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 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 Microscopic Study of Statistics Spin and Excitons in the Fractional Quantum Hall Effect written by Yuhe Zhang and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional quantum Hall effect (FQHE) is a marvelous physical phenomenon that arises in a two-dimensional electron gas subjected to a strong perpendicular magnetic field at low temperature. The microscopic origin of the FQHE for general filling factors is understood by the Composite Fermion theory, which explains FQHE of electrons as integer quantum Hall effect (IQHE) of bound objects of electrons and an even number of vortices, known as composite fermions (CFs). Despite tremendous advances over the last three decades in our understanding of the FQHE since its discovery, many puzzles remain unsolved and many hypotheses remain untested. The most interesting such hypothesis is probably the realization of certain exotic particles called ``anyons'', which interpolate between bosons and fermions. Anyons obey exotic braid statistics: fractional braid statistics refers to the property that braiding one particle around another produces a phase that is a nonintegral multiple of $2\pi$; non-Abelian braid statistics means that braiding non-Abelian anyons not only produces a phase in the wave function, but also transforms the system to a topologically distinct state. Anyon is of great interest both for a demonstration of new physics and because of its potential application in fault-tolerant topological quantum computers. Despite tremendous efforts in the last three decades, anyons have not been definitely detected in experiments. We proposed to create and manipulate anyons by introducing auxiliary particles into a FQHE system. These auxiliary particles bind quasiholes of the fractional quantum Hall (FQH) state, and thus inherit the exotic braiding properties of the quasiholes. We showed that the braiding property of a pair of auxiliary particles is manifested through the density distribution of one particle when holding another particle fixed. This density distribution can be directly measured with existing experimental techniques in cold atom system.The above demonstration of exotic braiding statistics, while still being at the level of a thought experiment, has the advantage that all the physics happens away from the edge of a FQHE system. Earlier proposals generally used interference of anyons moving along the edge of a FQHE system to reveal their non-Abelian braiding. The edge of a FQH state, however, may undergo a reconstruction due to edge exciton, and therefore lose its topological features. Motivated by certain discrepancies between theory and experimental measurements on the edge, we study in this thesis the edge physics of FQHE. We focus on the $\nu = 5/2$ state, which is believed to realize the Moore-Read Pfaffian state that supports non-Abelian excitations, and the $\nu = 7/3$ state, another state in the second Landau level that is studied in volumes of experiments. Using numerical simulations we find that the edge is unstable to a reconstruction for all experimental systems investigated so far, which must be taken into account when analyzing experimental results.Apart from the topological properties of the FQHE systems, we have also been interested in pursuing the quantitative accuracy of the theory of FQHE and explaining various experimental results in a quantitative way. Previous theories usually considered the ideal limit in which all the electrons in a FQH state are in the lowest Landau level (LLL). In reality, however, some electrons are excited to higher Landau levels in order to lower their correlation energy. This behavior is called Landau level (LL) mixing which can make significant quantitative corrections for measurable physical quantities, and sometimes may even play a qualitative role. Other physical factors that can lead to quantitative changes include the finite thickness of an two-dimensional electron layer.We study the transitions between differently spin-polarized states in the FQHE which provide a direct measure of the tiny energy differences between those states and thereby serve as an extremely sensitive test of the quantitative accuracy of the theory. Previous theoretical results for spin transitions were generally off by a factor of 2 or 3 compared to experimental data. We use a ``fixed-phase diffusion Monte Carlo'' algorithm to address the effect of LL mixing and also include finite-thickness effect based on realistic charge distribution. We find excellent agreement between our calculation and experiments. Our work demonstrates the most accurate comparison between theory and experiment in the FQHE field achieved so far, and also solves a long-standing puzzle about what the role LL mixing plays in breaking the particle-hole symmetry. In addition to spin physics, we notice that a quantitative understanding of the tunneling transport in a bilayer FQHE system is lacking. We identify the interlayer exciton responsible for the peak tunnel current and provide a quantitative account of the bias voltage at the peak current (denoted as $V_{max}$). The excitonic attraction is shown to be quantitatively significant, and its variation accounts for the increase of $V_{max}$ with the application of an in-plane magnetic field. We have included the effect of finite thickness but not the LL mixing in this calculation because LL mixing does not affect the excitation gaps substantially. The excellent agreements with experiment also validate our calculation.

Download or read book Quantum Hall Effect written by Saurabh Basu and published by Cambridge University Press. This book was released on 2024-07-31 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the discovery and explanation of the quantum Hall effect and its fundamental principles. It is meant for undergraduate and graduate students of physics, engineering, and applied sciences studying condensed matter physics. Doctoral students and researchers of this subject will also find it equally useful. It begins with a historical overview of this effect wherein the experiment and the physical systems are described. It progresses to cover discrete symmetries like inversion symmetry, time reversal symmetry, particle-hole symmetry, and chiral symmetry. It also examines how the Hamiltonian transforms under such symmetry operations. Two 1D models, namely the Su-Schrieffer-Heeger (SSH) model and a Kitaev chain with superconducting correlations, are discussed too. Then, the quantum Hall effect in graphene is explained. Further, the spin Hall effect is studied which may have prospects of using graphene as spintronic devices. The book ends with a brief review on fractional quantum Hall effect.

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 Investigating the Topological Order of an Ansatz for the Fractional Quantum Hall Effect in the Half filled Second Landau Level written by John J. McCord and published by . This book was released on 2016 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: The Moore-Read Pfaffian and anti-Pfaffian states have been under scrupulous review as candidates which describe the fractional quantum Hall effect at filling factor 5/2. Quantum states in the universality class of the Moore-Read Pfaffian/anti-Pfaffian have non-trivial intrinsic topological order and support low-energy non-Abelian excitations that have applications in fault-tolerant topological quantum computing schemes. Both states are exact ground states of three-body Hamiltonians that explicitly break particle-hole symmetry. We study the topological order of a competing ansatz state & PSgr;[subscript 2] that is the exact ground state of a two-body Hamiltonian that preserves particle-hole symmetry. In particular, we calculate the bipartite entanglement entropy and spectra in the lowest Landau level in the spherical geometry for & PSgr;[subscript 2]. We perform such calculations for a finite number of electrons up to 14. We then extrapolate to the thermodynamic limit the topological entanglement entropy [gamma] as a measure of the topological order of the ansatz and compare to the known value of the Moore-Read Pfaffian/anti-Pfaffian state. We also study the orbital entanglement spectra for & PSgr;[subscript 2] and compare with the Moore-Read Pfaffian and two-body Coulomb ground states. We show that our extrapolation of [gamma] lies within the uncertainty of the known value of [gamma] for the Moore-Read Pfaffian state, and that the orbital entanglement spectra of & PSgr;[subscript 2] assumes a similar structure to that of the two-body Coulomb interaction.

Download or read book Understanding the Physics of a Possible Non Abelian Fractional Quantum Hall Effect State written by and published by . This book was released on 2010 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: We wish to present in this report experimental results from a one-year Senior Council Tier-1 LDRD project that focused on understanding the physics of a possible non-Abelian fractional quantum Hall effect state. We first give a general introduction to the quantum Hall effect, and then present the experimental results on the edge-state transport in a special fractional quantum Hall effect state at Landau level filling [nu] = 5/2 - a possible non-Abelian quantum Hall state. This state has been at the center of current basic research due to its potential applications in fault-resistant topological quantum computation. We will also describe the semiconductor 'Hall-bar' devices we used in this project. Electron physics in low dimensional systems has been one of the most exciting fields in condensed matter physics for many years. This is especially true of quantum Hall effect (QHE) physics, which has seen its intellectual wealth applied in and has influenced many seemingly unrelated fields, such as the black hole physics, where a fractional QHE-like phase has been identified. Two Nobel prizes have been awarded for discoveries of quantum Hall effects: in 1985 to von Klitzing for the discovery of integer QHE, and in 1998 to Tsui, Stormer, and Laughlin for the discovery of fractional QHE. Today, QH physics remains one of the most vibrant research fields, and many unexpected novel quantum states continue to be discovered and to surprise us, such as utilizing an exotic, non-Abelian FQHE state at [nu] = 5/2 for fault resistant topological computation. Below we give a briefly introduction of the quantum Hall physics.

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 Perspectives in Quantum Hall Effects written by Sankar Das Sarma and published by Wiley-VCH. 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 Infinite Symmetry in the Fractional Quantum Hall Effect written by Michael Flohr and published by . This book was released on 1993 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 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 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 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 Composite Fermions written by Jainendra K. Jain and published by Cambridge University Press. This book was released on 2007-03-29 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book was first published in 2007. When electrons are confined to two dimensions, cooled to near absolute zero temperature, and subjected to a strong magnetic field, they form an exotic new collective state of matter. Investigations into this began with the observations of integral and fractional quantum Hall effects, which are among the most important discoveries in condensed matter physics. The fractional quantum Hall effect and a stream of other unexpected findings are explained by a new class of particles: composite fermions. This textbook is a self-contained, pedagogical introduction to the physics and experimental manifestations of composite fermions. Ideal for graduate students and academic researchers, it contains numerous exercises to reinforce the concepts presented. The topics covered include the integral and fractional quantum Hall effects, the composite-fermion Fermi sea, various kinds of excitations, the role of spin, edge state transport, electron solid, bilayer physics, fractional braiding statistics and fractional local charge.

Download or read book Nonperturbative Quantum Field Theory written by G. Hooft and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 603 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the past 15 years, quantum field theory and classical statistical mechanics have merged into a single field, and the need for nonperturbative methods for the description of critical phenomena in statistical mechanics as well as for problems in elementary particle physics are generally acknowledged. Such methods formed the central theme of the 1987 Cargese Advanced Study Institut. e on "Nonpert. urbat. ive Quantum Field Theory." The use of conformal symmet. ry has been of central interest in recent years, and was a main subject at. t. he ASI. Conformal invariant quantum field theory describes statistical mechanical systems exactly at a critical point, and can be analysed to a remarkable ext. ent. by group t. heoretical methods. Very strong results have been obtained for 2-dimensional systems. Conformal field theory is also the basis of string theory, which offers some hope of providing a unified t. heory of all interactions between elementary particles. Accordingly, a number of lectures and seminars were presented on these two topics. After syst. ematic introductory lectures, conformal field theory on Riemann surfaces, orbifolds, sigma models, and application of loop group theory and Grassmannians were discussed, and some ideas on modular geometry were presented. Other lectures combined' traditional techniques of constructive quant. um field theory with new methods such as the use of index-t. heorems and infinite dimensional (Kac Moody) symmetry groups. The problems encountered in a quantum mechanical description of black holes were discussed in detail.