Spontaneous polarization of composite fermions in the $n=1$ Landau level of graphene

TL;DR

This study investigates the spin polarization phenomena of composite fermions in the $n=1$ Landau level of graphene, revealing that strong exchange interactions induce full spin polarization and alter the expected quantum Hall states.

Contribution

It provides a detailed analysis of spin physics in the $n=1$ Landau level, showing deviations from mean-field predictions and identifying the nature of the ground states at specific fillings.

Findings

Composite fermions are fully spin polarized at certain fillings.

The spin wave mode persists even with negligible Zeeman energy.

The fully spin polarized Fermi sea is energetically favored over the Pfaffian state.

Abstract

Motivated by recent experiments that reveal expansive fractional quantum Hall states in the $n=1$ graphene Landau level and suggest a nontrivial role of the spin degree of freedom [Amet {\em et al.}, Nat. Common. {\bf 6}, 5838 (2014)], we perform accurate quantitative study of the the competition between fractional quantum Hall states with different spin polarizations. We find that the fractional quantum Hall effect is well described in terms of composite fermions, but the spin physics is qualitatively different from that in the $n=0$ Landau level. In particular, for the states at filling factors $n/(2n\pm 1)$, both exact diagonalization and the composite fermion theory show that the ground state is fully spin polarized and supports a robust spin wave mode even in the limit of vanishing Zeeman coupling. Thus, even though composite fermions are formed, a mean field description that treats them as weakly interacting particles breaks down, and the exchange interaction between them is strong enough to cause a qualitative change in the behavior by inducing full spin polarization. We also verify that the fully spin polarized composite fermion Fermi sea has lower energy than the paired Pfaffian state at the relevant half fillings in the $n=1$ graphene Landau level, indicating a lack of fractional quantum Hall effect at half filling in the $n=1$ graphene Landau level.