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Register a new userHigh-frequency hopping conductivity in the quantum Hall effect regime: Acoustical studies
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The high-frequency conductivity of Si delta-doped GaAs/AlGaAs heterostructures is studied in the integer quantum Hall effect (QHE) regime, using acoustic methods. Both the real and the imaginary parts of the complex conductivity are determined from the experimentally observed magnetic field and temperature dependences of the velocity and the attenuation of a surface acoustic wave. It is demonstrated that in the structures studied the mechanism of low-temperature conductance near the QHE plateau centers is hopping. It is also shown that at magnetic fields corresponding to filling factors 2 and 4, the doped Si delta- layer efficiently shunts the conductance in the two-dimensional electron gas (2DEG) channel. A method to separate the two contributions to the real part of the conductivity is developed, and the localization length in the 2DEG channel is estimated.
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The hopping ac conductance, which is realized at the transverse conductance minima in the regime of the integer Hall effect, has been measured using a combination of acoustic and microwave methods. Measurements have been made in the p-GeSi/Ge/GeSi structures with quantum wells in a wide frequency range (30-1200 MHz). The experimental frequency dependences of the real part of ac conductance $sigma_1$ have been interpreted on the basis of the model presuming hops between localized electronic states belonging to isolated clusters. At high frequencies, dominating clusters are pairs of close states; upon a decrease in frequency, large clusters that merge into an infinite percolation cluster as the frequency tends to zero become important. In this case, the frequency dependences of the ac conductance can be represented by a universal curve. The scaling parameters and their magnetic-field dependence have been determined.
We measure the longitudinal conductivity $sigma_{xx}$ at frequencies $1.246 {rm GHz} le f le 10.05$ GHz over a range of temperatures $235 {rm mK} le T le 4.2$ K with particular emphasis on the Quantum Hall plateaus. We find that $Re(sigma_{xx})$ scales linearly with frequency for a range of magnetic field around the center of the plateaus, i.e. where $sigma_{xx}(omega) gg sigma_{xx}^{DC}$. The width of this scaling region decreases with higher temperature and vanishes by 1.2 K altogether. Comparison between localization length determined from $sigma_{xx}(omega)$ and DC measurements on the same wafer show good agreement.
The dynamical transport properties near the integer quantum Hall transition are investigated at zero temperature by means of the Dirac fermion approach. These properties have been studied experimentally at low frequency omega and low temperature near the nu=1 filling factor Hall transition, with the observation of an anusual broadening and an overall increase of the longitudinal conductivity Re sigma_{xx} as a function of omega. We find in our approach that, unlike for normal metals, the longitudinal conductivity increases as the frequency increases, whilst the width Delta B (or Delta nu) of the conductivity peak near the Hall transition increases. These findings are in reasonable quantitative agreement with recent experiments by Engel et al. as well as with recent numerical work by Avishai and Luck.
A recent mean-field approach to the fractional quantum Hall effect (QHE) is reviewed, with a special emphasis on the application to single-electron tunneling through a quantum dot in a high magnetic field. The theory is based on the adiabatic principle of Greiter and Wilczek, which maps an incompressible state in the integer QHE on the fractional QHE. The single-particle contribution to the addition spectrum is analyzed, for a quantum dot with a parabolic confining potential. The spectrum is shown to be related to the Fock-Darwin spectrum in the integer QHE, upon substitution of the electron charge by the fractional quasiparticle charge. Implications for the periodicity of the Aharonov-Bohm oscillations in the conductance are discussed.
Electron pairing is a rare phenomenon appearing only in a few unique physical systems; e.g., superconductors and Kondo-correlated quantum dots. Here, we report on an unexpected, but robust, electron pairing in the integer quantum Hall effect (IQHE) regime. The pairing takes place within an interfering edge channel circulating in an electronic Fabry-Perot interferometer at a wide range of bulk filling factors, $2<{ u} _B<5$. The main observations are: (a) High visibility Aharonov-Bohm conductance oscillations with magnetic flux periodicity ${Delta}{phi}={varphi}_0/2=h/2e$ (instead of the ubiquitous $h/e$), with $e$ the electron charge and $h$ the Planck constant; (b) An interfering quasiparticle charge $e ^* {sim} 2e$ - revealed by quantum shot noise measurements; and (c) Full dephasing of the $h/2e$ periodicity by induced dephasing of the adjacent edge channel (while keeping the interfering edge channel intact) : a clear realization of inter-channel entanglement. While this pairing phenomenon clearly results from inter-channel interaction, the exact mechanism that leads to e-e attraction within a single edge channel is not clear.
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