Fractional Quasiexcitons in Photoluminescence of Quantum Hall Liquids

Abstract

Realistic calculations of photoluminescence spectra for a 20 nm quantum well at a filling factor ν = 1/3 are presented. The new states formed from charged excitons (trions) by correlation with the surrounding electrons are identified. These "quasiexcitons" differ from usual excitons and trions by having fractionally charged constituents. Their binding energies and emission intensities depend on the involved trion, leading to discontinuity in photoluminescence.

Energy Spectra of Isolated Trions in Asymmetric Quantum Wells

“…The X − sb is the ground state in narrow wells, crossing the X − td at w ≈ 15 nm (neglecting E Z ). Knowing that emission from a trion coupled to a 2DEG shows discontinuity at ν = 1 3 only when this trion is an X − td [6], we find that wells with w = 15 to 25 nm are most suitable for PL studies of Laughlin incompressibility.…”

“…The condition for a dilute system is ν 1, but the trions may remain bound even at ν ∼ 1 In Ref. [6] we show that the coupling of a trion to the Laughlin liquid depends on the particular trion wavefunction, leading to a qualitatively different behavior of PL at ν = 1 , when electrons form an incompressible Laughlin 3 liquid [5]. A recent calculation [6] shows that emission from this state is due to recombination of fractionally screened trions ("quasiexcitons").…”

Trion Binding Energies and Wave Functions in Doped Quantum Wells

“…The X − sb is the ground state in narrow wells, crossing the X − td at w ≈ 15 nm (neglecting E Z ). Knowing that emission from a trion coupled to a 2DEG shows discontinuity at ν = 1 3 only when this trion is an X − td [6], we find that wells with w = 15 to 25 nm are most suitable for PL studies of Laughlin incompressibility. The 20 nm well used in Ref.…”

“…In Ref. [6] we show that the coupling of a trion to the Laughlin liquid depends on the particular trion wave function, leading (because of E1) to a qualitatively different behavior of PL at ν = 1 3 in different wells. Namely the emission energy is discontinuous only when the trion coupled to a 2DEG is the X − td (and not an X − sb ).…”

“…The "radius<distance" diluteness condition is equivalent to ν < 1, suggesting [4] that the trions might remain bound even at n corresponding to ν ∼ 1 3 , when electrons form an incompressible Laughlin liquid [5]. Indeed, a recent calculation [6] shows that emission from this state is due to the recombination of fractionally screened trions ("quasiexcitons").…”