Abstract
Motivated by two independent experiments revealing a resistance minimum at the Landau level (LL) filling factor $\nu=2+4/9$, characteristic of the fractional quantum Hall effect (FQHE) and suggesting electron condensation into a yet unknown quantum liquid, we propose that this state likely belongs in a parton sequence, put forth recently to understand the emergence of FQHE at $\nu=2+6/13$. While the $\nu=2+4/9$ state proposed here directly follows three simpler parton states, all known to occur in the second LL, it is topologically distinct from the Jain composite fermion (CF) state which occurs at the same $\nu=4/9$ filling of the lowest LL. We predict experimentally measurable properties of the $4/9$ parton state that can reveal its underlying topological structure and definitively distinguish it from the $4/9$ Jain CF state.
Highlights
Motivated by two independent experiments revealing a resistance minimum at the Landau level (LL) filling factor ν = 2 + 4/9, characteristic of the fractional quantum Hall effect (FQHE) and suggesting electron condensation into a yet unknown quantum liquid, we propose that this state likely belongs in a parton sequence, put forth recently to understand the emergence of FQHE at ν = 2 + 6/13
In the lowest LL (LLL), as expected, we find that the Jain composite fermion (CF) state has lower energy than the parton state
For the sake of completeness, we have investigated the competition between the parton and Jain CF states in the n = 1 LL of monolayer graphene
Summary
The “n2 ̄111” parton states for n = 1, 2, 3 give a good description of the SLL FQHE states observed at ν = 2 + 2/3, 2 + 1/2 and 2 + 6/13 [33,34]. We find the 411 Jain CF state has lower energy here, consistent with the fact that experimentally observed FQHE states in the n = 1 LL of monolayer graphene are well described by the CF paradigm [49,50,51].
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