Download or read book Mass Term Effect on Fractional Quantum Hall States of Dirac Particles written by Kouki Yonaga and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the high-precision analysis of ground states and low-energy excitations in fractional quantum Hall states formed by Dirac electrons, which have attracted a great deal of attention. In particular the author focuses on the physics of fractional quantum Hall states in graphene on a hexagonal boron nitride substrate, which was recently implemented in experiments. The numerical approach employed in the book, which uses an exact numerical diagonalization of an effective model Hamiltonian on a Haldane's sphere based on pseudopotential representation of electron interaction, provides a better understanding of the recent experiments. The book reviews various aspects of quantum Hall effect: a brief history, recent experiments with graphene, and fundamental theories on integer and fractional Hall effects. It allows readers to quickly grasp the physics of quantum Hall states of Dirac fermions, and to catch up on latest research on the quantum Hall effect in graphene.
Download or read book Mass Term Effect on Fractional Quantum Hall States of Dirac Particles written by Kouki Yonaga and published by Springer Nature. This book was released on 2022-01-24 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the high-precision analysis of ground states and low-energy excitations in fractional quantum Hall states formed by Dirac electrons, which have attracted a great deal of attention. In particular the author focuses on the physics of fractional quantum Hall states in graphene on a hexagonal boron nitride substrate, which was recently implemented in experiments. The numerical approach employed in the book, which uses an exact numerical diagonalization of an effective model Hamiltonian on a Haldane’s sphere based on pseudopotential representation of electron interaction, provides a better understanding of the recent experiments. The book reviews various aspects of quantum Hall effect: a brief history, recent experiments with graphene, and fundamental theories on integer and fractional Hall effects. It allows readers to quickly grasp the physics of quantum Hall states of Dirac fermions, and to catch up on latest research on the quantum Hall effect in graphene.
Download or read book Fractional Quantum Hall Effects New Developments written by Bertrand I Halperin and published by World Scientific. This book was released on 2020-06-09 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fractional quantum Hall effect has been one of the most active areas of research in quantum condensed matter physics for nearly four decades, serving as a paradigm for unexpected and exotic emergent behavior arising from interactions. This book, featuring a collection of articles written by experts and a Foreword by Klaus von Klitzing, the discoverer of quantum Hall effect and winner of 1985 Nobel Prize in physics, aims to provide a coherent account of the exciting new developments and the current status of the field.
Download or read book Quantum Hall Effects written by Zyun Francis Ezawa and published by World Scientific Publishing Company. This book was released on 2008-01-21 with total page 740 pages. Available in PDF, EPUB and Kindle. Book excerpt: The quantum Hall effect (QHE) is one of the most fascinating and beautiful phenomena in all branches of physics. Tremendous theoretical and experimental developments are still being made in this sphere. In the original edition of this book, composite bosons, composite fermions and fractional charged excitations (anyons) were among the distinguished ideas presented. This new edition includes many novel ideas according to recent progress. Fantastic phenomena associated with the interlayer phase coherence and SU(4) quantum Hall ferromagnets in the bilayer system are extensively reviewed. The microscopic theory of the QHE is formulated based on noncommutative geometry, the underlying mathematical structure. Quasiparticles are described as noncommutative solitons. The coverage also includes the recent development of the unconventional QHE in graphene (a single atomic layer graphite), where the electron dynamics can be treated as relativistic Dirac fermions and even the supersymmetric quantum mechanics plays a key role. An instructive and comprehensive overview of the QHE, this book is also suitable as an introduction to quantum field theory with vivid applications. Only a knowledge of quantum mechanics is assumed.
Download or read book Quantum Hall Effect written by Michael Stone and published by World Scientific. This book was released on 1992 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a compilation of major reprint articles on one of the most intriguing phenomena in modern physics: the quantum Hall effect. Together with a detailed introduction by the editor, this volume serves as a stimulating and valuable reference for students and research workers in condensed matter physics and for those with a particle physics background. The papers have been chosen with the intention of emphasizing the topological aspects of the quantum Hall effect and its connections with other branches of theoretical physics, such as topological quantum field theories and string theory. The contents include sections on integer effect, fractional effect, effect of global topology, effective theories, edge states and non-Abelian statistics.
Download or read book The Fractional Quantum Hall Effect written by Tapash Chakraborty and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: The experimental discovery of the fractional quantum Hall effect (FQHE) at the end of 1981 by Tsui, Stormer and Gossard was absolutely unexpected since, at this time, no theoretical work existed that could predict new struc tures in the magnetotransport coefficients under conditions representing the extreme quantum limit. It is more than thirty years since investigations of bulk semiconductors in very strong magnetic fields were begun. Under these conditions, only the lowest Landau level is occupied and the theory predicted a monotonic variation of the resistivity with increasing magnetic field, depending sensitively on the scattering mechanism. However, the ex perimental data could not be analyzed accurately since magnetic freeze-out effects and the transitions from a degenerate to a nondegenerate system complicated the interpretation of the data. For a two-dimensional electron gas, where the positive background charge is well separated from the two dimensional system, magnetic freeze-out effects are barely visible and an analysis of the data in the extreme quantum limit seems to be easier. First measurements in this magnetic field region on silicon field-effect transistors were not successful because the disorder in these devices was so large that all electrons in the lowest Landau level were localized. Consequently, models of a spin glass and finally of a Wigner solid were developed and much effort was put into developing the technology for improving the quality of semi conductor materials and devices, especially in the field of two-dimensional electron systems.
Download or read book The Quantum Hall Effect written by Richard E. Prange and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: After a foreword by Klaus von Klitzing, the first chapters of this book discuss the prehistory and the theoretical basis as well as the implications of the discovery of the Quantum Hall effect on superconductivity, superfluidity, and metrology, including experimentation. The second half of this volume is concerned with the theory of and experiments on the many body problem posed by fractional effect. Specific unsolved problems are mentioned throughout the book and a summary is made in the final chapter. The quantum Hall effect was discovered on about the hundredth anniversary of Hall's original work, and the finding was announced in 1980 by von Klitzing, Dorda and Pepper. Klaus von KIitzing was awarded the 1985 Nobel prize in physics for this discovery.
Download or read book The Fractional Quantum Hall Effect and the Rotation Group written by and published by . This book was released on 1992 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fractional quantum Hall effect is thought to be the result of correlations between electrons induced by their mutual interactions. This paper explores the consequences of these correlations numerically and analytically. The problem is mapped onto the surface of a sphere, so that the number of states in the first Landau level is finite. The following three sections review this geometry, give the matrix elements of the Coulomb interaction, and compare exact wave functions with the Laughlin/Haldane ground state ansatz for fractional fillings 1/m, m an odd integer. While this ansatz accounts for many of the J = 0 ground states found in numerical diagonalizations, it does not explain all such states. To make progress on this problem. A complete characterization of the most general four-particle J = 0 wave function is given, including an algebraic enumeration of the number of such states. This construction provides one example of a 2/3-filled state, the particle-hole conjugate of the 3-particle Laughlin/Haldane m = 3 state. This result suggests a generalization that may give the particle-hole conjugates of all Laughlin/Haldane states of arbitrary N: the construction depends on an equivalence of single-particle spinors of rank N/2 and ones formed by coupling the elementary spinors of N different particles. This result is further generalized to produce a wave function ansatz that may account for other fractional fillings of physical interest.
Download or read book The Quantum Hall Effects written by Tapash Chakraborty and published by Springer. This book was released on 1995 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Fractional Quantum Hall Effect presents a general survery of most of the theoretical work on the subject and briefly reviews the experimental results on the excitation gap. Several new topics like anyons, radiative recombinations in the fractional regime, experimental work on the spin-reversed quasi-particles, etc. are added to render the monographic treatment up-to-date. To complete the picture this second edition includes three chapters on the integral quantum Hall effect.
Download or read book Particle hole Symmetry Breaking in the Fractional Quantum Hall Effect at nu written by William D. Hutzel and published by . This book was released on 2018 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: The fractional quantum Hall effect (FQHE) in the half-filled second Landau level (filling factor [nu] = 5/2) offers new insights into the physics of exotic emergent quasi-particles. The FQHE is due to the collective interactions of electrons confined to two-dimensions, cooled to sub-Kelvin temperatures, and subjected to a strong perpendicular magnetic field. Under these conditions a quantum liquid forms displaying quantized plateaus in the Hall resistance and chiral edge flow. The leading candidate description for the FQHE at 5/2 is provided by the Moore-Read Pfaffian state which supports non-Abelian anyonic low-energy excitations with potential applications in fault-tolerant quantum computation schemes. The Moore-Read Pfaffian is the exact zero-energy ground state of a particular three-body Hamiltonian and explicitly breaks particle-hole symmetry. In this thesis we investigate the role of two and three body interaction terms in the Hamiltonian and the role of particle hole symmetry (PHS) breaking at [nu] = 5/2. We start with a PHS two body Hamiltonian (H 2) that produces an exact ground state that is nearly identical with the Moore-Read Pfaffian and construct a Hamiltonian H([alpha]) = (1 – [alpha])H3 + [alpha] H 2 that tunes continuously between H3 and H2. We find that the ground states, and low-energy excitations, of H2 and H3 are in one-to-one correspondence and remain adiabatically connected indicating they are part of the same universality class and describe the same physics in the thermodynamic limit. In addition, evidently three body PHS breaking interactions are not a crucial ingredient to realize the FQHE at 5/2 and the non-Abelian quasiparticle excitations.
Download or read book Proceedings of the Santa Fe Meeting written by American Physical Society. Division of Particles and Fields. Meeting and published by . This book was released on 1985 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Advanced Solid State Physics written by Philip Phillips and published by Cambridge University Press. This book was released on 2012-03-01 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing an up-to-date and lucid presentation of phenomena across modern advanced-level solid state physics, this new edition builds on an elementary understanding to introduce students to the key research topics with the minimum of mathematics. It covers cutting-edge topics, including electron transport and magnetism in solids. It is the first book to explain topological insulators and strongly correlated electrons. Explaining solid state physics in a clear and detailed way, it also has over 50 exercises for students to test their knowledge. In addition to the extensive discussion of magnetic impurity problems, bosonization, quantum phase transitions, and disordered systems from the first edition, the new edition includes such topics as topological insulators, high-temperature superconductivity and Mott insulators, renormalization group for Fermi liquids, spontaneous symmetry breaking, zero and finite-temperature Green functions, and the Kubo formalism. Figures from the book and solutions to student exercises are available online at www.cambridge.org/solidstate.
Download or read book Topological Insulators and Topological Superconductors written by B. Andrei Bernevig and published by Princeton University Press. This book was released on 2013-04-07 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level textbook is the first pedagogical synthesis of the field of topological insulators and superconductors, one of the most exciting areas of research in condensed matter physics. Presenting the latest developments, while providing all the calculations necessary for a self-contained and complete description of the discipline, it is ideal for graduate students and researchers preparing to work in this area, and it will be an essential reference both within and outside the classroom. The book begins with simple concepts such as Berry phases, Dirac fermions, Hall conductance and its link to topology, and the Hofstadter problem of lattice electrons in a magnetic field. It moves on to explain topological phases of matter such as Chern insulators, two- and three-dimensional topological insulators, and Majorana p-wave wires. Additionally, the book covers zero modes on vortices in topological superconductors, time-reversal topological superconductors, and topological responses/field theory and topological indices. The book also analyzes recent topics in condensed matter theory and concludes by surveying active subfields of research such as insulators with point-group symmetries and the stability of topological semimetals. Problems at the end of each chapter offer opportunities to test knowledge and engage with frontier research issues. Topological Insulators and Topological Superconductors will provide graduate students and researchers with the physical understanding and mathematical tools needed to embark on research in this rapidly evolving field.
Download or read book Field Theories of Condensed Matter Physics written by Eduardo Fradkin and published by Cambridge University Press. This book was released on 2013-02-28 with total page 855 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting the physics of the most challenging problems in condensed matter using the conceptual framework of quantum field theory, this book is of great interest to physicists in condensed matter and high energy and string theorists, as well as mathematicians. Revised and updated, this second edition features new chapters on the renormalization group, the Luttinger liquid, gauge theory, topological fluids, topological insulators and quantum entanglement. The book begins with the basic concepts and tools, developing them gradually to bring readers to the issues currently faced at the frontiers of research, such as topological phases of matter, quantum and classical critical phenomena, quantum Hall effects and superconductors. Other topics covered include one-dimensional strongly correlated systems, quantum ordered and disordered phases, topological structures in condensed matter and in field theory and fractional statistics.
Download or read book Quantum Field Theory of Many Body Systems written by Xiao-Gang Wen and published by OUP Oxford. This book was released on 2004-06-04 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: For most of the last century, condensed matter physics has been dominated by band theory and Landau's symmetry breaking theory. In the last twenty years, however, there has been the emergence of a new paradigm associated with fractionalisation, topological order, emergent gauge bosons and fermions, and string condensation. These new physical concepts are so fundamental that they may even influence our understanding of the origin of light and fermions in the universe. This book is a pedagogical and systematic introduction to the new concepts and quantum field theoretical methods (which have fuelled the rapid developments) in condensed matter physics. It discusses many basic notions in theoretical physics which underlie physical phenomena in nature. Topics covered are dissipative quantum systems, boson condensation, symmetry breaking and gapless excitations, phase transitions, Fermi liquids, spin density wave states, Fermi and fractional statistics, quantum Hall effects, topological and quantum order, spin liquids, and string condensation. Methods covered are the path integral, Green's functions, mean-field theory, effective theory, renormalization group, bosonization in one- and higher dimensions, non-linear sigma-model, quantum gauge theory, dualities, slave-boson theory, and exactly soluble models beyond one-dimension. This book is aimed at teaching graduate students and bringing them to the frontiers of research in condensed matter physics.
Download or read book High Energy Physics Index written by and published by . This book was released on 1994 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Many Body Quantum Theory in Condensed Matter Physics written by Henrik Bruus and published by Oxford University Press. This book was released on 2004-09-02 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is an introduction to quantum field theory applied to condensed matter physics. The topics cover modern applications in electron systems and electronic properties of mesoscopic systems and nanosystems. The textbook is developed for a graduate or advanced undergraduate course with exercises which aim at giving students the ability to confront real problems.
