A non-Abelian parton state for the $ν=2+3/8$ fractional quantum Hall effect
Ajit C. Balram
Abstract
Fascinating structures have arisen from the study of the fractional quantum Hall effect (FQHE) at the even denominator fraction of 5/2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mn>5</mml:mn> <mml:mi>/</mml:mi> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> . We consider the FQHE at another even denominator fraction, namely \nu=2+3/8 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>ν</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> <mml:mo>+</mml:mo> <mml:mn>3</mml:mn> <mml:mi>/</mml:mi> <mml:mn>8</mml:mn> </mml:mrow> </mml:math> , 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} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mover> <mml:mn>3</mml:mn> <mml:mo accent="true">‾</mml:mo> </mml:mover> <mml:msup> <mml:mover> <mml:mn>2</mml:mn> <mml:mo accent="true">‾</mml:mo> </mml:mover> <mml:mn>2</mml:mn> </mml:msup> <mml:msup> <mml:mn>1</mml:mn> <mml:mn>4</mml:mn> </mml:msup> </mml:mrow> </mml:math> " parton wave function and numerically demonstrate it to be a feasible candidate for the ground state at \nu=2+3/8 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>ν</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> <mml:mo>+</mml:mo> <mml:mn>3</mml:mn> <mml:mi>/</mml:mi> <mml:mn>8</mml:mn> </mml:mrow> </mml:math> . We make predictions for experimentally measurable properties of the \bar{3}\bar{2}^{2}1^{4} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mover> <mml:mn>3</mml:mn> <mml:mo accent="true">‾</mml:mo> </mml:mover> <mml:msup> <mml:mover> <mml:mn>2</mml:mn> <mml:mo accent="true">‾</mml:mo> </mml:mover> <mml:mn>2</mml:mn> </mml:msup> <mml:msup> <mml:mn>1</mml:mn> <mml:mn>4</mml:mn> </mml:msup> </mml:mrow> </mml:math> state that can reveal its underlying topological structure.