A non-Abelian parton state for the $ν=2+3/8$ fractional quantum Hall effect

Fascinating structures have arisen from the study of the fractional quantum Hall effect (FQHE) at the even denominator fraction of 5/2 5 / 2 . We consider the FQHE at another even denominator fraction, namely ν=2+3/8 ν = 2 + 3 / 8 , where a well-developed and quantized Hall plateau has been observed in experiments. We examine the non-Abelian state described by the `` 3̄2̄²1⁴ 3 ‾ 2 ‾ 2 1 4 " parton wave function and numerically demonstrate it to be a feasible candidate for the ground state at ν=2+3/8 ν = 2 + 3 / 8 . We make predictions for experimentally measurable properties of the 3̄2̄²1⁴ 3 ‾ 2 ‾ 2 1 4 state that can reveal its underlying topological structure.