Observation of narrow-band noise accompanying the breakdown of insulating states in high Landau levels

Recent magnetotransport experiments on high mobility two-dimensional electron systems have revealed many-body electron states unique to high Landau levels. Among these are re-entrant integer quantum Hall states which undergo sharp transitions to conduction above some threshold field. Here we report that these transitions are often accompanied by narrow- and broad-band noise with frequencies which are strongly dependent on the magnitude of the applied dc current.Comment: 4 pages, 3 figure

Hydrodynamic Equations in Quantum Hall Systems at Large Currents

Hydrodynamic equations (HDEQs) are derived which describe spatio-temporal evolutions of the electron temperature and the chemical potential of two-dimensional systems in strong magnetic fields in states with large diagonal resistivity appearing at the breakdown of the quantum Hall effect. The derivation is based on microscopic electronic processes consisting of drift motions in a slowly-fluctuating potential and scattering processes due to electron-electron and electron-phonon interactions. In contrast with the usual HDEQs, one of the derived HDEQs has a term with an energy flux perpendicular to the electric field due to the drift motions in the magnetic field. As an illustration, the current distribution is calculated using the derived HDEQs.Comment: 10 pages, 2 Postscript figures, to be published in J. Phys. Soc. Jpn. 71 (2002) No.

Improved Theory of the Muonium Hyperfine Structure

Terms contributing to the hyperfine structure of the muonium ground state at the level of few tenths of kHz have been evaluated. The $\alpha^2 (Z\alpha)$ radiative correction has been calculated numerically to the precision of 0.02 kHz. Leading $\ln (Z\alpha )$ terms of order $\alpha^{4-n} (Z\alpha)^n , n=1,2,3,$ and some relativistic corrections have been evaluated analytically. The theoretical uncertainty is now reduced to 0.17 kHz. At present, however, it is not possible to test QED to this precision because of the 1.34 kHz uncertainty due to the muon mass.Comment: 11 pages + 2 figures (included), RevTeX 3.0, CLNS 94/127

Quantum Response at Finite Fields and Breakdown of Chern Numbers

We show that the response to an electric field, in models of the Integral Quantum Hall effect, is analytic in the field and has isolated essential singularity at zero field. We also study the breakdown of Chern numbers associated with the response of Floquet states. We argue, and give evidence, that the breakdown of Chern numbers in Floquet states is a discontinuous transition at zero field. This follows from an observation, of independent interest, that Chern numbers for finite dimensional Floquet operators are generically zero. These results rule out the possibility that the breakdown of the Hall conductance is a phase transition at finite fields for a large class of models.Comment: 16 pages, 8 eps figures, LaTeX2e with IOP style. Many changes, including new materia

Theory of Current-Induced Breakdown of the Quantum Hall Effect

By studying the quantum Hall effect of stationary states with high values of injected current using a von Neumann lattice representation, we found that broadening of extended state bands due to a Hall electric field occurs and causes the breakdown of the quantum Hall effect. The Hall conductance agrees with a topological invariant that is quantized exactly below a critical field and is not quantized above a critical field. The critical field is proportional to $B^{3/2}$ and is enhanced substantially if the extended states occupy a small fraction of the system.Comment: 5 pages, RevTeX, final version to appear in PR

Radiative Corrections to the Muonium Hyperfine Structure. I. The α2(Zα)\alpha^2 (Z\alpha) Correction

This is the first of a series of papers on a systematic application of the NRQED bound state theory of Caswell and Lepage to higher-order radiative corrections to the hyperfine structure of the muonium ground state. This paper describes the calculation of the $\alpha^2 (Z\alpha)$ radiative correction. Our result for the complete $\alpha^2 (Z\alpha)$ correction is 0.424(4) kHz, which reduces the theoretical uncertainty significantly. The remaining uncertainty is dominated by that of the numerical evaluation of the nonlogarithmic part of the $\alpha (Z\alpha )^2$ term and logarithmic terms of order $\alpha^4$.Comment: 56 pages, Rev.tex V3.0 and epsf.tex. 12 postscript files are called in the text. Version accepted by Phys. Rev. D. A new table is adde

Strong, Ultra-narrow Peaks of Longitudinal and Hall Resistances in the Regime of Breakdown of the Quantum Hall Effect

With unusually slow and high-resolution sweeps of magnetic field, strong, ultra-narrow (width down to $100 {\rm \mu T}$) resistance peaks are observed in the regime of breakdown of the quantum Hall effect. The peaks are dependent on the directions and even the history of magnetic field sweeps, indicating the involvement of a very slow physical process. Such a process and the sharp peaks are, however, not predicted by existing theories. We also find a clear connection between the resistance peaks and nuclear spin polarization.Comment: 5 pages with 3 figures. To appear in PR

Phonons in the quantum Hall effect: A nonlinear-dynamics picture

A model describing a system in which Landau electronic modes are coupled with phonons is proposed and discussed. A simplified version of the model is further analyzed, with special attention to the dynamical symmetries that characterize it. In particular, the corresponding equations of motion are thoroughly examined: they provide a variety of behaviors, ranging from completely integrable (in both the classical and quantum case) to chaotic (in the semiclassical approximation). The chaotic regime is believed to be suitable to eventually represent the stochastic behavior of the longitudinal voltage versus time, recently observed in several quantum Hall effect experiments

Thermohydrodynamics in Quantum Hall Systems

A theory of thermohydrodynamics in two-dimensional electron systems in quantizing magnetic fields is developed including a nonlinear transport regime. Spatio-temporal variations of the electron temperature and the chemical potential in the local equilibrium are described by the equations of conservation with the number and thermal-energy flux densities. A model of these flux densities due to hopping and drift processes is introduced for a random potential varying slowly compared to both the magnetic length and the phase coherence length. The flux measured in the standard transport experiment is derived and is used to define a transport component of the flux density. The equations of conservation can be written in terms of the transport component only. As an illustration, the theory is applied to the Ettingshausen effect, in which a one-dimensional spatial variation of the electron temperature is produced perpendicular to the current.Comment: 10 pages, 1 figur

Field-induced breakdown of the quantum Hall effect

A numerical analysis is made of the breakdown of the quantum Hall effect caused by the Hall electric field in competition with disorder. It turns out that in the regime of dense impurities, in particular, the number of localized states decreases exponentially with the Hall field, with its dependence on the magnetic and electric field summarized in a simple scaling law. The physical picture underlying the scaling law is clarified. This intra-subband process, the competition of the Hall field with disorder, leads to critical breakdown fields of magnitude of a few hundred V/cm, consistent with observations, and accounts for their magnetic-field dependence \propto B^{3/2} observed experimentally. Some testable consequences of the scaling law are discussed.Comment: 7 pages, Revtex, 3 figures, to appear in Phys. Rev.