Observation of quantized hall effect and vanishing resistance at fractional Landau level occupation

doi:10.1016/0378-4363(83)90624-1

Physica B+C

Volumes 117–118, Part 2, March 1983, Pages 688-690

https://doi.org/10.1016/0378-4363(83)90624-1 Get rights and content

Abstract

Quantization of the Hall resistance ϱ_xx and the approach of a zero-resistance state in ϱ_xx are observed at fractional filling of Landau levels in the magneto-transport of the two-dimensional electrons in GaAs(AlGa) As heterostructures. At the lowest temperatures (T∼0.5K), the Hall resistance is quantized to values $ϱ_{xy} = h/(13 e^{2}$ ) and $ϱ_{xy} = h/(23 e^{2}$ ). This observation, unexpected from current theoretical models for the quantized Hall effect, suggests the formation of a new electronic state at fractional level occupation.

References (13)

H. Aoki et al.
Solid State Comm.
(1981)
Th. Englert et al.
Surf. Sci.
(1982)
D.v. Klitzing et al.
Phys. Rev. Lett.
(1980)
D.C. Tsui et al.
Appl. Phys. Lett.
(1981)
D.C. Tsui et al.
Phys. Rev.
(1982)
M.A. Paalanen et al.
Phys. Rev.
(1982)

There are more references available in the full text version of this article.

Cited by (19)

Self-assembly of designed precursors: A route to crystallographically aligned new materials with controlled nanoarchitecture
2016, Journal of Solid State Chemistry
Citation Excerpt :
The lack of dopant atoms in the transport layer, which normally scatter the charge carriers, results in the exceptionally high mobility values. These new materials have led to the discovery of new phenomena including the fractional Hall effect [12,13]. The ability to anticipate structures that could be prepared via MBE resulted in theoretical predictions of new phenomena, which resulted in new technologies.
Modulated elemental reactants is a method by which new and complex intergrowth compounds can be synthesized by the self-assembly of designed precursors prepared by physical vapor deposition. Careful calibration of the composition and thickness of the precursors ensures the formation of the desired product by precise control of local composition and diffusion lengths. Superstructures of increasing complexity can be realized using binary and ternary systems as starting points. The synthesis of systems based on three different binary compounds, either alloyed together or separated into distinct layers, expands the number of possible superstructures that can be formed using this technique, but provides analytical challenges. The synthesis of [(SnSe)_1.15]₁([Ta_xV_1−x]Se₂)₁[(SnSe)_1.15]₁([V_yTa_1−y]Se₂)₁ compound is used to illustrate the preparation of precursors and the challenges in both measuring and limiting the interdiffusion of layers during self-assembly. Systematic changes in the electrical properties of (SnSe)_1+δ(Ta_xV_1−x)Se₂ alloys are observed as x is varied. The electrical resistivity of [(SnSe)_1.15]₁([Ta_xV_1−x]Se₂)₁[(SnSe)_1.15]₁([V_yTa_1−y]Se₂)₁ can be modeled as the two constituent layers in parallel.
Activation gaps in the energy spectrum and influence of disorder under fractional quantum Hall effect in silicon MOSFET
1986, Surface Science
In Si MOS structures with high mobility of 2D electrons in a strong magnetic field (H ≲ 20) applied perpendicularly to the space charge layer, the activated conductivity is used for determination of activation gaps W in the energy spectrum of interacting electrons at the fractional filling factors: $ν = 13, 23, 43 and 45$ . It was found that these gaps increase proportionally to the reciprocal magnetic length under the condition that the electron mobility μ_e is fixed with an accuracy of about ±3%. The dependence of the activation gaps on H and μ_e can be factorized within the simple relation: W ∼ √H(1 - const./μ_e. The magnitudes found for W, and their dependence on H and μ_e, correlate with the theoretical conception concerning the condensation of 2D electrons into the quantum incompressible Fermi fluid.
Fractional quantum hall effect at low temperatures
1984, Surface Science
We report results of low temperature (65 mK to 770 mK) magneto-transport measurements of the $23$ quantum Hall plateau in an n-type GaAsAl_xGa_1−x As heterostructure. Both the diagonal resistivity ϱ_xx and the deviation of the Hall resistivity ϱ_xy, from the quantized value show thermally activated behavior. The thermal activation energy was measured as a function of the Landau level filling factor, ν, at fixed magnetic fields, B, by varying the density of the two-dimensional electrons with a back-gate bias. The activation energy Δ of ϱ_xx is maximum at the center of the Hall plateau, when $ν = 23$ , and decreases on either side of it, as ν moves away from $23$ . This resonance-like dependence on ν is characterized by a maximum activation energy, Δ_m = 830 mK and $Δν ν = 8%$ at B = 92.5 kG. In addition, we have verified that the Hall conductance is quantized to ( $23$ ) $e^{2} h$ to an accuracy of 3 parts in 10⁴. The I-V relation is linear down to an electric field of less than 10 ⁻⁵ $V cm$ , indicating that the current carrying state is not pinned.
The ground state of the 2d electrons in a strong magnetic field and the anomalous quantized hall effect
1984, Surface Science
Numerical diagonalization of the Hamiltonian is done for a two dimensional system of up to six interacting electrons, in the lowest Landau level, in a rectangular box with periodic boundary conditions. It is found that the ground state is not a Wigner crystal but a liquid-like state. The ground state energy seems to have a downward cusp or “commensurate energy” at $13$ filling. Although the nature of the ground state is still not clear, the magnitude of the cusp is consistent with the experimentally observed anomaly in σ_xy and σ_xx at $13$ filling by Tsui, Störmer and Gossard (Phys. Rev. Letters 48 (1982) 1559). Several properties of the ground state are also investigated.
Disorder and the fractional quantum Hall effect
1984, Solid State Communications
Quantum hall effect in AlGaAs and graphite quantum dots
2013, Advanced Materials Research

View all citing articles on Scopus

View full text

Observation of quantized hall effect and vanishing resistance at fractional Landau level occupation

Abstract

Solid State Comm.

Surf. Sci.

Phys. Rev. Lett.

Appl. Phys. Lett.

Phys. Rev.

Phys. Rev.