Download or read book Fractional Quantum Hall Effect in Wide Quantum Wells written by Javad Shabani and published by . This book was released on 2011 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Daijiro Yoshioka and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fractional quantum Hall effect has opened up a new paradigm in the study of strongly correlated electrons and it has been shown that new concepts, such as fractional statistics, anyon, chiral Luttinger liquid and composite particles, are realized in two-dimensional electron systems. This book explains the quantum Hall effects together with these new concepts starting from elementary quantum mechanics.
Download or read book THEORETICAL STUDY OF FRACTIONAL QUANTUM HALL EFFECT UNDER REALISTIC CONDITIONS written by Tongzhou Zhao and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Perspectives in Quantum Hall Effects written by Sankar Das Sarma and published by John Wiley & Sons. This book was released on 2008-07-11 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: The discovery of the quantized and fractional Quantum Hall Effect phenomena is among the most important physics findings in the latter half of this century. The precise quantization of the electrical resistance involved in the quantized Hall effect phenomena has led to the new definition of the resistance standard and has metrologically affected all of science and technology. This resource consists of contributions from the top researchers in the field who present recent experimental and theoretical developments. Each chapter is self-contained and includes its own set of references guiding readers to original papers and further reading on the topic.
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 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 Liquid solid Transitions in a Multiple quantum well System written by Xiu Qiu and published by . This book was released on 1990 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Transport Spectroscopy of Confined Fractional Quantum Hall Systems written by Stephan Baer and published by Springer. This book was released on 2015-08-18 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Electrons in Solids written by Richard A Dunlap and published by Morgan & Claypool Publishers. This book was released on 2019-10-24 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: The transport of electric charge through most materials is well described in terms of their electronic band structure. The present book deals with two cases where the charge transport in a solid is not described by the simple band structure picture of the solid. These cases are related to the phenomena of the quantum Hall effect and superconductivity. Part I of this book deals with the quantum Hall effect, which is a consequence of the behavior of electrons in solids when they are constrained to move in two dimensions. Part II of the present volume describes the behavior of superconductors, where electrons are bound together in Cooper pairs and travel through a material without resistance.
Download or read book Exotic Emergent Phenomena in the Fractional Quantum Hall Effect written by Ajit Coimbatore Balram and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: When two-dimensional electron systems are subjected to a perpendicular magnetic field, they exhibit the marvelous phenomenon known as the fractional quantum Hall effect (FQHE). This arises as a result of the formation of composite fermions (CFs), which are bound states of electrons and an even number of vortices. The FQHE of electrons is understood as arising from the integer QHE (IQHE) of CFs. Alongside superconductivity, Bose-Einstein condensation and spin-liquids, the CF quantum fluid provides a model system for understanding strongly correlated systems and their collective behavior. Although it has been more than three decades since the experimental discovery of FQHE, the field continues to produce profound insights and pose interesting problems some of which have been addressed in this thesis.\\A major unanswered question in the field of FQHE is the mechanism of FQHE for the 1/3 state in the second Landau leve (7/3 state). Numerical studies of this state have brought out the following puzzle: exact diagonalization studies suggest that the ground state and excitations of 1/3 state in the second Landau level are different from its counterpart in the lowest Landau level (LLL), while entanglement spectra of the two states point to the fact that they fall in the same universality class. Using methods from CF theory we show that the excitations of the 7/3 FQHE lie in the same universality class as those of the 1/3 state but are strongly modified due to screening by CF excitons, thereby settling the above discrepancy. \\Armed with the exciton calculation, we illustrate that by imposing certain exclusion rules for CF excitons one can build the full spectrum of FQHE in the lowest Landau level. Equipped with the techniques to calculate the spectra of FQHE systems, we carry out an extensive study of FQHE of multi-component CFs (systems possessing degrees of freedom for eg: valley and spin degeneracy), which is applicable to FQHE in systems such as graphene, AlAs and GaAs quantum wells. We provide a comprehensive list of the possible fractions, their ground state energies and the critical ``Zeeman'' energies for the ``spin'' transitions between the states and compare them with the experimental observations. In the lowest Landau level of graphene, we find an excellent agreement between theory and experiments. However, in the second Landau level of graphene we find an unexpected spontaneous spin polarization of CFs. We predict that there are no spin transitions to be expected in the second Landau level of graphene, a result that could be tested out in experiments. We reanalyzed some old experimental data showing excitation modes below the Zeeman energy in the vicinity of 1/3 filling of the lowest Landau level whose theoretical origin was unexplained. Using methods of exact diagonalization and CF theory we demonstrate that these modes arise as a result of formation of trions of CFs which have sub-Zeeman energy due to skyrmion-like physics.\\In the past couple of years, the Fermi wave vector of CFs has been measured very accurately in pioneering experiments at Princeton University. Motivated by these experiments we address the issue of the validity of Luttinger's theorem (which is a fundamental tenet of Landau Fermi liquid theory) for the Fermi sea of CFs. Our calculations suggest that the CF Fermi sea may violate Luttinger's theorem slightly. This not only provides a nontrivial example of a non-Fermi liquid, but gives new insight into the nature of the CF Fermi sea state and opens a new line of inquiry in the field of FQHE.
Download or read book The Fractional Quantum Hall Effect Effect of Finite Width written by and published by . This book was released on 1985 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Theory of the Fractional Quantum Hall Effect with Tilted Magnetic Field written by James D. Nickila and published by . This book was released on 1991 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Excitations in the Fractional Quantum Hall Effect written by Pekka Pietiläinen and published by . This book was released on 1988 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Fractional Quantum Hall Effect written by Gregory Scott Boebinger and published by . This book was released on 1986 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Fractional Quantum Hall Effect written by Zeleke Deressa and published by LAP Lambert Academic Publishing. This book was released on 2011-12 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis captures the progress on Fractional Quantum Hall Effect based on the Ginsburg-Landau Chern-Simons field theoretical approach, i.e. theory that proceed from microscopic electronic Hamiltonian to the final solution via a sequence of transformations and approximations. The detailed theoretical review of the fractional quantised Hall Effect includes both the trial wave function approaches which were forwarded by Laughlin and Jian, and the field theoretical approaches which were forwarded by Lopez and Fradkin. The Ginsburg-Landau Chiron-Simons field theoretical approach, in which electrons are converted to Chiron-Simons composite bosons that carry attached flux tubes, is considered as a better theoretical approach to explain different phenomena of fractional quantum Hall effect.
