Quantized Hall effect and edge currents

MacDonald, Allan H.; Středa, P.

doi:10.1103/physrevb.29.1616

Cited by 315 publications

(165 citation statements)

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“…It is well known that such states appear when a highmobility two-dimensional electron gas is subjected to high magnetic fields [13]. In this quantum Hall effect (QHE) regime, the conduction proceeds exclusively through the edge states extending along the structure perimeter, provided that the electron states in the interior are localized [14,15]. Electron motion along the edges occurs only in one direction, as the magnetic field breaks the time reversal symmetry, and the one-dimensional edge channels are chiral, i.e., only one direction of propagation is allowed at each edge.…”

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confidence: 99%

Absence of nonlocal resistance in microstructures of PbTe quantum wells

Kolwas

Grabecki

Trushkin

et al. 2012

Physica Status Solidi (b)

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We report on experiments allowing to set an upper limit on the magnitude of the spin Hall effect and the conductance by edge channels in quantum wells of PbTe embedded between PbEuTe barriers. We reexamine previous data obtained for epitaxial microstructures of n-type PbSe and PbTe, in which pronounced nonlocal effects and reproducible magnetoresistance oscillations were found. Here we show that these effects are brought about by a quasi-periodic network of threading dislocations adjacent to the BaF 2 substrate, which give rise to a p-type interfacial layer and an associated parasitic parallel conductance. We then present results of transport measurements on microstructures of modulation doped PbTe/(Pb,Eu)Te:Bi heterostructures for which the influence of parasitic parallel conductance is minimized, and for which quantum Hall transport had been observed, on similar samples, previously. These structures are of H-shaped geometry and they are patterned of 12 nm thick strained PbTe quantum wells embedded between Pb 0.92 Eu 0.08 Te barriers. The structures have different lateral sizes corresponding to both diffusive and ballistic electron transport in non-equivalent L valleys. For these structures no nonlocal resistance is detected confirming that PbTe is a trivial insulator. The magnitude of spin Hall angle g is estimated to be smaller than 0.02 for PbTe/PbEuTe microstructures in the diffusive regime.

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confidence: 99%

Absence of nonlocal resistance in microstructures of PbTe quantum wells

Kolwas

Grabecki

Trushkin

et al. 2012

Physica Status Solidi (b)

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“…A description of the QIIE based on extended edge states and localized bulk states, äs in Fig. l, was first put forward by Halpcrin [23], and further developed by several authors [12,[24][25][26][27]. With the exception of Büttiker [12], these authors assume local equilibrium at the edge.…”

Section: Integer Edge Channelsmentioning

confidence: 99%

Adiabatic Transport in the Fractional Quantum Hall Effect Regime

Beenakker

1991

Quantum Coherence in Mesoscopic Systems

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l IntroductionThe quantum Hall effect (QHE) is the phenomenon that the Hall conductance GH is quantized in units of e 2 /h, äs expressed by the formula G -?T ω (p and q being mutually prime integers). The integer QHE (q = 1) was discovered 10 years ago by von Klitzing, Dorda, and Pepper [1] in the two-dimensional electron gas (2DEG) confined to a Si Inversion layer. The fractional QHE (q > l and odd) was first observed by Tsui, Stornier, and Gossard [2] in the 2DEG at the interface of a Al a; Ga 1 _ ; j.As/GaAs heterostructure. Microscopically the two effects are entirely different. The integer QHE, on the one hand, can be explained satisfactorily in terms of the states of non-interacting electrons in a magnetic field (the Landau levels). The fractional QHE, on the other hand, exists only because of electron-electron interactions [3]. Phenomenologically, however, the integer and fractional QHE are quite similar. In an unbounded 2 DEG this similarity is understood from Laughlin's general argument [4] that: (1) The Hall conductance shows a plateau äs a function of magnetic field (or Fermi energy) whenever the quasi-particle excitations in the bulk of the 2 DEG are localized by disorder; and that: (2) The value of GH on the plateau is precisely an integer multiple p of ee*/h, where e* = e/q is the quasi-particle charge. (The product ee* appears because one e is needed to change the unit of conductance from Amperes per electron Volts to Amperes per Volts). Theory and experiment on the QHE in an unbounded 2 DEG have been reviewed in the books by Prange and Girvin [5] and by Chakraborty and Pietiläinen [6] (see also the article by MacDonald in the present volume).In the past few years, a variety of experiments have uncovered a novel phenomenology of the QHE on short length scales. For example, in small sub-micron-size samples

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“…[35][36][37] Nevertheless important theoretical studies concerning topological aspects of nonrelativistic electrons in finite systems under strong magnetic fields have been performed by assuming hard-wall boundaries. Well known among such studies are the investigations [38][39][40][41][42][43] (initiated by Halperin 38 ) regarding the edge states related to the integer-quantum-Hall-effect (IQHE) and those [44][45][46][47] (initiated by Sivan and Imry 44 ) on the Aharonov-Bohm (AB) oscillations which are superimposed on the de Haas -van Alphen (dHvA) oscillations. Halperin introduced a hard boundary through an infinite-box-type confining potential, while Sivan and Imry used a 10 × 10 square-lattice tight-binding (TB) model.…”

Section: School Of Physics Georgia Institute Of Technology Atlantamentioning

confidence: 99%

Graphene flakes with defective edge terminations: Universal and topological aspects, and one-dimensional quantum behavior

2012

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Systematic tight-binding investigations of the electronic spectra (as a function of the magnetic field) are presented for trigonal graphene nanoflakes with reconstructed zigzag edges, where a succession of pentagons and heptagons, that is 5-7 defects, replaces the hexagons at the zigzag edge. For nanoflakes with such reczag defective edges, emphasis is placed on topological aspects and connections underlying the patterns dominating these spectra. The electronic spectra of trigonal graphene nanoflakes with reczag edge terminations exhibit certain unique features, in addition to those that are well known to appear for graphene dots with zigzag edge termination. These unique features include breaking of the particle-hole symmetry, and they are associated with nonlinear dispersion of the energy as a function of momentum, which may be interpreted as nonrelativistic behavior. The general topological features shared with the zigzag flakes include the appearance of energy gaps at zero and low magnetic fields due to finite size, the formation of relativistic Landau levels at high magnetic fields, and the presence between the Landau levels of edge states (the socalled Halperin states) associated with the integer quantum Hall effect. Topological regimes, unique to the reczag nanoflakes, appear within a stripe of negative energies ε b < ε < 0, and along a separate feature forming a constant-energy line outside this stripe. The ε b lower bound specifying the energy stripe is independent of size.Prominent among the patterns within the ε b < ε < 0 energy stripe is the formation of threemember braid bands, similar to those present in the spectra of narrow graphene nanorings; they are associated with Aharonov-Bohm-type oscillations, i.e., the reczag edges along the three sides of the triangle behave like a nanoring (with the corners acting as scatterers) enclosing the magnetic flux through the entire area of the graphene flake. Another prominent feature within the ε b < ε < 0 energy stripe is a subregion of Halperin-type edge states of enhanced density immediately below the zero-Landau level. Furthermore, there are features resulting from localization of the Dirac quasiparticles at the corners of the polygonal flake.A main finding concerns the limited applicability of the continuous Dirac-Weyl equation, since the latter does not reproduce the special reczag features. Due to this discrepancy between the tightbinding and continuum descriptions, one is led to the conclusion that the linearized Dirac-Weyl equation fails to capture essential nonlinear physics resulting from the introduction of a multiple topological defect in the honeycomb graphene lattice.

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Quantized Hall effect and edge currents

Cited by 315 publications

References 11 publications

Absence of nonlocal resistance in microstructures of PbTe quantum wells

Absence of nonlocal resistance in microstructures of PbTe quantum wells

Adiabatic Transport in the Fractional Quantum Hall Effect Regime

Graphene flakes with defective edge terminations: Universal and topological aspects, and one-dimensional quantum behavior

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