Possible realization of a chiralp-wave paired state in a two-component system

Abstract

There is much interest in the realization of systems with p-wave pairing in one dimension or chiral p-wave pairing in two dimensions, because these are believed to support Majorana modes at the ends or inside vortices. We consider a two component system of composite fermions and provide theoretical evidence that, under appropriate conditions, the screened interaction between the minority composite fermions is such as to produce an almost exact realization of p-wave paired state described by the so-called anti-Pfaffian wave function. This state is predicted to occur at filling ν = 3/8 or 13/8 in GaAs when the Zeeman energy is sufficiently small, and at ν = ±3/8 or ±13/8 in single layer graphene when either the Zeeman or the valley splitting is sufficiently small.

The enigma of theν=2+3/8fractional quantum Hall effect

“…Exact diagonalization studies up to N = 10 do not support the realization of any of these states for spinful electrons at zero Zeeman energy (the ground states at the appropriate N and 2Q values do not have the predicted quantum numbers). This should be contrasted with the situation at ν = 3/8 in the LLL, where a partially spin polarized 3/8 state is predicted to occur at sufficiently low Zeeman energies [50][51][52] , and to provide an almost exact representation for the APf pairing of composite fermions 51 .…”

Fractional quantum Hall effect at ν=2+4/9

“…Nevertheless, in the range of fillings 1/3 < ν < 2/5 very high-quality samples exhibit signatures of FQHE at ν = 4/11, 5/13, 6/17, 3/8, 3/10, 4/13, and 5/17 [4][5][6][7][8]. An understanding of these fragile states necessitates going beyond the framework of weakly interacting composite fermions as these states likely arise from an FQHE of CFs themselves [9][10][11][12]. This article focuses on one such state, namely the 6/17 FQHE.…”

Abelian parton state for the $ν=4/11$ fractional quantum Hall effect

“…However, in the range of filling factors 1/3 < ν < 2/5 samples with high mobility exhibit FQHE features at fractions ν = 4/11, 5/13, 6/17, 3/8, 3/10, 4/13, and 5/17 [4]. These states cannot be explained as IQHE states of CFs and likely arise from an FQHE of CFs themselves [5][6][7].…”