Quasiexcitons in incompressible quantum liquids

Abstract

Photoluminescence ͑PL͒ has been used to study two-dimensional incompressible electron liquids in high magnetic fields for nearly two decades. However, some of the observed anomalies coincident with the fractional quantum Hall effect are still unexplained. We show that emission in these systems occurs from fractionally charged "quasiexciton" states formed from trions correlated with the surrounding electrons. Their binding and recombination depend on the state of both the electron liquid and the involved trion, predicting discontinuities in PL and sensitivity to sample parameters.

The hierarchy of incompressible fractional quantum Hall states

“…Similar behavior has been observed (Byszewski et al, 2006;Goldberg et al, 1990). The χ The e − X − PDF for different QXs; curve for χ + resembles e − e PDF of Laughlin liquid; shoulders for χ and χ + reflect additional charge quanta pushed onto the hole (Wójs et al, 2006a). discontinuity is different from that due to anyon excitons (Chen and Quinn, 1994b;Parfitt and Portnoi, 2003;Portnoi and Rashba, 1996;Rashba and Portnoi, 1993;Wójs and Quinn, 2000b,c) anticipated in much wider wells (e.g., for w ≥ 40 nm at n = 2 × 10 11 cm −2 ).…”

“…The resulting PL spectrum would be expected to reflect the properties of the initial χ − or χ + FIG. 41 (color online) (a) Lowest subband electron and heavy-hole charge density profiles in the normal direction ρ(z) for one-sided doped GaAS quantum wells (b), (c) Displacements δ of the density maxima from the center of the quantum well as a function of electron concentration n and well width w (Wójs et al, 2006a). .…”

“…χ is the neutral QX (a bound state of χ − and a QH), while χ + is a positively charged QX + ( a bound state of χ and a QH). In this subsection we review the many-body correlations associated with negatively charged excitons (or trions) immersed in a Laughlin IQL state, and predict a discontinuity of the PL spectrum at ν = 1/3 (Byszewski et al, 2006;Goldberg et al, 1990;Wójs et al, 2006a) and for spin-polarized systems, we elucidate the earlier theory Rashba, 1992, 1993;Zang and Birman, 1995) by identifying the "dressed exciton" with χ, its suppressed dispersion with the χ −1/3 -QH pseudopotential of interaction among two Laughlin charge quanta, and the "magnetoroton-assisted emission" with the χ −1/3 recombination. Photoluminescence from systems containing a small number of quasiexcitons (χ − , χ, χ + ) reflect the properties of these quasiexcitons in the initial state.…”

Comparative Numerical Analysis of Quasi-Two-Dimensional Negative and Positive Trions in High Magnetic Fields

“…4 we show ∆(B) for one-sided doped quantum wells, calculated at a fixed LL filling factor ν = 1/3 (i.e., at concentration proportional to B). This graph could guide design of quantum wells with a desired trion ground state that could be used for an optical probe of the Laughlin liquid (it was shown [6] that only a dark triplet trion leads to discontinuities in PL at ν = 1/3 [7]). Compared to Fig.…”

Magneto-optical probing of weak disorder in a two-dimensional hole gas

“…The three-body dynamics of a trion might at first sight seem analogous to the familiar Hydrogen ion problem. However, comparable e and h masses, confinement, magnetic field, nonparabolic and anisotropic hole dispersion, and coupling to the crystal lattice, surrounding carriers, or impurities -all generate complexity making trions fascinating objects of intense experimental [15,16,17,18,19,20] and theoretical [21,22,23,24,25,26,27,28] research.Nonetheless, the role of trions or other e-h complexes in magneto-optical spectra is still far from being completely understood. Especially the hole gas remains relatively less thoroughly explored because of both more complicated valence band structure and a larger difficulty in achieving ultra-high carrier mobility.…”