The quantum Hall states at filling factors \(\nu=5/2\) and \(7/2\) are expected to have Abelian charge \(e/2\) quasiparticles and non-Abelian charge \(e/4\) quasiparticles. The non-Abelian statistics ...of the latter has been predicted to display a striking interferometric signature, the even-odd effect. By measuring resistance oscillations as a function of magnetic field in Fabry-Pérot interferometers using new high purity heterostructures, we for the first time report experimental evidence for the non-Abelian nature of excitations at \(\nu=7/2\). At both \(\nu=5/2\) and \(7/2\) we also examine, for the first time, the fermion parity, a topological quantum number of an even number of non-Abelian quasiparticles. The phase of observed \(e/4\) oscillations is reproducible and stable over long times (hours) near both filling factors, indicating stability of the fermion parity. At both fractions, when phase fluctuations are observed, they are predominantly \(\pi\) phase flips, consistent with either fermion parity change or change in the number of the enclosed \(e/4\) quasiparticles. We also examine lower-frequency oscillations attributable to Abelian interference processes in both states. Taken together, these results constitute new evidence for the non-Abelian nature of \(e/4\) quasiparticles; the observed life-time of their combined fermion parity further strengthens the case for their utility for topological quantum computation.
We study strongly correlated electrons on a kagome lattice at 1/6 and 1/3 filling. They are described by an extended Hubbard Hamiltonian. We are concerned with the limit |t|<<V<<U with hopping ...amplitude t, nearest-neighbor repulsion V and on-site repulsion U. We derive an effective Hamiltonian and show, with the help of the Perron-Frobenius theorem, that the system is ferromagnetic at low temperatures. The robustness of ferromagnetism is discussed and extensions to other lattices are indicated.
We show that the resistance of the v=5/2 quantum Hall state, confined to an interferometer, oscillates with magnetic field consistent with an Ising-type non-Abelian state. In three quantum Hall ...interferometers of different sizes, resistance oscillations at v=7/3 and integer filling factors have the magnetic field period expected if the number of quasiparticles contained within the interferometer changes so as to keep the area and the total charge within the interferometer constant. Under these conditions, an Abelian state such as the (3,3,1) state would show oscillations with the same period as at an integer quantum Hall state. However, in an Ising-type non-Abelian state there would be a rapid oscillation associated with the "even-odd effect" and a slower one associated with the accumulated Abelian phase due to both the Aharonov-Bohm effect and the Abelian part of the quasiparticle braiding statistics. Our measurements at v=5/2 are consistent with the latter.
Physica A, 279, 312--323 (2000) We consider the Ashkin-Teller model with negative four-spin coupling but
still in the region where the ground state is ferromagnetic. We establish the
standard ...Lebowitz inequality as well as the extension that is necessary to
prove a divergent susceptibility.
No sliding in time Shtengel, Kirill; Nayak, Chetan; Bishara, Waheb ...
Journal of physics. A, Mathematical and general,
09/2005, Letnik:
38, Številka:
36
Journal Article
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