An exactly solvable model of the disordered two-dimensional electron gas in a strong magnetic field

Benedict, K. A.; Chalker, J. T.

doi:10.1088/0022-3719/19/19/014

Cited by 35 publications

(32 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Although the experimental disorder potential is long ranged, it is instructive to consider also the case of short-range disorder, for which the SCBA [12] becomes exact in the limit of high LLs [14]. Assuming that the disorder broadening is small compared to the LL spacing, the conductivity tensorσ becomes [12] …”

mentioning

confidence: 99%

Oscillating Sign of Drag in High Landau Levels

Oppen

Simon²,

Stern

2001

Phys. Rev. Lett.

View full text Add to dashboard Cite

Motivated by experiments, we study the sign of the Coulomb drag voltage in a double layer system in a strong magnetic field. We show that the commonly used Fermi Golden Rule approach implicitly assumes a linear dependence of intra-layer conductivity on density, and is thus inadequate in strong magnetic fields. Going beyond this approach, we show that the drag voltage commonly changes sign with density difference between the layers. We predict that in the Quantum Hall regime the Hall and longitudinal drag resistivities are comparable. Our results are also relevant for pumping and acoustoelectric experiments.Drag experiments in coupled two-dimensional electron systems provide information on the response of a system at finite frequency and wavevector and are thus complementary to standard DC transport measurements [1,2]. In a typical drag experiment, a current is applied to the active layer of a double-layer system and the voltage V D induced in the other passive layer is measured, with no current allowed to flow in that layer. In a simple picture of drag, the current in the active layer leads -via interlayer Coulomb or phonon interaction -to a net transfer of momentum to the carriers in the passive layer. At conditions of zero current in the passive layer, this momentum transfer is counteracted by the build-up of the drag voltage V D . In the cases of two electron layers or two hole layers, the drag voltage points opposite to the voltage drop in the active layer. This is defined as positive drag. Negative drag occurs in systems with one electron layer and one hole layer [2,3].Prior theoretical work on drag [2,4,5] was often based on or reduced to a Fermi Golden Rule analysis (see, e.g., Zheng and MacDonald [1]). In this analysis, the sign of drag does not vary with magnetic field B, temperature T , or difference in Landau level (LL) filling factor ν between the two layers. By contrast, recent experiments at large perpendicular B [6-8] observe that the sign of drag changes with all of these parameters in systems of two coupled electron layers -specifically in the Shubnikovde-Haas (SdH) and integer quantum Hall (IQH) regimes. Feng et al.[6] find positive drag whenever the topmost partially filled LLs in both layers are either less than half filled or more than half filled. Negative drag is observed when the topmost LL is less than half-filled in one layer and more than half-filled in the other. Even more surprisingly, Lok et al. [7] maintained that the sign of drag was sensitive to the relative orientation of the majority spins of the two layers at the Fermi energy.In this paper, we show that the use of the Fermi Golden Rule approach is inappropriate in the SdH and IQH regimes and that a more careful analysis opens different routes to drag with changing sign. Remarkably, we find that Hall drag can be of the same magnitude as longitudinal drag in these regimes. We emphasize that a naive rationale for the experimental results of Feng et al. -which points to the similarity between a less (more) than half-filled Landau ...

show abstract

mentioning

confidence: 99%

Oscillating Sign of Drag in High Landau Levels

Oppen

Simon²,

Stern

2001

Phys. Rev. Lett.

View full text Add to dashboard Cite

show abstract

“…Note that for a low density of scatterers, ν < 1, a fraction 1 − ν of states in the plane remains unaffected. Such "condensation of states" was known also for the case of repulsive point-like scatterers with a constant scattering strength [6,7,10,11]. In fact, the analogy extends also to the intricate structure of the DOS away from the gap.…”

mentioning

confidence: 84%

“…The DOS of 2D disordered electronic systems in a quantizing magnetic field has been extensively studied for the last two decades [5][6][7][8][9][10][11][12][13][14][15]. The macroscopic degeneracy of the Landau levels (LL) makes impossible a perturbative treatment of even weak disorder and calls for non-perturbative approaches.…”

mentioning

confidence: 99%

“…The macroscopic degeneracy of the Landau levels (LL) makes impossible a perturbative treatment of even weak disorder and calls for non-perturbative approaches. For high LL, Ando's self-consistent Born approximation [5] was shown to be asymptotically exact for short-range disorder [11,13], while in the case of long-range disorder the DOS can be obtained within the eikonal approximation [13]. For low LL and uncorrelated disorder, the problem contains no small parameter and neither of those approximations apply.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Resonant Scattering in a Strong Magnetic Field: Exact Density of States

Shahbazyan

Ulloa

1997

Phys. Rev. Lett.

View full text Add to dashboard Cite

We study the structure of 2D electronic states in a strong magnetic field in the presence of a large number of resonant scatterers. For an electron in the lowest Landau level, we derive the exact density of states by mapping the problem onto a zero-dimensional field-theoretical model. We demonstrate that the interplay between resonant and non-resonant scattering leads to a non-analytic energy dependence of the electron Green function. In particular, for strong resonant scattering the density of states develops a gap in a finite energy interval. The shape of the Landau level is shown to be very sensitive to the distribution of resonant scatterers.

show abstract

“…[10] The studies of the associated eigenstates inferred a complicated nature described by multifractality. [11,12] The concept of multifractal states, also proposed by Kohmoto [13] for quasiperiodic systems, is an important related issue. Indeed, anomalous quantum diffusion in quantum Hall systems [14] (QHS) and in quasicrystals [4,15] may have some direct relations with the observed physical properties.…”

Section: Introductionmentioning

confidence: 99%

Quantum transport by means ofO(N)real-space methods

Roche

1999

Phys. Rev. B

111

View full text Add to dashboard Cite

We investigate quantum transport by a suitable development of the Kubo formula on a basis of orthogonal polynomials and using real space recursion approaches. We show that the method enable to treat systems close to a metal-insulator transition. On quantum Hall systems, results are given in the context of recent new universal relations between transport coefficients. RKKY mesoscopic interaction is also evaluated for two-dimensional quasiperiodic systems and insight of the usefulness of our method is given for large scale computational problems.PACS numbers: 72.90.+y 61.44.Br 72.10.-d

show abstract

An exactly solvable model of the disordered two-dimensional electron gas in a strong magnetic field

Cited by 35 publications

References 22 publications

Oscillating Sign of Drag in High Landau Levels

Oscillating Sign of Drag in High Landau Levels

Resonant Scattering in a Strong Magnetic Field: Exact Density of States

Quantum transport by means ofO(N)real-space methods

Contact Info

Product

Resources

About