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Author: Stephan Baer Publisher: Springer ISBN: 3319210513 Category : Science Languages : en Pages : 308
Book Description
This book provides an overview of recent developments in experiments probing the fractional quantum Hall (FQH) states of the second Landau level, especially the \nu=5/2 state. It summarizes the state-of-the-art understanding of these FQH states. It furthermore describes how the properties of the FQH states can be probed experimentally, by investigating tunneling and confinement properties. The progress towards the realization of an experiment, allowing to probe the potentially non-Abelian statistics of the quasiparticle excitations at \nu=5/2 is discussed. The book is intended as a reference for graduate students, PostDocs and researchers starting in the field. The experimental part of this book gives practical advice for solving the experimental challenges which researchers studying highly fragile FQH states are faced with.
Author: Stephan Baer Publisher: Springer ISBN: 3319210513 Category : Science Languages : en Pages : 308
Book Description
This book provides an overview of recent developments in experiments probing the fractional quantum Hall (FQH) states of the second Landau level, especially the \nu=5/2 state. It summarizes the state-of-the-art understanding of these FQH states. It furthermore describes how the properties of the FQH states can be probed experimentally, by investigating tunneling and confinement properties. The progress towards the realization of an experiment, allowing to probe the potentially non-Abelian statistics of the quasiparticle excitations at \nu=5/2 is discussed. The book is intended as a reference for graduate students, PostDocs and researchers starting in the field. The experimental part of this book gives practical advice for solving the experimental challenges which researchers studying highly fragile FQH states are faced with.
Author: Anatoly Kochubei Publisher: Walter de Gruyter GmbH & Co KG ISBN: 3110571625 Category : Mathematics Languages : en Pages : 490
Book Description
This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This first volume collects authoritative chapters covering the mathematical theory of fractional calculus, including fractional-order operators, integral transforms and equations, special functions, calculus of variations, and probabilistic and other aspects.
Author: Tongzhou Zhao Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
The fractional quantum Hall effect (FQHE) arises when electrons near zero temperature confined in a 2D plane are subjected to a strong perpendicular magnetic field. Since its first discovery [1], the FQHE has always been one of the most important topics in condensed matter physics. The origin of the FQHE can be understood by the composite fermion (CF) theory, according to which emergent particles called composite fermions are formed when an even number of vortices are attached to each electron. Because the vortices partially cancel the Aharonov-Bohm phase generated by the external magnetic field, CFs experience a reduced effective magnetic field, in which Landau-level-like energy bands called the [lambda] levels are formed and filled by CFs at an integer filling. The FQHE of electrons of filling factor [nu] = n 2pn±1 is therefore mapped into the integer quantum Hall effect (IQHE) of CFs. The CF theory successfully predicts many properties of the FQHE, such as filling fractions, collective excitations, spin structures, emergent Fermi sea of CFs with well-defined Fermi wave vectors, and many more. While many great achievements have been made, lots of questions remain to be answered. For example, a typical simplification in FQHE problems is that the electron system is treated as a strict 2D system. While this approximation has been proved to be useful in many cases, it turns out that there are exceptions. In experiments, electrons are usually confined within finite quantum wells. The finite width modifies the effective interaction between electrons. It also changes the nature of the ground state by including the new degree of freedom, as the finite well allows the mixing between different subbands. Another factor of importance is called the Landau level mixing, which is usually neglected in theoretical studies under the approximation that the magnetic field is strong enough to quench electrons to the lowest Landau level. However, under typical experimental conditions at present, the magnetic field is usually not that strong, and higher Landau level components are likely to mix into the system's ground state. The Landau level mixing brings a difference in the effective interaction between electrons, and it also introduces the three-body interaction, which breaks the particle-hole symmetry. The finite width effect and the Landau level mixing effect modify the effective interaction between electrons and may lead to new phases. For example, as the repulsion between electrons is reduced due to the finite width, it is possible that the vortices attached to electrons overscreen the repulsion and make the net interaction between composite fermions attractive. The attraction, therefore, can cause the pairing of composite fermions and lead to the so-called Moore-Read Pfaffian state or its particle-hole conjugation, the anti-Pfaffian state. To quantitatively describe the influence of the finite width and the iii Landau level mixing, we develop the three-dimensional fixed-phase diffusion Monte Carlo method. This method takes care of the finite width effect and the Landau level mixing effect in a single framework, and it is not a perturbative method, which makes it suitable for studying strongly-correlated systems. Equipped with the fixed-phase diffusion Monte Carlo method, especially its 3D version, we systematically study several different systems in this thesis. We find that the finite width together with the Landau level mixing effect can lead to new phases as well as affect the systems' quantitative properties, such as the transport gap. To be explicit, we find that the FQHE at filling factor 1/2 in finite GaAs quantum wells might be the Moore-Read Pfaffian state. We also find that the charge-imbalance in such quantum wells does not favor the Moore-Read Pfaffian state; we find that the Bloch ferromagnetism of composite fermions observed in Ref. [2] might be induced by the change of the Landau level mixing; we find that the Landau level mixing and the finite width cannot fully explain the discrepancy between the theoretical calculation and the experimental measurement of the transport gaps of the FQHEs in the sequence of n 2n+1.
Author: David Sánchez Publisher: MDPI ISBN: 3039433660 Category : Mathematics Languages : en Pages : 426
Book Description
Mesoscopic physics deals with systems larger than single atoms but small enough to retain their quantum properties. The possibility to create and manipulate conductors of the nanometer scale has given birth to a set of phenomena that have revolutionized physics: quantum Hall effects, persistent currents, weak localization, Coulomb blockade, etc. This Special Issue tackles the latest developments in the field. Contributors discuss time-dependent transport, quantum pumping, nanoscale heat engines and motors, molecular junctions, electron–electron correlations in confined systems, quantum thermo-electrics and current fluctuations. The works included herein represent an up-to-date account of exciting research with a broad impact in both fundamental and applied topics.
Author: T. Chakraborty Publisher: Elsevier ISBN: 008052575X Category : Technology & Engineering Languages : en Pages : 363
Book Description
This book deals with the electronic and optical properties of two low-dimensional systems: quantum dots and quantum antidots and is divided into two parts. Part one is a self-contained monograph which describes in detail the theoretical and experimental background for exploration of electronic states of the quantum-confined systems. Starting from the single-electron picture of the system, the book describes various experimental methods that provide important information on these systems. Concentrating on many-electron systems, theoretical developments are described in detail and their experimental consequences are also discussed. The field has witnessed an almost explosive growth and some of the future directions of explorations are highlighted towards the end of the monograph. The subject matter is dealt with in such a way that it is both accessible to beginners and useful for expert researchers as a comprehensive review of most of the developments in the field.Furthermore the book contains 37 reprinted articles which have been selected to provide a first-hand picture of the overall developments in the field. The early papers have been arranged to portray the developments chronologically, and the more recent papers provide an overview of future direction in the research.
Author: Publisher: Academic Press ISBN: 0080864333 Category : Technology & Engineering Languages : en Pages : 461
Book Description
Spectroscopic techniques are among the most powerful characterization methods used to study semiconductors. This volume presents reviews of a number of major spectroscopic techniques used to investigate bulk and artificially structured semiconductors including: photoluminescence, photo-reflectance, inelastic light scattering, magneto-optics, ultrafast work, piezo-spectroscopy methods, and spectroscopy at extremely low temperatures and high magnetic fields. Emphasis is given to major semiconductor systems, and artificially structured materials such as GaAs, InSb, Hg1-xCdxTe and MBE grown structures based upon GaAs/AlGaAs materials. Both the spectroscopic novice and the expert will benefit from the descriptions and discussions of the methods, principles, and applications relevant to today's semiconductor structures.Key Features* Discusses the latest advances in spectroscopic techniques used to investigate bulk and artificially structured semiconductors* Features detailed review articles which cover basic principles* Highlights specific applications such as the use of laser spectroscopy for the characterization of GaAs quantum well structures
Author: Stephan Baer
Author: Stephan Baer
Author: Anatoly Kochubei
Author: Tongzhou Zhao
Author: Jennifer Mallett
Author: 
Author: Jennifer Mallett
Author: David Sánchez
Author: T. Chakraborty
Author: 
Author: Jane Varpu Branch