Discovery of competing 5/2 fractional quantum Hall states

With an even denominator, $\backslash $nu $=$ 5/2 fractional quantum Hall state (FQH) is different from most of the other FQH states. Some of its proposed wave functions may exhibit novel non-Abelian statistics, which is related to topological quantum computation. We carried out tunneling measurements within a quantum point contact (QPC) at the 5/2 state and we were able to match the QPC's density to the two-dimensional electron gas bulk density. Such a density match guarantees the uniform filling factor inside and outside the QPC. The interaction parameter g and the effective charge e* can be extracted through the weak tunneling theory [1]. We found g and e* similar to what people believed to be the Abelian 331 state [2, 3]. By tuning the confinement, we observed another region where the experimental data agree well with the weak tunneling theory, which leads to e*$=$0.25 and g$=$0.52, implying non-Abelian wavefunctions such as anti-Pfaffian or U(1)×SU2(2). Our discovery suggests that there are competing 5/2 fractional quantum Hall ground states depending on the confinement. [1] Science 320, 899 (2008). [2] Phys. Rev. B 85, 165321 (2012). [3] Phys. Rev. B 90, 075403 (2014).