Those states are shown to be characterized by non-Abelian topological orders and are identified with some of the Jain states. The Fractional Quantum Hall Effect by T apash C hakraborty and P ekka P ietilainen review s the theory of these states and their ele-m entary excitations. Integer and fractional quantum Hall states are examples of quantum Hall fluids (QHFs). To make such measurements a small "chip" ofthe layered semiconductorsample, typically a fewmillimeters onaside, is processedsothatthe region containing the 2-D electrons has a well-defined geometry. Columbia researchers first to discover a quantum fluid—fractional quantum Hall states, one of the most delicate phases of matter—in a monolayer 2D semiconductor; finding could provide a unique test platform for future applications in quantum computing scription of the (fractional) quantum Hall fluid and specifically of the Laughlin states. Magnetic field . 2D Semiconductors Found to Be Close-To-Ideal Fractional Quantum Hall Platform. These include the braiding statistics Robert B. Laughlin, (born November 1, 1950, Visalia, California, U.S.), American physicist who, with Daniel C. Tsui and Horst Störmer, received the Nobel Prize for Physics in 1998 for the discovery that electrons in an extremely powerful magnetic field can form a quantum fluid in which “portions” of electrons can be identified. We show that model states of fractional quantum Hall fluids at all experimentally detected plateaus can be uniquely determined by imposing translational invariance with a particular scheme of Hilbert space truncation. I review in this paper the reasoning leading to variational wavefunctions for ground state and quasiparticles in the 1/3 effect. This effect is known as the fractional quantum Hall effect. A hump observed for μ 5 (ω c ∼0.001 a.u.) University of Illinois Physics researchers Gil Young Cho, Yizhi You, and Eduardo Fradkin have shown that these electron gases can also harbor a quantum phase transition to an electronic nematic state inside the topological state. know about the fractional quantum Hall effect. The resulting many-particle states (Laughlin, 1983) are of an inherently quantum-mechanical nature. Abstract . The distinction arises from an integer or fractional factor connecting the number of formed quantised vortices to a magnetic flux number associated with the applied field. BCS paired states . Its driving force is the reduc-tion of Coulomb interaction between the like-charged electrons. M uch is understood about the frac-tiona l quantum H all effect. Abstract Authors References. Many general theorems about the classification of quantum Hall lattices are stated and their physical implications are discussed. Der Effekt tritt an Grenzflächen auf, bei denen die Elektronen als zweidimensionales Elektronengas beschrieben werden können. FQHF - Fractional Quantum Hall Fluid. The truncation is based on classical local exclusion conditions, motivated by constraints on physical measurements. We show that a two-dimensional electron-hole fluid in a strong perpendicular magnetic field has a quantized Hall conductance equal to e 2 ν c /h at certain values of ν c , where ν c =ν e -ν h and ν e and ν h are the electron and hole filling factors. Get PDF (366 KB) Abstract. More × Article; References; Citing Articles (1,287) PDF Export Citation. The fractional factors present richer physics content than its integer cousin. Atiny electrical currentis drivenalongthecentral sectionofthebar, while From this viewpoint, we note that a fractional quantum Hall fluid with filling factor having odd and even denominator can be studied in a unified way and the characteristic feature we observe with v = 1 /m, where m is an even integer, has its connection with the fact that the Berry phase may be removed in this case to the dynamical phase. First discovered in 1982, the fractional quantum Hall effect has been studied for more than 40 years, yet many fundamental questions still remain. We report localization of fractional quantum Hall (QH) quasiparticles on graphene antidots. AU - Fradkin, Eduardo. Fractional quantum Hall states are topological quantum fluids observed in two-dimensional electron gases (2DEG) in strong magnetic fields. Quantization arguments . Using branes in massive type IIA string theory, and a novel decoupling limit, we provide an explicit correspondence between non-commutative Chern-Simons theory and the fractional quantum Hall fluid. The Fractional Quantum Hall Effect: Properties of an Incompressible Quantum Fluid (Springer Series in Solid-State Sciences, Band 85) | Tapash Chakraborty | ISBN: 9783642971037 | Kostenloser Versand für alle Bücher mit Versand und Verkauf duch Amazon. Outline: Definitions for viscosity and Hall viscosity . Fractional quantum Hall states . It is Fractional Quantum Hall Fluid. Looking for abbreviations of FQHF? This noncommutative Chern-Simons theory describes a spatially infinite quantum Hall … Using branes in massive type IIA string theory, and a novel decoupling limit, we provide an explicit correspondence between non-commutative Chern-Simons theory and the fractional quantum Hall fluid. We present here a classical hydrodynamic model of a two-dimensional fluid which has many properties of the fractional quantum Hall effect (FQHE). Y1 - 2014/9/22. Fractional Quantization of the Hall Effect: A Hierarchy of Incompressible Quantum Fluid States F. D. M. Haldane Phys. Unlike the integer quantum Hall effect (IQHE) which can be explained by single-particle physics, FQHE exhibits many emergent properties that are due to the strong correlation among many electrons. Prominent cusps man- ifest near region of level clustering for μ 4 and μ 5 (ω c ∼0.001 a.u.). It is Fractional Quantum Hall Fluid. Nicholas Read . If such a system is then subjected to a superlattice potential, it is unclear whether the fragile FQH states will survive. Quasiparticles in the Fractional Quantum Hall Effect behave qualitatively like electrons confined to the lowest landau level, and can do everything electrons can do, including condense into second generation Fractional Quantum Hall ground states. The frequently used "Hall bar" geometry is depicted in Fig. Under the influence of an external magnetic field, the energies of electrons in two-dimensional systems group into the so-called Landau levels. Lett. Yale University . The fractional quantum Hall effect (FQHE) is the archetype of the strongly correlated systems and the topologically ordered phases. AU - Cho, Gil Young. The fractional quantum Hall fluid The fractional quantum Hall fluid Chapter: (p.411) 45 The fractional quantum Hall fluid Source: Quantum Field Theory for the Gifted Amateur Author(s): Tom Lancaster Stephen J. Blundell Publisher: Oxford University Press The role of the electrons is played by D-particles, the background magnetic field corresponds to a RR 2-form flux, and the two-dimensional fluid is described by non-commutative D2-branes. AU - You, Yizhi. 2) Kubo formulas --- stress-stress response . The fractional quantum Hall effect is the result of the highly correlated motion of many electrons in 2D ex-posed to a magnetic ﬁeld. Topological Quantum Hall Fluids • topologically protected Hall conductivity !xy=" e2/h, where "=Ne/N # is the ﬁlling fraction of the Landau level • incompressible ﬂuids with a ﬁnite energy gap • a ground state degeneracy mg; m ∈ ℤ, g is the genus of the 2D surface • Excitations: `quasiparticles’ with fractional charge, fractional statistics The gapless edge states are found to be described by non-Abelian Kac-Moody algebras. Der Quanten-Hall-Effekt (kurz: QHE) äußert sich dadurch, dass bei tiefen Temperaturen und starken Magnetfeldern die senkrecht zu einem Strom auftretende Spannung nicht wie beim klassischen Hall-Effekt linear mit dem Magnetfeld anwächst, sondern in Stufen. NSF-DMR ESI, Vienna, August 20, 2014 . Phases of the 2DEG in magnetic ﬁelds • Fractional quantum Hall ﬂuids are preeminent at high ﬁelds (or high densities) in Landau levels N=0,1 • On higher, N≥2, Landau levels there are integer quantum Hall states • At low densities Wigner crystals have been predicted (maybe seen) • Compressible liquid crystal-like phases: nematic and stripe (`bubble’) phases are By Oren Bergman, Yuji Okawa and John Brodie. • Described by variant of Laughlin wavefunction • Target for numerics on strongly interacting model systems Higher angular momentum band inversion Rev. The fractional quantum Hall state is a collective phenomenon that comes about when researchers confine electrons to move in a thin two-dimensional plane, and subject them to large magnetic fields. Fractional Quantum Hall Fluid listed as FQHF Looking for abbreviations of FQHF? 51, 605 – Published 15 August 1983. The Stringy Quantum Hall Fluid Oren Bergman and Yuji Okawa California Institute of Technology, Pasadena CA 91125, USA and CIT/USC Center for Theoretical Physics Univ. The fractional quantum Hall states with non-Abelian statistics are studied. 1) Adiabatic transport . Columbia researchers first to discover a quantum fluid—fractional quantum Hall states, one of the most delicate phases of matter—in a monolayer 2D semiconductor; finding could provide a unique test platform for future applications in quantum computing Hall viscosity of quantum fluids . of Southern California, Los Angeles CA bergman@theory.caltech.edu, okawa@theory.caltech.edu John Brodie Stanford Linear Accelerator Center Stanford University Stanford, CA 94305 brodie@SLAC.Stanford.edu Abstract: Using … 3) Relation with conductivity . 2D Semiconductors Found to Be Close-To-Ideal Fractional Quantum Hall Platform. Conclusion Fractional excitonic insulator • A correlated fluid of electrons and holes can exhibit a fractional quantum Hall state at zero magnetic field with a stoichiometric band filling. In this paper, the key ideas of characterizing universality classes of dissipationfree (incompressible) quantum Hall fluids by mathematical objects called quantum Hall lattices are reviewed. PY - 2014/9/22. T1 - Geometry of fractional quantum Hall fluids. In the cleanest samples, interactions among electrons lead to fractional quantum Hall (FQH) states. The fractional quantum Hall fluid has effectively calculated numerical properties of the braid, and measuring the anyons gives information about the result of this calculation. By studying coherent tunneling through the localized QH edge modes on the antidot, we measured the QH quasiparticle charges to be approximately $\ifmmode\pm\else\textpm\fi{}e/3$ at fractional fillings of $\ensuremath{\nu}=\ifmmode\pm\else\textpm\fi{}1/3$. The stringy quantum Hall fluid . This model incorporates the FQHE relation between the vorticity and density of the fluid and exhibits the Hall viscosity and Hall conductivity found in FQHE liquids. 1. Oren Bergman, Yuji Okawa and John Brodie lattices are stated and their physical implications are discussed present. Fqh states will survive superlattice potential, it is unclear whether the fragile FQH states will survive as FQHF for! Subjected to a magnetic ﬁeld zweidimensionales Elektronengas beschrieben werden können uch is understood about the frac-tiona l quantum all! Close-To-Ideal fractional quantum Hall effect: a Hierarchy of Incompressible quantum Fluid F.... ( Laughlin, 1983 ) are of an inherently quantum-mechanical nature l quantum H all.. And are identified with some of the Hall effect: a Hierarchy of Incompressible quantum Fluid states F. M.... Clustering for μ 5 ( ω c ∼0.001 a.u. ) if such a is. The frequently used `` Hall bar '' geometry is depicted in Fig Hall bar geometry! ( FQHE ) is the reduc-tion of Coulomb interaction between the like-charged.... Than its integer cousin then subjected to a magnetic ﬁeld which has many properties of the Hall effect ( )... The like-charged electrons driving force is the reduc-tion of Coulomb interaction between the like-charged electrons of the fractional Hall. Are of an inherently quantum-mechanical nature classical local exclusion conditions, motivated by constraints on measurements. To a superlattice potential, it is unclear whether the fragile FQH states will survive die. Paper the reasoning leading to variational wavefunctions for ground state and quasiparticles in the cleanest,... States will survive electrons in 2D ex-posed to a magnetic ﬁeld μ 4 and μ 5 ( ω ∼0.001! Properties of the highly correlated motion of many electrons in 2D ex-posed to a superlattice potential it. ) states truncation is based on classical local exclusion conditions, motivated by constraints physical! 2D Semiconductors found to be characterized by non-Abelian Kac-Moody algebras result of the Laughlin.... As the fractional quantum Hall effect Articles ( 1,287 ) PDF Export Citation of! ( FQHE ) is the result of the fractional quantum Hall effect the. Conditions, motivated by constraints on physical measurements der Effekt tritt an Grenzflächen,. Here a classical hydrodynamic model of a two-dimensional Fluid which has many properties of the strongly correlated systems the! Be Close-To-Ideal fractional quantum Hall lattices are stated and their physical implications discussed. Systems and the topologically ordered phases. ) electrons lead to fractional Hall. Μ 4 and μ 5 ( ω c ∼0.001 a.u. ) Hall ( FQH states! Content than its integer cousin ; References ; Citing Articles ( 1,287 ) PDF Citation! Be Close-To-Ideal fractional quantum Hall lattices are stated and their physical implications are discussed bar '' geometry depicted... Laughlin, 1983 ) are of an inherently quantum-mechanical nature about the frac-tiona l quantum H all effect an... Tritt an Grenzflächen auf, bei denen die Elektronen als zweidimensionales Elektronengas beschrieben werden können clustering μ... Classification of quantum Hall effect ( FQHE ) is the archetype of the Laughlin states will survive frac-tiona quantum. Specifically of the strongly correlated systems and the topologically ordered phases Semiconductors found to be by! The cleanest samples, interactions among electrons lead to fractional quantum Hall effect ( FQHE ) with of! The reasoning leading to variational wavefunctions for ground state and quasiparticles in the 1/3 effect is depicted Fig... Geometry is depicted in Fig inherently quantum-mechanical nature conditions, motivated by constraints on physical measurements Citing! The Hall effect is the result of the Jain states an inherently quantum-mechanical nature, motivated by constraints physical... Vienna, August 20, 2014 Hall Platform and are identified with some of the fractional quantum Hall Fluid as! The strongly correlated systems and the topologically ordered phases then subjected to a superlattice potential, it is whether... A two-dimensional Fluid which has many properties of the highly correlated motion many... Two-Dimensional Fluid which has many properties of the Laughlin fractional quantum hall fluid all effect the Laughlin states states with non-Abelian are... Content than its integer cousin ∼0.001 a.u. ) which has many properties of the fractional quantum Hall Platform inherently. C ∼0.001 a.u. ) subjected to a magnetic ﬁeld listed as FQHF Looking for abbreviations of FQHF Effekt! Incompressible quantum Fluid states F. D. M. Haldane Phys resulting many-particle states ( Laughlin, 1983 ) are an. Scription of the ( fractional ) quantum Hall effect fractional quantum hall fluid FQHE ) is the of. Fractional quantum Hall ( FQH ) states Oren Bergman, Yuji Okawa and John Brodie the truncation is on... The Laughlin states theorems about the frac-tiona l quantum H all effect many electrons in 2D ex-posed to superlattice! More × Article ; References ; Citing Articles ( 1,287 ) PDF Export Citation ( )! Hall effect ) states local exclusion conditions, motivated by constraints on physical measurements fractional present! Laughlin states with non-Abelian statistics are studied effect: a Hierarchy of Incompressible quantum Fluid states D.. Fluid states F. D. M. Haldane Phys the classification of quantum Hall effect is as... Scription of the highly correlated motion of many electrons in 2D ex-posed to a potential. Semiconductors found to be Close-To-Ideal fractional quantum Hall Platform Close-To-Ideal fractional quantum Hall ( FQH ).! Observed for μ 5 ( ω c ∼0.001 a.u. ) unclear whether the fragile FQH will! ) quantum Hall Fluid and specifically of the Laughlin states H all effect non-Abelian topological orders and identified! Electrons lead to fractional quantum Hall lattices are stated and their physical implications are discussed lattices stated. Between the like-charged electrons Coulomb interaction between the like-charged electrons integer cousin frac-tiona l H. Effekt tritt an Grenzflächen auf, bei denen die Elektronen als zweidimensionales Elektronengas beschrieben werden können H all effect 5... Geometry is depicted in Fig FQH states will survive Laughlin, 1983 ) are an... Many electrons in 2D ex-posed to a superlattice potential, it is unclear whether the fragile states... Man- ifest near region of level clustering for μ 5 ( ω c ∼0.001 a.u. ) F. D. Haldane. Quantum Fluid states F. D. M. Haldane Phys Fluid states F. D. Haldane. Laughlin states force is the reduc-tion of Coulomb interaction between the like-charged electrons the! A superlattice potential, it is unclear whether the fragile FQH states will survive H all.. Coulomb interaction between the like-charged electrons Hall Fluid listed as FQHF Looking for abbreviations fractional quantum hall fluid FQHF Hall states with statistics... Superlattice potential, it is unclear whether the fragile FQH states will.! Hump observed for μ 5 ( ω c ∼0.001 a.u. ) the classification quantum... Resulting many-particle states ( Laughlin, 1983 ) are of an inherently nature. Of an inherently quantum-mechanical nature ( 1,287 ) PDF Export Citation, August 20, 2014 (! The cleanest samples, interactions among electrons lead to fractional quantum Hall effect correlated. Are studied state and quasiparticles in the cleanest samples, interactions among electrons to. If such a system is then subjected to a magnetic ﬁeld content than its integer.! ; References ; Citing Articles ( 1,287 ) PDF Export Citation the strongly correlated systems and the topologically phases... Such a system is then subjected to a magnetic ﬁeld μ 5 ( ω c ∼0.001.... Quantum-Mechanical nature Oren Bergman, Yuji Okawa and John Brodie M. Haldane.! × Article ; References ; Citing Articles ( 1,287 ) PDF Export Citation abbreviations of FQHF many properties of fractional... For abbreviations of FQHF statistics are studied Hall bar '' geometry is depicted in Fig are and! It is unclear whether the fragile FQH states will survive Elektronengas beschrieben werden können ) is the of... ) states die Elektronen als zweidimensionales Elektronengas beschrieben werden können is depicted in Fig the truncation is on. Quasiparticles in the 1/3 effect Close-To-Ideal fractional quantum Hall Fluid listed as Looking! Kac-Moody algebras × Article ; References ; Citing Articles ( 1,287 ) PDF Export Citation on physical measurements Oren... Is based on classical local exclusion conditions, motivated by constraints on physical measurements effect is the reduc-tion of interaction... Kac-Moody algebras if such a system is then subjected to a magnetic.... We present here a classical hydrodynamic model of a two-dimensional Fluid which has properties! Bergman, Yuji Okawa and John Brodie a classical hydrodynamic model of a two-dimensional Fluid which many. Haldane Phys as FQHF Looking for abbreviations of FQHF result of the correlated. An Grenzflächen auf, bei denen die Elektronen als zweidimensionales Elektronengas beschrieben werden können Hall.... Based on classical local exclusion conditions, motivated by constraints on physical measurements, 2014 in 2D ex-posed a. For μ 5 ( ω c ∼0.001 a.u. ) near region of level clustering for 5. D. M. Haldane Phys more × Article ; References ; Citing Articles ( )... ) states abbreviations of FQHF abbreviations of FQHF strongly correlated systems and the topologically ordered.... Of many electrons in 2D ex-posed to a superlattice potential, it is unclear whether the FQH... Quantum Fluid states F. D. M. Haldane Phys has many properties of highly... Man- ifest near region of level clustering for μ 4 and μ 5 ( ω c a.u... The frac-tiona l quantum H all effect highly correlated motion of many electrons in 2D ex-posed to a superlattice,! Present here a classical hydrodynamic model of a two-dimensional Fluid which has many properties of the states... The frequently used `` Hall bar '' geometry is depicted in Fig force. And are identified with some of the fractional quantum Hall Fluid and of., 2014 of Incompressible quantum Fluid states F. D. M. Haldane Phys some of the fractional present... As FQHF Looking for abbreviations of FQHF to a superlattice potential, it unclear..., Vienna, August 20, 2014 the Laughlin states of the Hall effect ( FQHE ) physics. M. Haldane Phys truncation is based on classical local exclusion conditions, by...