{(CN)}_3$. Our results suggest the diverging feature of dielectric response comes from percolation effects near a first-order MIT, where metallic and insulator domains present simultaneously as long as the materials have defects or impurities. Our findings suggest a similar 'dielectric catastrophe' in many other correlated materials and can explain previous observations that were assigned to multiferroicity or ferroelectricity. Second we summarize both experimental and theoretical observations of the criticality around the Mott transition, in three types of systems: 2-dimensional electron gas (2DEG) in Si-MOSFE, Mott organic material ($\\\\kappa\\\\text{-(BEDT-TTF)}_2\\\\text{Cu}_2\\\\text{(CN)}_3$), and transition metal dichalcogenide (TMD) moire bilayer $\\\\text{MoTe}_2/\\\\text{WSe}_2$. Particularly, we find robust resistivity maxima are clearly seen in all these materials. We then use dynamical mean field theory (DMFT) and 'hybrid' DMFT correspondingly to show that dielectric response can be used to identify the origin of these resistivity maxima. We find that near the MIT, it corresponds to the percolation effect within the (spatially inhomogeneous) metal-insulator phase coexistence region, where a colossal enhancement of the dielectric response has been found. Deep in the metallic phase, it signals the thermal destruction of coherent quasiparticles due to strong correlation effects, and a dramatic drop and a change of sign in the dielectric constant would be found. Third we study the disorder dominated MIT in TMD moiré bilayer. In this material, a long-range geometric moiré pattern emerges when two atomically thin materials are misaligned or have a lattice mismatch. This drastically reduces the electronic kinetic energy, paving the way for new strongly correlated phases. We proposed a minimal theoretical model describing the interplay of interactions and disorder, which is solved at DMFT + coherent potential approximation (CPA) level. The results capture most experimental trends at almost a perfect level. We investigate the quantum criticality near MIT with a fully occupied flat band (f=2), which is found to be in a disorder-dominated regime. Finally, we consider long-range Coulomb interaction in low band filling cases, where one expects Wigner crystallization to occur. To investigate the nontrivial electronic phases appearing away from commensurate fillings, we first used the spinless Hartree method to calculate the total free energy, and then we used DMFT and Kubo formula to obtain the transport behavior. We find that, for most fillings, an amorphous charge-ordered metallic state - the electron slush - appears in strongly correlated TMD hetero-bilayers. Our results suggest performing transport and Scanning Tunneling Microscopy (STM) experiments on TMD hetero-bilayers to study the interplay between doping a Wigner-Mott insulator and amorphous charge order.

A comprehensive theory of the correlation driven metal insulator transition in 1D and 2D strongly correlated electron systems is given. In both the 1D and 2D Hubbard model the metal insulator transition encountered close to half filling is of Pokrovsky-Talapov type. An important consequence of this in the 2D Hubbard model is the break down of the Fermi liquid theory. We also describe in detail the properties of the Pokrovsky-Talapov transition in 2D ferroelectrics.

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.

This is a second edition of a classic book. Written by the late, great Sir Nevill Mott (Britain's last Nobel Prize winner for Physics), Metal Insulator Transitions has been greatly updated and expanded to further enhance its already enviable reputation.

Little do we reliably know about the Mott transition, and we are far from a complete understanding of the metal --insulator transition due to electr- electron interactions. Mott summarized his basic ideas on the subject in his wonderful book Metal--Insulator nansitions that first appeared in 1974 11. 1). In his view, a Motk insulator displays a gap for charge-carrying excitations due to electron cowelations, whose importance is expressed by the presence of local magnetic moments regardless of whether or not they are ordered. Since the subject is far from being settled, different opinions on specific aspects of the Mott transition still persist. This book naturally embodies my own understanding of the phenomenon, inspired by the work of the late Sir Kevill Mott. The purpose of this book is twofold: first, to give a detailed presen- tion of the basic theoretical concopts for Mott insulators and, second, to test these ideas against the results from model calculations. For this purpose the Hubbard model and some of its derivatives are best suited. The Hubbard model describes a Mott transition with a mere minimum of tunable par- eters, and various exact statements and even exact solutions exist in certain limiting cases. Exact solutions not only allow us to test our basic ideas, but also help to assess the quality of approxin~ate theories for correlated electron systems.

The metal-insulator transition due to electron-electron interactions is one of the most celebrated but least understood problems in condensed matter physics. Here this subject is comprehensively reviewed for the first time since Sir Nevill Mott's monograph of 1990. A pedagogical introduction to the basic concepts for the Mott transition, the Hubbard model, and various analytical approaches to correlated electron systems is presented. A new classification scheme for Mott insulators as Mott-Hubbard and Mott-Heisenberg insulators is proposed. Traditional methods are critically examined for their potential to describe the Mott transition. This book will make an excellent reference for scientists researching in the field of electron transport in condensed matter.