Measurements of composite fermion masses from the spin polarization of two-dimensional electrons in the region 1<ν<2

Abstract

Measurements of the reflectivity of a 2-D electron gas are used to deduce the polarization of the Composite Fermion hole system formed for Landau level occupancies in the regime 1 < ν < 2. The measurements are consistent with the formation of a mixed spin CF system and allow the density of states or 'polarization' effective mass of the CF holes to be determined. The mass values at ν = 3/2 are found to be ∼ 1.9me for electron densities of 4.4 × 10 11 cm −2 , which is significantly larger than those found from measurements of the energy gaps at finite values of effective magnetic field.The fractional quantum Hall effect has been very successfully described in terms of the picture of Composite Fermions [1] [2], however considerable uncertainties exist about both the Composite Fermion masses and the role of spin and the formation of partially polarized states [3][4][5][6][7]. In particular Park and Jain [3] have pointed out that the CF mass measured from activation measurements of the energy gap may be substantially smaller than the thermodynamic or "polarization" mass which determines the equilibrium spin populations of the carriers, an idea which has received some recent experimental support [6]. In this paper we describe a direct measurment of the polarization of the 2D Composite Fermion (CF) gas and deduce values for the polarization mass.In the Composite Fermion model 2D electrons at filling factor ν = 1/2 form a new collective state with quasiparticle excitations, known as Composite Fermions, and zero effective magnetic field. If the Zeeman energy is small compared to the equivalent Fermi energy in the Composite Fermion system the spin polarization of the 2D electrons around ν = 1/2 deviates from 100% even at zero temperature. Cyclotron-like quantization of the energy spectra of the Composite Fermions away from ν = 1/2 causes oscillations in the spin polarization of the 2D electrons at integer filling factors for Composite Fermions. Simultaneously, transport properties of the 2DEG become controllable by the ratio of the cyclotron energy for the Composite Fermions to the Zeeman energy [4] [8]. In spite of this evidence for partial polarization of the CF system direct measurements of the CF Fermi wavevector suggest that the system is close to fully polarized both at ν = 1/2 [9] and at ν = 3/2 [10].In this work we report direct measurements of the properties of Composite Fermion holes in the region of level occupancy 1 < ν < 2. For small values of the Zeeman energy a very convenient way to treat the unoccupied states in the zeroth Landau level in the region 1 < ν < 2 is as "holes" [4] with an effective filling factor given by ν h = 2 − ν e relative to completely filled electron sublevels of both spins. The properties of such holes in the region 1 < ν e < 2 are equivalent to the properties of electrons in the region 0 < ν e < 1 if the energy scale for the Coulomb interaction is much less than the cyclotron energy. Thus a new Composite Fermion system is generated around filling factor ν h = 1/2 which corresponds to...

Spin Transition in theν=8/3Fractional Quantum Hall Effect

“…Beyond this density, Δ 8/3 increases with increasing density. This change observed in the 8/3 energy gap is very similar to what was observed in the ν=2/3 FQHE in the lowest Landau level [49,50] and demonstrates a spin transition [49][50][51][52][53][54][55][56][57] from a spin unpolarized ground state at low densities to a spin polarized one at higher densities. For comparison, Δ 7/3 shows a monotonic density dependence, supporting that the 7/3 state is spin-polarized down to 0.5×10 11 cm -2 .…”

Density dependence of valley polarization energy for composite fermions

“…5 For other states, e.g. those which form around ν = 1/2 and 3/2, numerous transport, 6,7,8,9,10 optical, 11,12 and nuclear spin resonance and relaxation 13,14,15,16,17 studies have aided the understanding of the role of spin in the CF picture. 18,19 It was recently shown 20 that CFs which form at ν = 3/2 in AlAs quantum wells possess a valley degree of freedom which in principle is analogous to spin.…”

Depolarization of the ground state in the quantum Hall ferromagnet and its dependence ong-factor

“…The strength of the magnetoreflectivity signal is determined by the density of unoccupied states and hence the density of 'holes' in the Landau levels. The absorption coefficient is directly related to dispersion in the refractive index through the Kramers-Kronig relation and it has been shown theoretically that the magnitude of the excursion of the reflectivity around the transition energy is proportional to the absorption coefficient [17,18]. Figure 1 shows a series of optical reflectivity spectra in the region of occupancy 0.9 < ν < 1.4 for both σ + and σ − z where I − and I + are the amplitudes of the excursion of the reflectivity around the energy of the interband transitions between the zeroth Landau levels of the heavy holes and 2D electrons.…”