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

Abstract

In two-beam magneto-photoluminescence spectra of a two-dimensional valence hole gas we identify the three-level energy spectrum of a free positive trion with a field-induced singlet-triplet transition. The recombination spectrum of acceptor-bound trions is also detected, including a cyclotron replica corresponding to the hole shake-up process. The emergence of a shake-up peak at low temperature is shown to be a sensitive probe of the presence of a small number of impurities inside the high-mobility quantum well, and its relative position is directly related to the hole cyclotron mass.PACS numbers: 71.35.Ji, 71.35.Pq, 73.20.Mf Quantization of single-particle energy into macroscopically degenerate, widely separated Landau levels (LLs) makes the two-dimensional (2D) gas of charge carriers in a strong magnetic field a unique setting for studying the non-perturbative many-body interaction phenomena. Eminent examples of discoveries made in these systems include fractional quantum Hall effect [1], emergence of incompressible fluids with fractional or nonabelian quasiparticles [2, 3, 4], or formation of topological "skyrmion" excitations [5,6] carrying massive spin per unit charge.A powerful tool used to study interacting 2D carriers is photoluminescence (PL) spectroscopy [7,8]. In a PL experiment, additional electron-hole (e-h) pairs are introduced into the system through photon absorption, and response of the surrounding carriers makes the recombination spectrum sensitive to their many-body dynamics.Since their prediction [9,10] and successful experimental detection [11], trions (X ± = 2e + h or 2h + e) have been recognized to play a crucial role in the PL spectra of 2D gases [12,13,14]. 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. The last point invokes the puzzling question of the role played by localization or, alternatively, of the influence of weak disorder − polarized PL spectrum of the 2D valence hole gas as a function of the magnetic field. Energy is measured from the exciton line. Arrows mark several peaks identified at high fields: exciton X, trions X + (red for spinsinglet and blue for two triplets), and emission spectrum of the acceptor-bound trion AX + , including a shake-up line AX + SU .in strongly interacting 2D systems of carriers.This very question is addressed in the present paper. We repo...

Positively versus negatively charged excitons: A high magnetic field study of CdTe/Cd1−xMgxTe quantum wells

“…Positively charged trions T + are observed in different QW systems as well: GaAs/(Al,Ga)As, 5,12,[21][22][23][24] CdTe-based, [25][26][27] and ZnSe/(Zn,Mg)(S,Se) structures. 8,10 The triplet T + t state is stabilized in high magnetic fields.…”

“…8,10 The triplet T + t state is stabilized in high magnetic fields. 12,21,22,24 Comparative studies of negatively and positively charged excitons in the very same QW, where the type of resident carrier is tuned either by a gate voltage or by above-barrier illumination, have been reported for GaAs/(Al,Ga)As 12,23 and ZnSe/(Zn,Mg)(S,Se) 10 QW structures. Experimentally, it is established that at zero magnetic field, B = 0, the binding energies of the singlet trions T + .…”

Cyclotron-resonant exciton transfer between the nearly free and strongly localized radiative states of a two-dimensional hole gas in a high magnetic field

“…The exchange gap ∆ and the relative intensities I of the unmixed transitions were read from the experimental spectra (away from the crossings). For the "charged" scenario (left), degeneracy of the two final states h + A + s and 2h + A (i.e., zero A + s binding energy in the relevant M = −1 channel), is needed (and, actually, justified by the previous calculation [9]) to maximally reduce the predicted anticrossing pattern. Yet, regardless of the coupling constant δ, the experimental behavior cannot be reproduced, as it is shown in Fig.…”

“…The hypothetical charged complex AX + would consist of a bare interface acceptor (negative point charge), one electron, and three holes. Previous calculations [9] hint that its ground state would have a doublet spin configuration, corresponding to the unpolarized holes (total three-hole spin of 1/2; we adopt a convention assigning spin projections ±1/2 to the "up" and "down" heavy hole states), with the quadruplet configuration (polarized holes) excited by several meV. Thus, only the doublet state AX + d would be populated at low temperatures.…”

“…Thus, its emission would be split by a small exchange energy gap in the final state (A + ; in the optically active angular momentum channel M = −1 [9]). At first sight, this agrees with the observed 0.3 meV splitting of the CR-AX lines, but the exact course of the anti-crossing lines turns out incorrect.…”