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 5/25/2. We consider the FQHE at another even denominator fraction, namely \nu=2+3/8ν=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 ``\bar{3}\bar{2}^{2}1^{4}3‾2‾214" parton wave function and numerically demonstrate it to be a feasible candidate for the ground state at \nu=2+3/8ν=2+3/8. We make predictions for experimentally measurable properties of the \bar{3}\bar{2}^{2}1^{4}3‾2‾214 state that can reveal its underlying topological structure.