Charged excitons in a dilute two-dimensional electron gas in a high magnetic field

Abstract

A theory of charged excitons X − in a dilute 2D electron gas in a high magnetic field is presented. In contrast to previous calculations, three bound X − states (one singlet and two triplets) are found in a narrow and symmetric GaAs quantum well. The singlet and a "bright" triplet are the two optically active states observed in experiments. The bright triplet has the binding energy of about 1 meV, smaller than the singlet and a "dark" triplet. The interaction of bound X − 's with a dilute 2D electron gas is investigated using exact diagonalization techniques. It is found that the short-range character of the e-X − interactions effectively isolates bound X − states from a dilute e-h plasma. This results in the insensitivity of the photoluminescence spectrum to the filling factor ν, and an exponential decrease of the oscillator strength of the dark triplet X − as a function of ν −1 .71. 35.Ji, 71.35.Ee, 73.20.Dx

Charged Excitons in the Quantum Hall Regime

“…Consistent with the behavior predicted in Ref. [19], the binding energy of the X − td increases with magnetic field and the PL line approaches X − s at high field. However, we note here that up to the highest field in our experiment (16 T) we did not observe the predicted singlet-triplet crossing.…”

“…Instead, a saturation of the X − t binding energy was found at high fields [11,14,31,32]. Recent theoretical [19] and experimental work [6,7] solved this puzzle. It was found [19] that at high magnetic field two different triplet excitons exist as bound states.…”

“…Recent theoretical [19] and experimental work [6,7] solved this puzzle. It was found [19] that at high magnetic field two different triplet excitons exist as bound states. One of these excitons has a total angular momentum of L = 0, and is therefore called the bright triplet, X − tb .…”

“…However, one of the striking differences of optical experiments, compared to transport, is the presence of photoexcited holes in the system, which can significantly influence its properties. In samples with very low carrier concentration, the Coulomb interaction between electrons and holes leads to the formation of negatively charged excitons, which have been a subject of intense research during the past decade (see, e.g., [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]). For samples with relatively strong disorder, the commonly accepted picture is that at low density the two-dimensional electron system (2DES) breaks up into areas with finite density (electron puddles) and completely depleted regions, where neutral excitons (X 0 ) can form.…”

Photoluminescence of Charged Excitons in Fractional Quantum Hall Systems

“…While breaking the dynamical symmetry at B < ∞ is by no means surprising, the fact that collisions of an X − with surrounding electrons do not relax the geometrical selection rule associated with the angular momentum conservation is a nice demonstration of Laughlin correlations of an X − with other negative charges [21]. As a result of these correlations, at least at small values of the filling factor ν, the X − 's remain spatially isolated and avoid high energy collisions with one other or with electrons to become true QP's of a 2DEG containing additional valence holes [22].…”