Absorption in the Fractional Quantum Hall Regime: Trion Dichroism and Spin Polarization

Abstract

We present measurements of optical interband absorption in the fractional quantum Hall regime in a GaAs quantum well in the range 0 < ν ≤ 1. We investigate the mechanism of singlet trion absorption, and show that its circular dichroism can be used as a probe of the spin polarization of the ground state of the two-dimensional electron system (2DES). We find that at ν ≤ 1/3 the 2DES is fully spin-polarized. Increasing the filling factor results in a gradual depolarization, with a sharp minimum in the dichroism near ν = 2/3. We find that in the range 0.5 ≤ ν < 0.85 the 2DES remains partially polarized for the broad range of magnetic fields from 2.75 to 11 Tesla. This is consistent with the presence of a mixture of polarized and depolarized regions.The electron-electron Coulomb interaction plays an important role in determining the spin polarization (P) of a two-dimensional electron system (2DES) in a perpendicular magnetic field B. The effect of the interactions on the spin is most readily seen in in the filling factor range ν ≤ 1, where the level degeneracy exceeds the number of electrons. The exchange part of the Coulomb interactions favors a ferromagnetic state. However, a manybody wavefunction in which all electrons have the same spin is restricted by the Pauli principle and may not constitute in general an optimal spatial distribution that minimizes the total Coulomb energy. Inclusion of components of the opposite spin in the wavefunction opens a larger phase space for the electrons and may result in a lower Coulomb repulsion. Thus, the ground state of the 2DES in this regime is determined by the competition between the gain in Coulomb energy and the cost in Zeeman energy.Several methods have been used to determine the 2DES spin polarization in the fractional quantum Hall regime. The direct method is measuring the shift in the nuclear magnetic resonance (NMR) caused by the 2DES magnetization. Indeed, NMR measurements have yielded quantitative measurements of P throughout a broad range of filling factors [1,2]. Transport experiments have also been used and were successful in identifying transitions in the spin polarization, although are less effective in providing a quantitative value of P [3, 4].An alternative approach for measuring P is using optical spectroscopy: photoluminescence [5], reflectivity [6], and absorption spectroscopy [7]. In these techniques, the occupation of each spin levels are obtained from measurements of the circular dichroism of the interband transitions. In quantum wells (QW), however, establishing the relation between the optical oscillator strengths (OS) and P presents a major difficulty. As a result of the strong interaction between the photo-created valence hole and the electrons, the spectrum in QWs is dominated by resonance peaks, associated with the neutral exciton, and charged excitons (trions). A further complication is introduced by the fact that in a trion, the two electrons can form a singlet or triplet wavefunctions [8,9]. Hence, it is essential to take into account the nat...

Phonon and transport measurements in the fractional quantum Hall effect

“…This interpretation is also supported by recent theoretical works by Apalkov et al [30] and experiments by Freytag et al [31] and Groshaus et al [32], were the presence of a mixture of polarized and depolarized regions is proposed. As a result, we may speculate that the complexity of the 2/3 state is responsible for the appearance of a spin-forbidden transition in the phonon absorbtion.…”

Quantum Hall effect of two-component bosons at fractional and integral fillings

“…We have carried out an extensive study of quantum Hall effect for two-component bosons, studying a number of 10), which are [3,3], [4,2], [5,1], and [6,0] (from left to right). The arrows in (a) and (b) show the corresponding levels in the RSES, which nicely match the starting points of various edge branches.…”

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“…ν = 2/3 and 4/3 (ν CF = −2), are expected to have the same α C because of particle-hole symmetry ν ↔ (2−ν) [2]. Experimentally, the spin-polarization of CFs has been probed through measurements of transitions of FQHSs in both transport and optical studies [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. In these studies, E Z /V C is increased by either increasing the 2DES density or adding a parallel magnetic field.…”