Local charge of the ν = 5/2 fractional quantum Hall state

Abstract

Electrons moving in two dimensions under the influence of strong magnetic fields effectively lose their kinetic energy and display exotic behaviour dominated by Coulomb forces. When the ratio of electrons to magnetic flux quanta in the system (ν) is near 5/2, the electrons are predicted to condense into a correlated phase with fractionally charged quasiparticles and a ground-state degeneracy that grows exponentially as these quasiparticles are introduced. The only way for electrons to transform between the many ground states would be to braid the fractional excitations around each other. This property has been proposed as the basis of a fault-tolerant quantum computer. Here we present observations of localized quasiparticles at ν = 5/2, confined to puddles by disorder. Using a local electrometer to compare how quasiparticles at ν = 5/2 and ν = 7/3 charge these puddles, we were able to extract the ratio of local charges for these states. Averaged over several disorder configurations and samples, we found the ratio to be 4/3, suggesting that the local charges are = e/3 and = e/4, where e is the charge of an electron. This is in agreement with theoretical predictions for a paired state at ν = 5/2. Confirming the existence of localized e/4 quasiparticles shows that proposed interferometry experiments to test statistics and computational ability of the state at ν = 5/2 would be possible.

Measurements of quasiparticle tunneling in theυ=52fractional quantum Hall state

“…14 A great deal of theoretical and experimental work has been done on the 5/2 state 3 recently. [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] Experimentally, the quasi-particle charge * e has been found to be consistent with the predicted value e/4. 24,25,31 Numerical simulations indicate a preference for the non-Abelian…”

Spin and Charge Ordering in the Quantum Hall Regime

“…The question of the charge of the 5 ⁄2 quasiparticles has been addressed in a number of experiments by different means: tunneling through a quantum point contact [139], noise measurements [145], Aharanov-Bohm interference [140] and experiments using a single electron transistor [146]. The obtained results are consistently in agreement with a fractional charge of /4.…”

“…The discovery of a fully polarized state confirms the prediction of the Moore-Read theory. Together with the observed /4 fractional charge [139,145,146] these results strongly favor the (anti-)Pfaffian wavefunction as proper description of the 5 ⁄2 state [151,202,203]. Likewise, this would imply a non-abelian nature of the 5 ⁄2 quasiparticles [13,14,127].…”

Majorana zero modes and topological quantum computation

“…In the Moore-Read Pfaffian state 24,25 and the anti-Pfaffian state, 40,41 proposed as candidate non-Abelian states for the 5/2-FQHS, charge-e/4 quasiparticles are Ising anyons. 26,[42][43][44][45][46][47][48] There is theoretical 28,[49][50][51][52][53][54][55][56] and experimental [29][30][31][32][57][58][59][60][61][62] evidence that the ν = 5/2 fractional quantum Hall state is in one of these two universality classes. However, there are also some experiments [63][64][65][66] that do not agree with this hypothesis.…”