The Quantum Hall Effect: Novel Excitations And Broken Symmetries

Girvin, S. M.

doi:10.1007/3-540-46637-1_2

Cited by 138 publications

(250 citation statements)

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“…By fitting the critical region to a line on a log-log graph we find ν c = 1.25 ± 0.05 (26) where the error bars reflect the uncertainty associated with choosing the critical region. This value compares well with the exact result from percolation theory ν c = 4/3 11 .…”

Section: A Classical Motionmentioning

confidence: 99%

Correlated quantum percolation in the lowest Landau level

Sandler¹,

Maei²,

Kondev³

2004

Phys. Rev. B

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Our understanding of localization in the integer quantum Hall effect is informed by a combination of semi-classical models and percolation theory. Motivated by the effect of correlations on classical percolation we study numerically electron localization in the lowest Landau level in the presence of a power-law correlated disorder potential. Careful comparisons between classical and quantum dynamics suggest that the extended Harris criterion is applicable in the quantum case. This leads to a prediction of new localization quantum critical points in integer quantum Hall systems with powerlaw correlated disorder potentials. We demonstrate the stability of these critical points to addition of competing short-range disorder potentials, and discuss possible experimental realizations.

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Section: A Classical Motionmentioning

confidence: 99%

Correlated quantum percolation in the lowest Landau level

Sandler¹,

Maei²,

Kondev³

2004

Phys. Rev. B

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“…By applying a field-effect transistor structure (FET, see Methods), the Fermi energy (E F ) of the TI heterostructures can be precisely controlled in a large energy range over the bulk bandgap. In particular, the quantum AHE realized in the magnetic TIs offers an interesting scenario where the two different physical mechanisms merge-namely, skyrmion formation around the doped carrier into the quantum Hall ferromagnet 23 and skyrmion formation at the interface of magnets [24][25][26][27] . First, we investigate the gate voltage (V G ) and temperature (T ) dependence of the Hall effect for a 2-nm CBST/5-nm BST heterostructure as shown in Fig.…”

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confidence: 99%

Geometric Hall effects in topological insulator heterostructures

et al. 2016

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Geometry, both in momentum and in real space, plays an important role in the electronic dynamics of condensed matter systems. Among them, the Berry phase associated with nontrivial geometry can be an origin of the transverse motion of electrons, giving rise to various geometric e ects such as the anomalous 1 , spin 2 and topological Hall e ects 3-6 . Here, we report two unconventional manifestations of Hall physics: a sign-reversal of the anomalous Hall e ect, and the emergence of a topological Hall e ect in magnetic/non-magnetic topological insulator heterostructures, Cr x (Bi 1−y Sb y ) 2−x Te 3 /(Bi 1−y Sb y ) 2 Te 3 . The sign-reversal in the anomalous Hall e ect is driven by a Rashba splitting at the bulk bands, which is caused by the broken spatial inversion symmetry. Instead, the topological Hall e ect arises in a wide temperature range below the Curie temperature, in a region where the magnetic-field dependence of the Hall resistance largely deviates from the magnetization. Its origin is assigned to the formation of a Néel-type skyrmion induced by the Dzyaloshinskii-Moriya interaction.The geometry and topology in Hilbert space constitute a central issue in quantum physics, which has recently also shed a new light on the electronic states in solids. The wavefunctions are characterized by the Berry connection between two neighbouring points, in both momentum space and real space, which plays the role of the vector potential leading to the concept of emergent electromagnetic field (EEMF). Global topology of the manifold in Hilbert space is represented by topological integers. As integers cannot change continuously, it gives a certain stability to the system. For example, the Chern number, which is given by the integral of the emergent magnetic field over the first Brillouin zone, protects the surface or edge states supporting the dissipationless current flows (that is, bulk-edge correspondence). The one-dimensional chiral edge mode in the quantum Hall effect and the Dirac surface state in three-dimensional topological insulators (TI; refs 7,8) are the representative examples of this phenomenon. In addition, it has recently been proposed 9,10 and observed 11-14 that TI with doped magnetic ions-namely, Cr or V-produces the quantized version of the anomalous Hall effect (AHE) in the absence of an external magnetic field.Topology in real space, on the other hand, is exemplified by skyrmion spin texture 15-17 found in chiral-lattice magnets such as MnSi (ref. 15) or Fe 1−x Co x Si (ref. 16). Here, the solid angle subtended by the spins forms an emergent magnetic field in real space, and its integral over the two-dimensional space defines a topological integer called the skyrmion number. Namely, the skyrmion number counts the number of times the spin direction wraps around a unit sphere. This integer protects the skyrmion from annihilation and allows it to behave as a single particle.Thus far, the EEMF in momentum and real spaces have mostly been studied separately. Recent advances in fabricating artificial stru...

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“…1,2,3,4 The fractional effect has yielded fractional charge, spin and statistics, as well as unprecedented order parameters. 5 There are beautiful connections with a variety of different topological and conformal field theories of interest in nuclear and high energy physics.…”

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confidence: 99%

“…The pseudospin stiffness ρ s physically arises from the loss of optimal Coulomb exchange in the presence of a phase gradient. 4 Because momentum in a magnetic field is related to position in real space 4 a phase gradient of the order parameter corresponds to a spatial displacement of the correlation hole so that it is no longer directly on top of the mbtfinal2: submitted to World Scientific on May 28, 2018…”

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Broken Symmetry and Josephson-Like Tunnelling in Quantum Hall Bilayers

Girvin

2002

Recent Progress in Many-Body Theories

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I review recent novel experimental and theoretical advances in the physics of quantum Hall effect bilayers. Of particular interest is a broken symmetry state which optimizes correlations by putting the electrons into a coherent superposition of the two different layers.The various quantum Hall effects are among the most remarkable many-body phenomena discovered in the second half of the twentieth century. 1, 2, 3, 4 The fractional effect has yielded fractional charge, spin and statistics, as well as unprecedented order parameters. 5 There are beautiful connections with a variety of different topological and conformal field theories of interest in nuclear and high energy physics.The quantum Hall effect (QHE) takes place in a two-dimensional electron gas formed in a quantum well in a semiconductor host material and subjected to a very high magnetic field. In essence it is a result of a commensuration between the number of electrons, N , and the number of flux quanta, N Φ , in the applied magnetic field. The electrons condense into distinct and highly non-trivial ground states ('vacua') formed at each rational fractional value of the filling factor ν ≡ N/N Φ .The essential feature of (most) of these exotic states is the existence of an excitation gap. The electron fluid is incompressible and flows rigidly past obstacles (impurities in the sample) with no dissipation. A weak external electric field will cause the fluid to move, but the excitation gap prevents the fluid from absorbing any energy from the electric field. Hence the current flow must be exactly at right angles to the field and the conductivity tensor takes the remarkable universal formIronically, this ideal behavior occurs because of imperfections and disorder in the samples which localize topological defects (vortices) whose motion would otherwise dissipate energy. In a two-dimensional superconductor, such vortices undergo a confinement phase transition at the Kosterlitz-Thouless temperature and dissipation ceases. In most cases in the QHE, an analog of the Anderson-Higgs mechanism causes the vortices to be deconfined 5 so that dissipation is strictly zero only at zero temperature. In practice, values of σ xx /σ xy as small as 10 −13 are not difficult to obtain at dilution refrigerator tempertures. Recent technological progress in molecular beam epitaxy techniques has led to the ability to produce pairs of closely spaced two-dimensional electron gases. Strong correlations between the electrons in different layers lead a great deal of completely new physics involving spontaneous interlayer phase coherence. 6,

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The Quantum Hall Effect: Novel Excitations And Broken Symmetries

Abstract: To be published by Springer Verlag and Les Editions de Physique in 1999.ii S.M. Girvin These lectures are dedicated to the memory of Heinz Schulz, a great friend and a wonderful physicist.

Cited by 138 publications

References 89 publications

Correlated quantum percolation in the lowest Landau level

Correlated quantum percolation in the lowest Landau level

Geometric Hall effects in topological insulator heterostructures

Broken Symmetry and Josephson-Like Tunnelling in Quantum Hall Bilayers

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