Thomas Ihn
- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199534425
- eISBN:
- 9780191715297
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199534425.003.0016
- Subject:
- Physics, Condensed Matter Physics / Materials
This chapter discusses a number of quantum phenomena brought about by electronic transport at high magnetic fields. As a first step, the Shubnikov–de Haas effect is introduced. In order to understand ...
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This chapter discusses a number of quantum phenomena brought about by electronic transport at high magnetic fields. As a first step, the Shubnikov–de Haas effect is introduced. In order to understand the underlying physics, the quantized motion of electrons in Landau levels under the influence of magnetic fields is discussed. Ideas behind the broadening of Landau levels are presented, and magnetocapacitance measurements are introduced as a means to measure the modulated density of states. Electron localization in high magnetic fields as a result of disorder and interactions is discussed. The integer quantum Hall effect is shown to be in close relation to the quantized conductance in quantum point contacts, if described within the Landauer–Büttiker formalism. The half-integer quantum Hall effect in graphene is discussed. Then, the fractional quantum Hall effect is introduced and discussed on a phenomenological level using the composite Fermion picture. Contact is made to Chapter 14 with a discussion of edge-channel interference in the electronic Mach–Zehnder interferometer.Less
This chapter discusses a number of quantum phenomena brought about by electronic transport at high magnetic fields. As a first step, the Shubnikov–de Haas effect is introduced. In order to understand the underlying physics, the quantized motion of electrons in Landau levels under the influence of magnetic fields is discussed. Ideas behind the broadening of Landau levels are presented, and magnetocapacitance measurements are introduced as a means to measure the modulated density of states. Electron localization in high magnetic fields as a result of disorder and interactions is discussed. The integer quantum Hall effect is shown to be in close relation to the quantized conductance in quantum point contacts, if described within the Landauer–Büttiker formalism. The half-integer quantum Hall effect in graphene is discussed. Then, the fractional quantum Hall effect is introduced and discussed on a phenomenological level using the composite Fermion picture. Contact is made to Chapter 14 with a discussion of edge-channel interference in the electronic Mach–Zehnder interferometer.
Mark O. Goerbig
- Published in print:
- 2011
- Published Online:
- September 2011
- ISBN:
- 9780199603657
- eISBN:
- 9780191729515
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199603657.003.0006
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This chapter yields an introduction to quantum Hall effects both for non-relativistic electrons in conventional two-dimensional electron gases (such as in semiconductor heterostructures) and ...
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This chapter yields an introduction to quantum Hall effects both for non-relativistic electrons in conventional two-dimensional electron gases (such as in semiconductor heterostructures) and relativistic electrons in graphene. After a brief historical overview follows a detailed discussion of the kinetic-energy quantisation of non-relativistic and relativistic electrons in a strong magnetic field (section 2). Section 3 is devoted to the transport characteristics of the integer quantum Hall effect, and the basic aspects of the fractional quantum Hall effect are described in section 4. In section 5, several multicomponent quantum Hall systems are briefly discussed, namely the quantum Hall ferromagnetism, bilayer systems and graphene that may be viewed as a four-component system.Less
This chapter yields an introduction to quantum Hall effects both for non-relativistic electrons in conventional two-dimensional electron gases (such as in semiconductor heterostructures) and relativistic electrons in graphene. After a brief historical overview follows a detailed discussion of the kinetic-energy quantisation of non-relativistic and relativistic electrons in a strong magnetic field (section 2). Section 3 is devoted to the transport characteristics of the integer quantum Hall effect, and the basic aspects of the fractional quantum Hall effect are described in section 4. In section 5, several multicomponent quantum Hall systems are briefly discussed, namely the quantum Hall ferromagnetism, bilayer systems and graphene that may be viewed as a four-component system.
Alexei L. Ivanov and Sergei G. Tikhodeev (eds)
- Published in print:
- 2007
- Published Online:
- May 2008
- ISBN:
- 9780199238873
- eISBN:
- 9780191716652
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199238873.001.0001
- Subject:
- Physics, Condensed Matter Physics / Materials
The book, which is dedicated to Prof. Leonid V. Keldysh on his 75th anniversary, is a collection of review papers written by experts in condensed matter physics such as V. M. Agranovich, B. L. ...
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The book, which is dedicated to Prof. Leonid V. Keldysh on his 75th anniversary, is a collection of review papers written by experts in condensed matter physics such as V. M. Agranovich, B. L. Altshuler, E. Burstein, V. L. Ginzburg, K. Von Klitzing, P. B. Littlewood, M. Pepper, A. Pinczuk, L. P. Pitaevskii, E. I. Rashba, T. M. Rice, etc. This is a guide-book of modern condensed matter physics, where the most important and hot topics of the field are reviewed. Topics covered include spintronics and quantum computation, Bose-Einstein condensation of excitons and the excitonic insulator, electron-hole liquid, metal-dielectric transition, coherent optical phenomena in semiconductor nanostructures, composite fermions and the quantum Hall effect, semiconductor and organic quantum wells, microcavities and other nanostructures, disordered systems in condensed matter, many-body theory and the Keldysh diagram technique, resonant acousto-optics, and inelastic electron tunneling spectroscopy.Less
The book, which is dedicated to Prof. Leonid V. Keldysh on his 75th anniversary, is a collection of review papers written by experts in condensed matter physics such as V. M. Agranovich, B. L. Altshuler, E. Burstein, V. L. Ginzburg, K. Von Klitzing, P. B. Littlewood, M. Pepper, A. Pinczuk, L. P. Pitaevskii, E. I. Rashba, T. M. Rice, etc. This is a guide-book of modern condensed matter physics, where the most important and hot topics of the field are reviewed. Topics covered include spintronics and quantum computation, Bose-Einstein condensation of excitons and the excitonic insulator, electron-hole liquid, metal-dielectric transition, coherent optical phenomena in semiconductor nanostructures, composite fermions and the quantum Hall effect, semiconductor and organic quantum wells, microcavities and other nanostructures, disordered systems in condensed matter, many-body theory and the Keldysh diagram technique, resonant acousto-optics, and inelastic electron tunneling spectroscopy.
John Orton
- Published in print:
- 2008
- Published Online:
- January 2010
- ISBN:
- 9780199559107
- eISBN:
- 9780191712975
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199559107.003.0006
- Subject:
- Physics, Crystallography: Physics
During the 1970s, III-V compounds and epitaxial crystal growth provided the basis for low dimensional structures (or nanostructures). The best known example is a GaAs quantum well within AlGaAs ...
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During the 1970s, III-V compounds and epitaxial crystal growth provided the basis for low dimensional structures (or nanostructures). The best known example is a GaAs quantum well within AlGaAs barriers, electrons, and holes being confined in well defined energy levels that determine the optical properties. Quantum wires and dots are also described. The quantum well laser and the vertical cavity laser (VCSEL) show considerable advantages over their heterostructure predecessor. Another exciting development was that of the two-dimensional electron gas (2DEG) at an interface between semiconductors with different band gaps. By doping only the wide gap material so as to separate the doping atoms from the resulting free electrons, ionised impurity scattering can be minimised and extremely high electron mobilities achieved. Such samples led to the discovery of the fractional quantum Hall effect and to high mobility FETs (HEMTs) for microwave applications. Mesoscopic systems and heterojunction bipolar transistors (HBTs) are also described.Less
During the 1970s, III-V compounds and epitaxial crystal growth provided the basis for low dimensional structures (or nanostructures). The best known example is a GaAs quantum well within AlGaAs barriers, electrons, and holes being confined in well defined energy levels that determine the optical properties. Quantum wires and dots are also described. The quantum well laser and the vertical cavity laser (VCSEL) show considerable advantages over their heterostructure predecessor. Another exciting development was that of the two-dimensional electron gas (2DEG) at an interface between semiconductors with different band gaps. By doping only the wide gap material so as to separate the doping atoms from the resulting free electrons, ionised impurity scattering can be minimised and extremely high electron mobilities achieved. Such samples led to the discovery of the fractional quantum Hall effect and to high mobility FETs (HEMTs) for microwave applications. Mesoscopic systems and heterojunction bipolar transistors (HBTs) are also described.
Thomas Ihn
- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199534425
- eISBN:
- 9780191715297
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199534425.001.0001
- Subject:
- Physics, Condensed Matter Physics / Materials
This book presents the physics of semiconductor nanostructures with emphasis on their electronic transport properties. At its heart are five fundamental transport phenomena: quantized conductance, ...
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This book presents the physics of semiconductor nanostructures with emphasis on their electronic transport properties. At its heart are five fundamental transport phenomena: quantized conductance, tunneling transport, the Aharonov–Bohm effect, the quantum Hall effect, and the Coulomb blockade effect. The book starts out with basics of solid state and semiconductor physics, such as crystal structure, band structure, and effective mass approximation, including spin-orbit interaction effects important for research in semiconductor spintronics. It deals with material aspects such as band engineering, doping, gating, and a selection of nanostructure fabrication techniques. The book discusses the Drude–Boltzmann–Sommerfeld transport theory as well as conductance quantization and the Landauer–Büttiker theory. These concepts are extended to mesoscopic interference phenomena and decoherence, magnetotransport, and interaction effects in quantum-confined systems, guiding the reader from fundamental effects to specialized state-of-the-art experiments.Less
This book presents the physics of semiconductor nanostructures with emphasis on their electronic transport properties. At its heart are five fundamental transport phenomena: quantized conductance, tunneling transport, the Aharonov–Bohm effect, the quantum Hall effect, and the Coulomb blockade effect. The book starts out with basics of solid state and semiconductor physics, such as crystal structure, band structure, and effective mass approximation, including spin-orbit interaction effects important for research in semiconductor spintronics. It deals with material aspects such as band engineering, doping, gating, and a selection of nanostructure fabrication techniques. The book discusses the Drude–Boltzmann–Sommerfeld transport theory as well as conductance quantization and the Landauer–Büttiker theory. These concepts are extended to mesoscopic interference phenomena and decoherence, magnetotransport, and interaction effects in quantum-confined systems, guiding the reader from fundamental effects to specialized state-of-the-art experiments.
I. V. Kukushkin, J. H. Smet, and K. von Klitzing
- Published in print:
- 2007
- Published Online:
- May 2008
- ISBN:
- 9780199238873
- eISBN:
- 9780191716652
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199238873.003.0008
- Subject:
- Physics, Condensed Matter Physics / Materials
This chapter analyzes the fractional quantum Hall effect and composite fermions in a two-dimensional electron system. The underlying picture of a composite fermion, a quasi-particle consisting of one ...
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This chapter analyzes the fractional quantum Hall effect and composite fermions in a two-dimensional electron system. The underlying picture of a composite fermion, a quasi-particle consisting of one electron, and two magnetic flux quanta is detailed and qualitatively illustrated. Detection of the comosite fermions in cryogenic transport and optical experiments is also discussed.Less
This chapter analyzes the fractional quantum Hall effect and composite fermions in a two-dimensional electron system. The underlying picture of a composite fermion, a quasi-particle consisting of one electron, and two magnetic flux quanta is detailed and qualitatively illustrated. Detection of the comosite fermions in cryogenic transport and optical experiments is also discussed.
Xiao-Gang Wen
- Published in print:
- 2007
- Published Online:
- February 2010
- ISBN:
- 9780199227259
- eISBN:
- 9780191713019
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199227259.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
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 an emergence of a new ...
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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 an emergence of a new paradigm associated with fractionalization, emergent gauge bosons and fermions, topological order, string-net condensation, and long range entanglements. These new physical concepts are so fundamental that they may even influence our understanding of the origin of light and electrons in the universe. This book is a pedagogical and systematic introduction to the new concepts and quantum field theoretical methods in condensed matter physics. It discusses many basic notions in theoretical physics which underlie physical phenomena in nature, including a notion that unifies light and electrons. Topics covered include 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/quantum order, and spin liquid and string-net condensation. Methods discussed include 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, projective construction, and exactly soluble models beyond one-dimension.Less
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 an emergence of a new paradigm associated with fractionalization, emergent gauge bosons and fermions, topological order, string-net condensation, and long range entanglements. These new physical concepts are so fundamental that they may even influence our understanding of the origin of light and electrons in the universe. This book is a pedagogical and systematic introduction to the new concepts and quantum field theoretical methods in condensed matter physics. It discusses many basic notions in theoretical physics which underlie physical phenomena in nature, including a notion that unifies light and electrons. Topics covered include 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/quantum order, and spin liquid and string-net condensation. Methods discussed include 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, projective construction, and exactly soluble models beyond one-dimension.
Sandip Tiwari
- Published in print:
- 2017
- Published Online:
- August 2017
- ISBN:
- 9780198759874
- eISBN:
- 9780191820847
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198759874.003.0003
- Subject:
- Physics, Condensed Matter Physics / Materials, Atomic, Laser, and Optical Physics
Unique nanoscale phenomena arise in quantum and mesoscale properties and there are additional intriguing twists from effects that are classical in origin. In this chapter, these are brought forth ...
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Unique nanoscale phenomena arise in quantum and mesoscale properties and there are additional intriguing twists from effects that are classical in origin. In this chapter, these are brought forth through an exploration of quantum computation with the important notions of superposition, entanglement, non-locality, cryptography and secure communication. The quantum mesoscale and implications of nonlocality of potential are discussed through Aharonov-Bohm effect, the quantum Hall effect in its various forms including spin, and these are unified through a topological discussion. Single electron effect as a classical phenomenon with Coulomb blockade including in multiple dot systems where charge stability diagrams may be drawn as phase diagram is discussed, and is also extended to explore the even-odd and Kondo consequences for quantum-dot transport. This brings up the self-energy discussion important to nanoscale device understanding.Less
Unique nanoscale phenomena arise in quantum and mesoscale properties and there are additional intriguing twists from effects that are classical in origin. In this chapter, these are brought forth through an exploration of quantum computation with the important notions of superposition, entanglement, non-locality, cryptography and secure communication. The quantum mesoscale and implications of nonlocality of potential are discussed through Aharonov-Bohm effect, the quantum Hall effect in its various forms including spin, and these are unified through a topological discussion. Single electron effect as a classical phenomenon with Coulomb blockade including in multiple dot systems where charge stability diagrams may be drawn as phase diagram is discussed, and is also extended to explore the even-odd and Kondo consequences for quantum-dot transport. This brings up the self-energy discussion important to nanoscale device understanding.
Maciej Lewenstein, Anna Sanpera, and Verònica Ahufinger
- Published in print:
- 2012
- Published Online:
- December 2013
- ISBN:
- 9780199573127
- eISBN:
- 9780191775048
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199573127.003.0011
- Subject:
- Physics, Atomic, Laser, and Optical Physics
This chapter discusses the physics of ultracold gases in ‘artificial’ magnetic fields. The analogy between electronic systems in the presence of external magnetic fields and ultracold gases in ...
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This chapter discusses the physics of ultracold gases in ‘artificial’ magnetic fields. The analogy between electronic systems in the presence of external magnetic fields and ultracold gases in rotating traps leads to the familiar concepts of Landau Levels, the integer Hall effect, the fractional quantum Hall effect, and laughing states for neutral particles. The second part analyses the possibility of simulating Abelian and non Abelian Lattice Gauge theories with ultracold gases. Finally, the state-of-the-art in generating artificial magnetic fields for ultracold gases is reviewed.Less
This chapter discusses the physics of ultracold gases in ‘artificial’ magnetic fields. The analogy between electronic systems in the presence of external magnetic fields and ultracold gases in rotating traps leads to the familiar concepts of Landau Levels, the integer Hall effect, the fractional quantum Hall effect, and laughing states for neutral particles. The second part analyses the possibility of simulating Abelian and non Abelian Lattice Gauge theories with ultracold gases. Finally, the state-of-the-art in generating artificial magnetic fields for ultracold gases is reviewed.
Lucjan Jacak, Piotr Sitko, Konrad Wieczorek, and Arkadiusz Wojs
- Published in print:
- 2003
- Published Online:
- January 2010
- ISBN:
- 9780198528708
- eISBN:
- 9780191713477
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528708.003.0001
- Subject:
- Physics, Condensed Matter Physics / Materials, Theoretical, Computational, and Statistical Physics
This introductory chapter starts with short review of experimental and theoretical description of integral and fractional quantum Hall effects. The standard quantization of states of charged ...
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This introductory chapter starts with short review of experimental and theoretical description of integral and fractional quantum Hall effects. The standard quantization of states of charged particles moving on the plane in a magnetic field, the so called Landau quantization, is presented. The Laughlin wave function and Jain's idea of composite fermions are introduced and discussed with regard to fractional statistics and statistics transmutation. The Chern–Simons theory is presented as a theoretically complete and effective method for implementation of nonstandard statistics. The Haldane generalization of Pauli exclusion principle for fermions is also reported.Less
This introductory chapter starts with short review of experimental and theoretical description of integral and fractional quantum Hall effects. The standard quantization of states of charged particles moving on the plane in a magnetic field, the so called Landau quantization, is presented. The Laughlin wave function and Jain's idea of composite fermions are introduced and discussed with regard to fractional statistics and statistics transmutation. The Chern–Simons theory is presented as a theoretically complete and effective method for implementation of nonstandard statistics. The Haldane generalization of Pauli exclusion principle for fermions is also reported.
John Orton and Tom Foxon
- Published in print:
- 2015
- Published Online:
- August 2015
- ISBN:
- 9780199695829
- eISBN:
- 9780191748844
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199695829.003.0006
- Subject:
- Physics, History of Physics
Low-dimensional structures consisting of semiconductor heterostructures of thickness down to a very few atomic monolayers were grown ideally by MBE and resulted in a surge of interest in MBE itself. ...
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Low-dimensional structures consisting of semiconductor heterostructures of thickness down to a very few atomic monolayers were grown ideally by MBE and resulted in a surge of interest in MBE itself. Short period superlattices, doping superlattices, quantum wells, wires and dots and two-dimensional electron gases (2DEGs) all proved of significance from scientific and commercial viewpoints. Superlattices and quantum wells showed negative electrical resistance, doping superlattices provided tuneable energy gaps, and quantum wells, quantum wires and quantum dots were characterised by confined energy states which offered photon energies tuneable by varying their dimensions. They also demonstrated increasingly sharp density of state functions, of interest for semiconductor lasers. 2DEGs showed very high electron mobilities by minimising ionised impurity scattering. The 2D localisation in 2DEGs resulted in discovery of the quantum Hall effect and fractional quantum Hall effect.Less
Low-dimensional structures consisting of semiconductor heterostructures of thickness down to a very few atomic monolayers were grown ideally by MBE and resulted in a surge of interest in MBE itself. Short period superlattices, doping superlattices, quantum wells, wires and dots and two-dimensional electron gases (2DEGs) all proved of significance from scientific and commercial viewpoints. Superlattices and quantum wells showed negative electrical resistance, doping superlattices provided tuneable energy gaps, and quantum wells, quantum wires and quantum dots were characterised by confined energy states which offered photon energies tuneable by varying their dimensions. They also demonstrated increasingly sharp density of state functions, of interest for semiconductor lasers. 2DEGs showed very high electron mobilities by minimising ionised impurity scattering. The 2D localisation in 2DEGs resulted in discovery of the quantum Hall effect and fractional quantum Hall effect.
Nicolas Regnault
- Published in print:
- 2017
- Published Online:
- March 2017
- ISBN:
- 9780198785781
- eISBN:
- 9780191827600
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198785781.003.0004
- Subject:
- Physics, Condensed Matter Physics / Materials
Entanglement spectroscopy has stimulated an extensive range of studies. The entanglement spectrum is the spectrum of the reduced density matrix when the system is partitioned into two. For many ...
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Entanglement spectroscopy has stimulated an extensive range of studies. The entanglement spectrum is the spectrum of the reduced density matrix when the system is partitioned into two. For many quantum systems, when computed from the bulk ground-state wavefunction, it gives access to the physics of edge excitations. It is thus a valuable tool to diagnose topological ordering. These lecture notes provide an overview of entanglement spectroscopy, mostly in the context of the fractional quantum Hall effect. The basic concepts are introduced through the example of quantum spin chains. The connection with entanglement entropy and the matrix product state representation is discussed. The entanglement spectrum can be computed for non-interacting topological phases, revealing edge excitation from the ground state. Application to fractional quantum Hall phases shows how much information is encoded within the ground state and how different partitions probe different types of excitations. Application to fractional Chern insulators is discussed.Less
Entanglement spectroscopy has stimulated an extensive range of studies. The entanglement spectrum is the spectrum of the reduced density matrix when the system is partitioned into two. For many quantum systems, when computed from the bulk ground-state wavefunction, it gives access to the physics of edge excitations. It is thus a valuable tool to diagnose topological ordering. These lecture notes provide an overview of entanglement spectroscopy, mostly in the context of the fractional quantum Hall effect. The basic concepts are introduced through the example of quantum spin chains. The connection with entanglement entropy and the matrix product state representation is discussed. The entanglement spectrum can be computed for non-interacting topological phases, revealing edge excitation from the ground state. Application to fractional quantum Hall phases shows how much information is encoded within the ground state and how different partitions probe different types of excitations. Application to fractional Chern insulators is discussed.
Joel E. Moore
- Published in print:
- 2017
- Published Online:
- March 2017
- ISBN:
- 9780198785781
- eISBN:
- 9780191827600
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198785781.003.0001
- Subject:
- Physics, Condensed Matter Physics / Materials
These lecture notes seek to present a coherent picture of some key aspects of topological insulators and the quantum Hall effect. Rather than aiming for completeness or historical accuracy, the goal ...
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These lecture notes seek to present a coherent picture of some key aspects of topological insulators and the quantum Hall effect. Rather than aiming for completeness or historical accuracy, the goal is to show that a few important ideas, such as the Berry phase and Chern and Chern–Simons differential forms, occur repeatedly and serve as links between superficially different areas of physics. Non-interacting topological phases, electrical polarization, and some transport phenomena in metals can all be understood in a unified framework as consequences of Abelian and non-Abelian Berry phases. The fractional quantum Hall effect is discussed as an example of topological order, and its description by (Abelian) Chern–Simons topological field theory is introduced.Less
These lecture notes seek to present a coherent picture of some key aspects of topological insulators and the quantum Hall effect. Rather than aiming for completeness or historical accuracy, the goal is to show that a few important ideas, such as the Berry phase and Chern and Chern–Simons differential forms, occur repeatedly and serve as links between superficially different areas of physics. Non-interacting topological phases, electrical polarization, and some transport phenomena in metals can all be understood in a unified framework as consequences of Abelian and non-Abelian Berry phases. The fractional quantum Hall effect is discussed as an example of topological order, and its description by (Abelian) Chern–Simons topological field theory is introduced.
Nigel R. Cooper
- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199661886
- eISBN:
- 9780191748356
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199661886.003.0005
- Subject:
- Physics, Atomic, Laser, and Optical Physics
This chapter reviews the theoretical understanding of Bose and Fermi superfluids under rotation (or in an effective magnetic field) while placing this in context of the current experimental status. ...
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This chapter reviews the theoretical understanding of Bose and Fermi superfluids under rotation (or in an effective magnetic field) while placing this in context of the current experimental status. It focuses on theoretical predictions of the novel phases that can appear. One goal is to establish the connections with the physics of the fractional quantum Hall effect of electrons in semiconductors. As the chapter is intended to be tutorial in nature, it concentrates on the qualitative features and simple model calculations to present the essential ideas in as physically transparent a way as possible. It begins with a brief review of the properties of Bose–Einstein condensates subjected to rotation.Less
This chapter reviews the theoretical understanding of Bose and Fermi superfluids under rotation (or in an effective magnetic field) while placing this in context of the current experimental status. It focuses on theoretical predictions of the novel phases that can appear. One goal is to establish the connections with the physics of the fractional quantum Hall effect of electrons in semiconductors. As the chapter is intended to be tutorial in nature, it concentrates on the qualitative features and simple model calculations to present the essential ideas in as physically transparent a way as possible. It begins with a brief review of the properties of Bose–Einstein condensates subjected to rotation.
Tom Lancaster and Stephen J. Blundell
- Published in print:
- 2014
- Published Online:
- June 2014
- ISBN:
- 9780199699322
- eISBN:
- 9780191779435
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199699322.003.0046
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
The fractional quantum Hall effect is introduced in this chapter and it explains how quasiparticles carrying fractional charge emerge in this theory.
The fractional quantum Hall effect is introduced in this chapter and it explains how quasiparticles carrying fractional charge emerge in this theory.
Lucjan Jacak, Piotr Sitko, Konrad Wieczorek, and Arkadiusz Wojs
- Published in print:
- 2003
- Published Online:
- January 2010
- ISBN:
- 9780198528708
- eISBN:
- 9780191713477
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528708.003.0007
- Subject:
- Physics, Condensed Matter Physics / Materials, Theoretical, Computational, and Statistical Physics
This chapter analyzes the fractional quantum Hall effect in composite fermion systems. The basic idea of composite fermions conceived by Jain and its relation with the Laughlin wave function are ...
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This chapter analyzes the fractional quantum Hall effect in composite fermion systems. The basic idea of composite fermions conceived by Jain and its relation with the Laughlin wave function are presented. The Hall conductivity in a system of composite fermions within Chern–Simons field theory is discussed. The ground state energy of composite fermion systems is found. The metal of composite fermions is also considered. The BCS paired Hall state in the composite Fermi liquid is also discussed.Less
This chapter analyzes the fractional quantum Hall effect in composite fermion systems. The basic idea of composite fermions conceived by Jain and its relation with the Laughlin wave function are presented. The Hall conductivity in a system of composite fermions within Chern–Simons field theory is discussed. The ground state energy of composite fermion systems is found. The metal of composite fermions is also considered. The BCS paired Hall state in the composite Fermi liquid is also discussed.
J. B. Ketterson
- Published in print:
- 2016
- Published Online:
- December 2016
- ISBN:
- 9780198742906
- eISBN:
- 9780191821523
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198742906.003.0048
- Subject:
- Physics, Condensed Matter Physics / Materials
This chapter first analyses the integer quantum Hall effect, covering an electron in two dimensions in a magnetic field; a two-dimensional electron gas in a magnetic field; motion under orthogonal ...
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This chapter first analyses the integer quantum Hall effect, covering an electron in two dimensions in a magnetic field; a two-dimensional electron gas in a magnetic field; motion under orthogonal electric and magnetic fields; the quantization of the Hall voltage; an electron in two dimensions in a magnetic field; edge states; and localized states. The chapter then turns to the fractional quantum Hall effect, discussing a semi-empirical accounting for observed filling fractions; many-body ground states for non-interacting electrons in the lowest Landau level; adding flux tubes to the non-interacting many-body ground state wave function; and trial ground states for the fractional quantum Hall effect. Sample problems are also provided at the end of the chapter.Less
This chapter first analyses the integer quantum Hall effect, covering an electron in two dimensions in a magnetic field; a two-dimensional electron gas in a magnetic field; motion under orthogonal electric and magnetic fields; the quantization of the Hall voltage; an electron in two dimensions in a magnetic field; edge states; and localized states. The chapter then turns to the fractional quantum Hall effect, discussing a semi-empirical accounting for observed filling fractions; many-body ground states for non-interacting electrons in the lowest Landau level; adding flux tubes to the non-interacting many-body ground state wave function; and trial ground states for the fractional quantum Hall effect. Sample problems are also provided at the end of the chapter.
John Orton
- Published in print:
- 2008
- Published Online:
- January 2010
- ISBN:
- 9780199559107
- eISBN:
- 9780191712975
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199559107.003.0004
- Subject:
- Physics, Crystallography: Physics
This chapter describes the establishment of silicon as the dominant semiconductor in modern electronics. Not only was it the preferred material for the manufacture of integrated circuits, but also ...
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This chapter describes the establishment of silicon as the dominant semiconductor in modern electronics. Not only was it the preferred material for the manufacture of integrated circuits, but also for the development of power devices. The invention of the integrated circuit by Jack Kilby at Texas Instruments is described, together with that of the planar IC by Robert Noyce at Fairchild Semiconductor. The subsequent growth of IC technology is outlined, depending very largely on the invention of the MOS transistor in 1960. A brief outline is given of silicon wafer production and the application of photolithography in defining IC patterns. Moore's Law is explained and a short discussion of Japanese successes in the IC business during the 1970s is interpolated. The parallel development of silicon power devices is described, together with a selection of typical applications. The chapter concludes with an account of some exciting developments in silicon physics, including the discovery of the quantum Hall effect.Less
This chapter describes the establishment of silicon as the dominant semiconductor in modern electronics. Not only was it the preferred material for the manufacture of integrated circuits, but also for the development of power devices. The invention of the integrated circuit by Jack Kilby at Texas Instruments is described, together with that of the planar IC by Robert Noyce at Fairchild Semiconductor. The subsequent growth of IC technology is outlined, depending very largely on the invention of the MOS transistor in 1960. A brief outline is given of silicon wafer production and the application of photolithography in defining IC patterns. Moore's Law is explained and a short discussion of Japanese successes in the IC business during the 1970s is interpolated. The parallel development of silicon power devices is described, together with a selection of typical applications. The chapter concludes with an account of some exciting developments in silicon physics, including the discovery of the quantum Hall effect.
E. L. Wolf
- Published in print:
- 2013
- Published Online:
- January 2014
- ISBN:
- 9780199645862
- eISBN:
- 9780191767852
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199645862.003.0008
- Subject:
- Physics, Condensed Matter Physics / Materials
The disintegration of graphene near 5,000 K is modeled by Ito and Nakamura to produce linear chain fragments. It appears from modelling that the disintegrations initiate in “locally crumpled” ...
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The disintegration of graphene near 5,000 K is modeled by Ito and Nakamura to produce linear chain fragments. It appears from modelling that the disintegrations initiate in “locally crumpled” regions, where pentagonal and seven-member rings first form. A corollary of the unique electric field effect in graphene is its sensitivity to stray electric fields leading to “charge puddles” in practical samples, obscuring the metal–insulator transition. An anomalous non-local transport effect in magnetic field was reported by Abanin et al. in 2011. Anomalous fractional quantum Hall effects and the Klein tunneling effect are clearly observed in graphene. The anomalous vanishing of backscattering is explained by the dual sublattice aspect of the honeycomb lattice, leading to a carrier’s pseudo-spin that resists reversal. A nematic electron–electron induced transition in bilayer graphene is suggested with some experimental support.Less
The disintegration of graphene near 5,000 K is modeled by Ito and Nakamura to produce linear chain fragments. It appears from modelling that the disintegrations initiate in “locally crumpled” regions, where pentagonal and seven-member rings first form. A corollary of the unique electric field effect in graphene is its sensitivity to stray electric fields leading to “charge puddles” in practical samples, obscuring the metal–insulator transition. An anomalous non-local transport effect in magnetic field was reported by Abanin et al. in 2011. Anomalous fractional quantum Hall effects and the Klein tunneling effect are clearly observed in graphene. The anomalous vanishing of backscattering is explained by the dual sublattice aspect of the honeycomb lattice, leading to a carrier’s pseudo-spin that resists reversal. A nematic electron–electron induced transition in bilayer graphene is suggested with some experimental support.
Alexandre Guay and Olivier Sartenaer
- Published in print:
- 2018
- Published Online:
- October 2018
- ISBN:
- 9780190636814
- eISBN:
- 9780190636845
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780190636814.003.0010
- Subject:
- Philosophy, Philosophy of Science
Among the very architects of the recent reemergence of emergentism in the physical sciences, Robert B. Laughlin certainly occupies a prominent place. Through a series of works beginning as early as ...
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Among the very architects of the recent reemergence of emergentism in the physical sciences, Robert B. Laughlin certainly occupies a prominent place. Through a series of works beginning as early as his Nobel lecture in 1998, he relentlessly advocated a strongly anti-reductionist view of physics. In spite of this, rare are the philosophers who have paid serious attention to Laughlin’s insights, even among those sympathetic to the idea of emergence. The starting point of this chapter is a willingness to remedy this situation by taking seriously Laughlin’s emergentism. More specifically, reflecting on Laughlin’s idea, according to which “one of the things an emergent phenomenon can do is create new particles,” the authors propose an exploration of the way in which emergence can shed light on the ontological status of some quantum entities—more particularly, so-called quasiparticles—that would come into being on the occasion of certain physical transformations.Less
Among the very architects of the recent reemergence of emergentism in the physical sciences, Robert B. Laughlin certainly occupies a prominent place. Through a series of works beginning as early as his Nobel lecture in 1998, he relentlessly advocated a strongly anti-reductionist view of physics. In spite of this, rare are the philosophers who have paid serious attention to Laughlin’s insights, even among those sympathetic to the idea of emergence. The starting point of this chapter is a willingness to remedy this situation by taking seriously Laughlin’s emergentism. More specifically, reflecting on Laughlin’s idea, according to which “one of the things an emergent phenomenon can do is create new particles,” the authors propose an exploration of the way in which emergence can shed light on the ontological status of some quantum entities—more particularly, so-called quasiparticles—that would come into being on the occasion of certain physical transformations.