Bulletin of the American Physical Society
2008 APS March Meeting
Volume 53, Number 2
Monday–Friday, March 10–14, 2008; New Orleans, Louisiana
Session U4: Interferometry in the Quantum Hall Regime |
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Sponsoring Units: DCMP Chair: Steven Simon, Lucent Tech/Bell Labs-Murray Room: Morial Convention Center 206 |
Thursday, March 13, 2008 8:00AM - 8:36AM |
U4.00001: Measuring Fractional Statistics with Fabry-Perot Quantum Hall Interferometers Invited Speaker: Laughlin quasiparticles are the elementary excitations of a highly-correlated fractional quantum Hall electron fluid. They have fractional charge and obey fractional statistics. The quasiparticles can propagate quantum-coherently in chiral edge channels, and constructively or destructively interfere. Unlike electrons, the interference condition for Laughlin quasiparticles has a non-vanishing statistical contribution that can be observed experimentally. Two kinds of interferometer devices have been realized. In the primary-filling interferometer, the entire device has filling 1/3, and the e/3 edge channel quasiparticles encircle identical e/3 island quasiparticles. Here the flux period is h/e, same as for electrons, but the back-gate charge period is e/3. In the second kind of interferometer, a lower density edge channel at filling 1/3 forms around a higher density island at filling 2/5, so that e/3 edge quasiparticles encircle e/5 island quasiparticles. Here we observe superperiodic oscillations with 5h/e flux and 2e charge periods, both corresponding to excitation of ten island quasiparticles. These periods can be understood as imposed by the anyonic braiding statistics of Laughlin quasiparticles. This work was done in collaboration with Fernando E. Camino, Ping Lin and Wei Zhou. [Preview Abstract] |
Thursday, March 13, 2008 8:36AM - 9:12AM |
U4.00002: Interactions and Disorder in Quantum Hall Interferometers Invited Speaker: Quantum Hall (QH) devices are supposed to be an ideal laboratory for the study of interference effects, because within a conductance plateau, the bulk of a sample is insulating and the current is confined to conducting edge states. Closed interference paths can be defined with the help of two narrow constrictions, which mediate tunneling from one edge to the other. Quantum interference should then manifest itself in flux- and gate-voltage-dependent conductance oscillations. When there is an integer quantized Hall state within the constrictions, a region between them, with higher electron density, may form a compressible island. Electron-tunneling through this island can lead to residual transport, modulated by Coulomb-blockade type effects. Then, the coupling between the fully occupied lower Landau levels and the higher partially occupied level gives rise to flux subperiods smaller than one flux quantum [1]. We generalize this scenario to other geometries and to fractional quantum Hall systems, and compare our predictions to experiments. For interferometers probing non-abelian statistics in the $\nu=5/2$ QH state, current-carrying quasiparticles flow along edges that encircle $N_{qp}$ bulk quasiparticles, which are localized at impurities. The interference pattern depends on whether $N_{qp}$ is even or odd, and is affected by a coupling that allows tunneling of neutral Majorana fermions between the bulk and edge. While at weak coupling this tunneling degrades the interference signal, at strong coupling the bulk quasiparticle becomes essentially absorbed by the edge and the interference signal is fully restored [2]. These works have been done in collaboration with B.I.~Halperin, S.H.~Simon, and A.~Stern. \\ $[1]$ B. Rosenow and B.I.~Halperin, Phys. Rev. Lett. 98, 106801 (2007).\\ $[2]$ B.~Rosenow, B.I.~Halperin, S.H.~Simon, and A.~Stern, arXiv:0707.4474. [Preview Abstract] |
Thursday, March 13, 2008 9:12AM - 9:48AM |
U4.00003: Quantum Oscillations and the $\nu = 5/2$ Fractional Quantum Hall State in Mesoscopic Quantum Hall Interferometers Invited Speaker: Magnetotransport study of mesoscopic quantum Hall corrals fabricated from a high mobility GaAs/AlGaAs quantum well structure will be presented. Prominent Aharonov-Bohm-like quantum oscillations are observed at magnetic fields just below even integer quantum Hall plateaus at low temperatures. We establish the fundamental flux period of these oscillations as $\Phi_{0}/f$, where $\Phi_{0}$ is the universal flux quantum and $f$ is the integer number of fully filled Landau levels. The flux period of the observed quantum oscillations thus fundamentally differs from that of Aharonov-Bohm effect which has a period of one flux quantum, $\Phi_{0}$. The observed quantum oscillations in the quantum Hall corrals can be understood within the Coulomb blockade model of quantum Hall interferometers [1] as forward tunneling and backscattering, respectively, through the center island of the corral from the bulk and the edge states. In the second Landau level, we observe an extended series of oscillations with flux period of $\Phi_{0}/2$. The Aharonov-Bohm-Like oscillations are found to coexist with the $\nu = 5/2$ fractional quantum Hall effect. We detail the transport properties of the $\nu = 5/2$ fractional quantum Hall state and the mesoscopic quantum Hall corral in the second Landau level. \newline \newline [1] R. Rosenow and B.I. Halperin, Phys. Rev. Lett. {\bf 98}, 106801 (2007). [Preview Abstract] |
Thursday, March 13, 2008 9:48AM - 10:24AM |
U4.00004: Non-Abelian Interferometry Invited Speaker: Topologically-ordered phases supporting excitations with non-Abelian braiding statistics are expected to occur at several observed fractional quantum Hall plateaux. These states are of particular interest as they may provide a platform for topological quantum computation. Interferometric experiments are likely to play a crucial role in both determining the non-Abelian nature of these states and in their potential applications for quantum computing. I will discuss interferometric experiments designed to detect such non-Abelian quasiparticle statistics -- one of the hallmark characteristics of the Moore-Read and Read-Rezayi states, which are likely candidates for the observed fractional quantum Hall plateaux at $\nu=5/2$ and $12/5$ respectively. Aside from their potential utility for experimental verification of non-Abelian anyonic statistics, such interferometric experiments would provide the most promising route to qubit read-out in a topological quantum computation. With these potential applications in mind, I will also address interferometric measurements of states having superpositions of anyonic charges and discuss their measurement collapse behavior. [Preview Abstract] |
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