Spontaneous polarization of composite fermions in then=1Landau level of graphene

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 et al., Nat. Commun. 6, 5838 (2014)], we perform accurate quantitative study of the the competition between fractional quantum Hall states with different spin polarizations in the n = 1 graphene Landau level. 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 ν = s/(2s ± 1), s integer, a combination of exact diagonalization and the composite fermion theory shows 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 an absence of composite-fermion pairing at half filling in the n = 1 graphene Landau level.

Fractional quantum Hall effect at Landau level fillingν=4/11

“…3(b), we show the R xx value at =4/11 as a function of 1/T in a semi-log plot. From the linear fit to the data, though within a very limited range, an energy gap of ~ 7 mK is obtained.We notice that the measured activation energy gap is much smaller than the numerical calculations, where the energy gap for a (partially) spin polarized 4/11 state has been estimated [14,17] The so obtained  is merely ~ 10 mK, much smaller than the theoretical calculated vales.On reduces the critical Zeeman energy due to softening of the short-range interaction and the reduction of the interaction energy difference between different spin-polarization states [18]. Comparing to the sample used in the light scattering experiments, the samples in our electronic transport studies have a much wider quantum well, 50nm.…”

“…On reduces the critical Zeeman energy due to softening of the short-range interaction and the reduction of the interaction energy difference between different spin-polarization states [18]. Comparing to the sample used in the light scattering experiments, the samples in our electronic transport studies have a much wider quantum well, 50nm.…”

“…In fact, almost all the existing finite-size numerical calculations [13][14][15][16][17][18] seem to favor a partially spin polarized ground state for the experimentally observed 4/11 state. However, the numerical simulations were carried out in 2DES of zero thickness.…”

“…Comparing to the sample used in the light scattering experiments, the samples in our electronic transport studies have a much wider quantum well, 50nm. Consequently, the critical Zeeman energy (or  c ) at the spin transition is reduced, probably by half at /l B = 1.5 (the value estimated for our samples) [18,24]. Here  is the effective width of the 2DES.…”

“…Yet, its origin remains elusive. Several proposals [13][14][15][16][17][18] have been made. Among them, the numerical simulations by Wójs, Yi, and Quinn (WYQ) [15] showed that a spin-polarized 4/11 FQHE state is an unconventional FQHE state of CFs and, possibly, a new nonAbelian state.…”