https://doi.org/10.1142/9789811217494_0002. This has simplified the picture of the FQHE. It has been recognized that the time reversal symmetry may be spontaneously broken when flux has the long range order. The Integer Quantum Hall Effect: PDF Conductivity and Edge Modes. In this final section, we recall some phenomena which have been observed recently in physics laboratories, and which presumably deserve considerable efforts to overcome the heuristic level of explanation. Inclusion of electron–electron interaction significantly complicates calculations, and makes the physics much richer. Furthermore, with the aim of predicting the sequence of magic proton and neutron numbers accurately, physicists have constructed a higher-dimensional representation of a fractional rotation group with mixed derivative types. Fractional statistics can occur in 3D between pointlike and linelike objects, so a genuinely fractional 3D phase must have both types of excitations. Starting from the Luttinger model for the band structure of GaAs, we derive an effective theory that describes the coupling of the fractional quantum Hall (FQH) system with photon The TSG effect with spin is well described by a generalization of the CF theory. The statistics of quasiparticles entering the quantum Hall effect are deduced from the adiabatic theorem. For the integer quantum Hall effect (IQHE), ρ xy = {h/νe 2}, where h is the Planck constant, e is the charge of an electron and ν is an integer, while for the fractional quantum Hall effect (FQHE), ν is a simple fraction. In a later theoretical description, the electrons and flux quanta present in the system have been combined with new quasiparticles – the so-called composite particles which have either fermionic or bosonic character depending on whether the number of flux quanta attached to an electron is even or odd. In wide wells, even when the system hosts a fractional quantum Hall state at ν = ½, we observe a CF Fermi sea that is consistent with the total carrier density, favoring a single-component state. The existence of an energy gap is essential for the fractional quantum Hall effect (FQHE). Sometimes, the effect of electron–electron interaction on measurable quantities (e.g., conductance) is rather dramatic. Finite size calculations (Makysm, 1989) were in agreement with the experimental assignment for the spin polarization of the fractions. The particles condense into Zhang & T. Chakraborty: Ground State of Two-Dimensional Electrons and the Reversed Spins in the Fractional Quantum Hall Effect, Phys. The quantum Hall effect (QHE) is the remarkable observation of quantized transport in two dimensional electron gases placed in a transverse magnetic field: the longitudinal resistance vanishes while the Hall resistance is quantized to a rational multiple of h / e 2. We use cookies to help provide and enhance our service and tailor content and ads. While (13) is an (antisymmetric) product state (15)is not, and indeed its expansion in product states is not known in general. Landau levels, Landau gauge and symmetric gauge. We pay special attention to the filling factor 5/2 in the first excited Landau level (in two-dimensional electron gas in GaAs), where experimental evidence of a non-Abelian topological order was found. In some 2D systems, such as that of the fractional quantum Hall effect, new approaches and techniques have been developed, but exact solutions are not known. This is the case of two-dimensional electron gas showing fractional quantum Hall effect. It is a property of a collective state in which electrons bind magnetic flux lines to make new quasiparticles , and excitations have a fractional elementary charge and possibly also fractional statistics. https://doi.org/10.1142/9789811217494_0009. The variational argument has shown that the antiferromagnetic exchange coupling J in the t – J model favors the appearance of the flux state. Non-Abelian quantum Hall states bring to culmination the unique properties of fractionalized topological states of matter, such as fractional quantum numbers, topological ground state degeneracy and anyonic statistics. Sometimes, the effect of electron–electron interaction on measurable quantities (e.g., conductance) is rather dramatic. In the TCP model the plasma is made up of plasma ions of density ρp and impurity ions of density ρi (note change of notation, ie., now the object of the calculation is gpp(r) = 1 + hpp(r), and the ipp-correction is Δhpp(1,2∣ 0) etc.). One approach to constructing a 3D fractional topological insulator, at least formally, uses “partons”: the electron is broken up into three pieces, which each go into the “integer” topological insulator state, and then a gauge constraint enforces that the wavefunction actually be an allowed state of electrons [65,66]. It implies that many electrons, acting in concert, can create new particles having a charge smaller than the charge of any indi-vidual electron. The fractional quantum Hall effect is an example of the new physics that has emerged from the enormous progress made during the past few decades in material synthesis and device processing. We also review the wire construction approach to the analysis of non-Abelian quantum Hall states, and focus on a few special cases where this analysis may be carried out explicitly. Topics discussed include a successful cooling technique used, novel odd denominator fractional quantum Hall states, new transport results on even denominator fractional quantum Hall states and on re-entrant integer quantum Hall states, and phase transitions observed in half-filled Landau levels. Electron–electron interaction plays a central role in low-dimensional systems. The fractional Hall effect has led to many new concepts such as fractional statistics, composite quasi-particles (bosons and fermions), and braid groups. At even-denominator Landau level filling fractions, such as ν = ½, the ground state, in most cases, has no energy gap, and there is no quantized plateau in the Hall conductance. https://doi.org/10.1142/9789811217494_fmatter, https://doi.org/10.1142/9789811217494_0001. Ground State for the Fractional Quantum Hall Effect, Phys. As compared to a number of other recent reviews, most of this review is written so as to not rely on results from conformal field theory — although a short discussion of a few key relations to CFT are included near the end. 18.14). J.K. Jain, in Encyclopedia of Mathematical Physics, 2006, At small Zeeman energies, partially spin-polarized or spin-unpolarized FQHE states become possible. Indeed, some of the topological arguments in the previous chapter are so compelling that you might think the Hall resistivity of an insulator has to be an integer. In the latter, the gap already exists in the single-electron spectrum. Particular examples of such phenomena are: the multi-component, . 53, 722 (1984) - Fractional Statistics and the Quantum Hall Effect The statistics of quasiparticles entering the quantum Hall effect are deduced from the adiabatic theorem. It indicates that regularly frustrated spin systems with the ordinary form of exchange coupling is not likely to show the chiral order. I want to emphasize first that despite the superficial similarity of (13) and (15), they are very different beasts. The quantum Hall effect (QHE) (), in which the Hall resistance R xy of a quasi–two-dimensional (2D) electron or hole gas becomes quantized with values R xy =h/e 2 j (where his Planck's constant, e is the electron charge, andj is an integer), has been observed in a variety of inorganic semiconductors, such as Si, GaAs, InAs, and InP.At higher magnetic fields, fractional quantum Hall … By continuing you agree to the use of cookies. The quantum Hall effect (or integer quantum Hall effect) is a quantized version of the Hall effect, observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall resistance Rxy exhibits steps that take on the quantized values at certain level 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. 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. Around fractional ν of even denominators, such as ν=1/2,3/2,1/4,3/4,5/4,…, composite fermions are formed which do not see any effective magnetic field at the respective filling factor ν. The fractional quantum Hall effect reveals a new state of matter. The chapter concludes by making contact with other physical platforms where bosonic fractional quantum Hall states are expected to appear: in quantum magnets, engineered qubit arrays and polariton systems. 3. Electron–electron interaction in 1D systems leads to new physical concepts such as Tomonaga–Luttinger liquids (a manifestation of the deviation from Fermi liquid behavior). (This symmetric structure around ν = 1/2 can be seen in the data of Figure 3 for FQHE by comparing the low magnetic field region of the IQHE with the regions ∼12.6 T, which corresponds to ν = 1/2 in this sample.) The latter data are consistent with the 5/2 fractional quantum Hall effect being a topological p-wave paired state of CFs.

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