Test for non-abelian statistics

1. Theoretical Problems in Condensed Matter and Statistical PhysicsBertrand Halperin, Harvard University, DMR-0233773 Test for non-abelian statistics It was proposed in 1991, by Moore and Read, that charged “quasiparticles”, in certain highly-correlated two-dimensional electron systems, could exhibit a very surprising property, called “non-abelian statistics”, and that such quasiparticles might exist in the observed state with quantized Hall conductance  = 5/2.We have proposed an “interference” experiment to test this proposal.. Experiments would be done on 2D electron systems in GaAs, similar to those used in cell-phone transistors, but of ultra-high quality. Electrical resistance would be measured between two ends of system,(shown in figure), while voltage VS on side gate is varied, and applied magnetic field is fixed. 1 VS 2 Proposed experiment on 2D electron system in quantized Hall state with n=5/2. Constrictions due to voltages applied to gates 1 and 2 cause extra resistance, which depends on area of island, controlled by side gate voltage VS. Number of quasiparticles in island can also be varied by center gate VA. Arrows show direction of particle flow around edges.

2. Theoretical Problems in Condensed Matter and Statistical PhysicsBertrand Halperin, Harvard University, DMR-0233773 Educationand outreach Research projects supported by the grant have involved four graduate students and eight postdoctoral fellows at Harvard, over a three year period More than thirty individuals, at eighteen institutions in the US and abroad, were collaborators on these projects. Last year, the principal investigator gave lectures at summer schools in Boulder, Colorado, and in Zuoz, Switzerland. He serves as a member of the Publications Oversight Committee of the American Physical Society, and is a contributor to the On-Line Journal Club in Condensed Matter, designed to alert members of the physics community to exciting new developments in the field. R A Change in electrical resistance as area A of island is varied: predicted result of interference experiment, if quasiparticles have non-abelian statistics. Measurements should jump between blue curve and pink curve according to whether an even or odd number of quasiparticles are trapped in the island