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Register a new userBerry phases for composite fermions: effective magnetic field and fractional statistics
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The quantum Hall superfluid is presently the only viable candidate for a realization of quasiparticles with fractional Berry phase statistics. For a simple vortex excitation, relevant for a subset of fractional Hall states considered by Laughlin, non-trivial Berry phase statistics were demonstrated many years ago by Arovas, Schrieffer, and Wilczek. The quasiparticles are in general more complicated, described accurately in terms of excited composite fermions. We use the method developed by Kjonsberg, Myrheim and Leinaas to compute the Berry phase for a single composite-fermion quasiparticle, and find that it agrees with the effective magnetic field concept for composite fermions. We then evaluate the fractional statistics, related to the change in the Berry phase for a closed loop caused by the insertion of another composite-fermion quasiparticle in the interior. Our results support the general validity of fractional statistics in the quantum Hall superfluid, while also giving a quantitative account of corrections to it when the quasiparticle wave functions overlap. Many caveats, both practical and conceptual, are mentioned that will be relevant to an experimental measurement of the fractional statistics. A short report on some parts of this article has appeared previously.
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The relation between the conductivity tensors of Composite Fermions and electrons is extended to second generation Composite Fermions. It is shown that it crucially depends on the coupling matrix for the Chern-Simons gauge field. The results are applied to a model of interacting Composite Fermions that can explain both the anomalous plateaus in spin polarization and the corresponding maxima in the resistivity observed in recent transport experiments.
We review the construction of a low-energy effective field theory and its state space for abelian quantum Hall fluids. The scaling limit of the incompressible fluid is described by a Chern-Simons theory in 2+1 dimensions on a manifold with boundary. In such a field theory, gauge invariance implies the presence of anomalous chiral modes localized on the edge of the sample. We assume a simple boundary structure, i.e., the absence of a reconstructed edge. For the bulk, we consider a multiply connected planar geometry. We study tunneling processes between two boundary components of the fluid and calculate the tunneling current to lowest order in perturbation theory as a function of dc bias voltage. Particular attention is paid to the special cases when the edge modes propagate at the same speed, and when they exhibit two significantly distinct propagation speeds. We distinguish between two geometries of interference contours corresponding to the (electronic) Fabry-Perot and Mach-Zehnder interferometers, respectively. We find that the interference term in the current is absent when exactly one hole in the fluid corresponding to one of the two edge components involved in the tunneling processes lies inside the interference contour (i.e., in the case of a Mach-Zehnder interferometer). We analyze the dependence of the tunneling current on the state of the quantum Hall fluid and on the external magnetic flux through the sample.
We study the role of anisotropy on the transport properties of composite fermions near Landau level filling factor $ u=1/2$ in two-dimensional holes confined to a GaAs quantum well. By applying a parallel magnetic field, we tune the composite fermion Fermi sea anisotropy and monitor the relative change of the transport scattering time at $ u=1/2$ along the principal directions. Interpreted in a simple Drude model, our results suggest that the scattering time is longer along the longitudinal direction of the composite fermion Fermi sea. Furthermore, the measured energy gap for the fractional quantum Hall state at $ u=2/3$ decreases when anisotropy becomes significant. The decrease, however, might partly stem from the charge distribution becoming bilayer-like at very large parallel magnetic fields.
The response of composite Fermions to large wavevector scattering has been studied through phonon drag measurements. While the response retains qualitative features of the electron system at zero magnetic field, notable discrepancies develop as the system is varied from a half-filled Landau level by changing density or field. These deviations, which appear to be inconsistent with the current picture of composite Fermions, are absent if half-filling is maintained while changing density. There remains, however, a clear deviation from the temperature dependence anticipated for 2k_F scattering.
Two-dimensional systems can host exotic particles called anyons whose quantum statistics are neither bosonic nor fermionic. For example, the elementary excitations of the fractional quantum Hall effect at filling factor $ u=1/m$ (where m is an odd integer) have been predicted to obey abelian fractional statistics, with a phase $varphi$ associated with the exchange of two particles equal to $pi/m$. However, despite numerous experimental attempts, clear signatures of fractional statistics remain elusive. Here we experimentally demonstrate abelian fractional statistics at filling factor $ u=1/3$ by measuring the current correlations resulting from the collision between anyons at a beam-splitter. By analyzing their dependence on the anyon current impinging on the splitter and comparing with recent theoretical models, we extract $varphi=pi/3$, in agreement with predictions.
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