Definitive observation of the dark triplet ground state of charged excitons in high magnetic fields

Abstract

The ground state of negatively charged excitons (trions) in high magnetic fields is shown to be a dark triplet state, confirming long-standing theoretical predictions. Photoluminescence (PL), reflection, and PL excitation spectroscopy of CdTe quantum wells reveal that the dark triplet trion has lower energy than the singlet trion above 24 Tesla. The singlet-triplet crossover is "hidden" (i.e., the spectral lines themselves do not cross due to different Zeeman energies), but is confirmed by temperature-dependent PL above and below 24 T. The data also show two bright triplet states. PACS numbers: 71.35.Pq, 71.35.Ji, 78.66.Hf A central problem found in atomic, solid state, and nuclear physics is the case of a three-particle system of fermions, bound together by long-range Coulomb interactions. In atomic physics, this situation is most simply realized by the two-electron hydrogen ion, H − , in which the two identical electrons can exist in either a singlet or triplet state with total electron spin S e = 0 or 1, depending on external parameters. The semiconductor analog of the H − ion is the negatively charged exciton (trion), consisting of two conduction electrons bound to a single valence hole. Optical signatures from trions have been observed in GaAs, CdTe, and ZnSe quantum wells (QWs) [1,2,3,4]. Unlike the H − ion, the hole and two electrons comprising the trion have comparable masses and typically experience strong QW confinement in one dimension, making trions a genuine quantum three-particle system with Coulomb interactions for which no general analytical solutions exist.Much attention has focused on the evolution of trion optical signatures with applied magnetic field [5,6,7,8,9]. In the limit of zero magnetic field, theory predicts just one bound trion state: the S e = 0 singlet trion (T s ) [10,11]. This is consistent with Hill's theorem [12], which states that the H − ion (with an infinitely massive proton) supports exactly one bound singlet state. In the opposite limit of extremely high magnetic fields, it can be rigorously shown that a S e = 1 triplet is the only bound trion state in a strictly 2D system [11,13]. Modelindependent symmetry considerations [14] demonstrate that this lowest triplet state is "dark" (T td ) (i.e., optically inactive), due to the exact selection rules imposed by spatial axial and translational symmetries that exist in a disorder-free QW. Thus, at finite magnetic fields one expects both singlet and triplet bound trions [11,13]. More importantly, at some critical magnetic field B c the spin configuration of the trion ground state must cross over from the singlet to the triplet. Theoretical estimates suggest this crossover field is very large (B c > 20 T) and depends sensitively on the strength of the Coulomb interaction (dielectric constant) and the details of the QW confinement [11,15,16,17,18]. Numerical calculations also point to the existence of weakly-bound, optically active "bright" triplet states (T tb ), although there is large disparity amongst the predicted regions of...

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

“…It is worthwhile to note that the bright triplet states, as seen in Ref. 7, are not observed in the present structure, which we explain by the relatively low electron concentration.…”

“…Further, the binding energy of the triplet trion states approaches the singlet binding energy. 7 The experimental results presented in Figs. 10 and 11 are measured at two temperatures, 0.4 and 4.2 K, which gives us the additional opportunity to identify the PL lines due to the changes of the thermal occupation of the exciton and trion states.…”

“…5,[11][12][13] Two types of triplet states-dark and bright-are studied theoretically [14][15][16][17][18] and experimentally. 7,19,20 In magnetic fields above 20 T the binding energy of the triplet state, which is dark, may exceed the singlet state binding energy, so that the triplet state is the ground state of T − . This depends sensitively on the signs and values of the electron and hole Zeeman splittings and on the details of the quasi-2D confinement in the QW (QW depth and width, effective masses of the carriers).…”

“…The negatively charged species T − are studied in detail in various material systems, such as GaAs/(Al,Ga)As, [3][4][5] CdTe-based, 6,7 and ZnSe-based [8][9][10] structures. Magnetooptical techniques play a key role in these investigations and allow one to obtain comprehensive information about the energy and the spin structure of the T − complex.…”

“…Such a singlet-triplet crossover can either be observed directly, as a crossing of the corresponding optical lines, e.g., in emission spectra, or it may be hidden and affect only the intensities of these transitions. 7 A comprehensive spectroscopic study, involving the analysis of circularly polarized emission, absorption, and reflectivity spectra is required, in order to get a reliable separation of the Coulomb and Zeeman contributions to the trion binding energies. Such an analysis is hampered by the fact that the hole Zeeman splitting in QWs is typically a nonlinear function of the magnetic field strength and, as such, is not described by a field-independent g factor, as shown below.…”