Anomalous magnetophotoluminescence as a result of level repulsion in arrays of quantum dots

Selectively excited photoluminescence (SPL) of an array of self-organized In0.5Ga0.5As quantum dots has been measured in a magnetic field up to 11T. Anomalous magnetic field sensitivity of the SPL spectra has been observed under conditions for which the regular photoluminescence spectra is insensitive to the magnetic field due to large inhomogeneous broadening. The anomalous sensitivity is interpreted in terms of the repulsion of excited levels of the dots in a random potential. A theory presented to describe this phenomena is in excellent agreement with the experimental data. The data estimated the correlation in the positions of excited levels of the dots to be 94%. The magnetic field dependence allows the determination of the reduced cyclotron effective mass in a dot. For our sample we have obtained memh/(me+mh) = 0.034m0. 71.35.+z, 78.55.-m, 78.55.Cr, 76.40.+b Typeset using REVTEX 2 An array of self-organized quantum dots (QDs) is a unique system consisting of very small atomic-like objects each with a few energy levels [1–4]. The studies of this system have shown the possibility to attain three-dimensional confinement of carriers within QDs. Such quantum dots are formed in highly strained semiconductor heterostructures by what is known as Stranski-Krastanow growth, where growth starts two-dimensionally, but after a certain critical thickness is reached, islands are formed spontaneously, and a thin wetting layer is left under the islands. In this process, the growth is interrupted immediately after the formation of the islands and before strain relaxation and misfit dislocations occur. Such insitu formation of 0D quantum dots results in high quality defect-free materials. In addition, the coherent islanding and strain effects can produce QDs with a size uniformity within ±10% which is very promising for 0D quantum devices where the sharper density of states is exploited. Photoluminescence (PL) spectrum of such an array has a broad line which is supposed to be mainly due to inhomogeneous broadening [5,6]. Photoluminescence excitation (PLE) and selectively-excited photoluminescence (SPL) reveal a fine structure. This fine structure has been interpreted by one of us [7] as a result of splitting of the excited levels in quantum dots due to violation of cylindrical symmetry of the dots by a random potential. Though the splitting is much less than the PL linewidth, it can be observed because of the effect of repulsion of energy levels inside a dot. Here we give an experimental proof of this point and a detailed study of the level repulsion in quantum dots by applying magnetic field which affects the splitting of excited levels. We found an anomalous sensitivity of the SPL to a magnetic field under conditions for which the regular photoluminescence spectra is insensitive to the magnetic field due to large inhomogeneous broadening. We show that this sensitivity is a direct result of the level repulsion. A preliminary discussion of this effect has been given earlier [8]. The dot layer studied here is pseudomorphically grown by MBE on (100) GaAs substrate, and the QDs are formed by the coherent relaxation into islands of a few monolayers (ML) of In0.5Ga0.5As between GaAs buffer and cap layers. The actual amount of indium incorporated 3 in the dots can differ due to the complex dynamics of the adatoms during island formation. The growth and QD structural details have been reported earlier [9]. Fig. 1(a) shows PLE and regular PL spectra. Regular PL reveals a broad line with the FWHM=57meV. PLE spectra consists of significantly narrower lines. PL spectrum is redshifted with respect to PLE by about 80 meV. This shift occurs since the PLE experiment detects the light emitted only by the levels below the level excited by the pumping light. The SPL spectra for different excitation energies are presented in Fig. 1(b). The complicated character of the SPL spectra were analyzed earlier [7]. For our purposes it is important that at some energy of excitation (Eex = 1.3672eV) the SPL spectrum shows two symmetric peaks. At larger and smaller Eex these peaks become asymmetric. For an intuitive picture it is helpful to assume that each dot has two optically active excited levels E± relatively close to each other (see Fig. 2). The dots are isolated from each other, so the light is emitted from the same dot it is absorbed to. The dots are excited into E+ or E− and, after thermalization, emit light from E0. The red shift mentioned above originates from the difference E± − E0. In some dots the excitation energy h̄ωex may be close either to E− or to E+. These two types of dots can be considered as two different subsets. These subsets should give two peaks in the SPL curve if we assume the correlation between the positions of E± and E0. If this correlation is of such kind that the dots with larger E± have, in general, larger E0, the excitation of E+ will cause the lower peak in SPL. This is a natural proposal and it corresponds to our experimental data (see Fig. 1(b)). At some energy of excitation there are the same amounts of dots in each subset. However, if the energy of excitation is shifted upward, the number of the dots which have the lowest excited level at this energy is smaller, so the intensity of the higher-energy peak decreases. Correspondingly, the low-energy peak disappears as the excitation energy decreases. In our interpretation two close optically active excited levels originate from the doubly degenerate lowest excited level of a cylindrically symmetric dot. These levels are split by a random potential which may include a deviation of a dot shape from cylindrical symmetry. It is crucial that both the distance between the peaks and their width, as well as the linewidth 4 of the nonselective PL have the same origin. They are determined by the random potential which splits degenerate levels and shifts randomly all energy levels in QDs. At the excitation energy Eex = 1.3672eV, which gives two symmetric peaks in the SPL, we have studied the magnetic field dependence of the SPL spectrum. The results presented in Fig. 3 show anomalous sensitivity to the magnetic field. The relative intensity of the dip between two peaks decreases by 11% in the magnetic field of 2T. Note that the wide line of the regular (non-selective) PL is insensitive to a magnetic field up to ∼10T [10]. We show below that the two-level structure of SPL at zero field and its anomalous sensitivity to the magnetic field are both the results of the level repulsion. For an axially symmetric dot two degenerate wave functions with an angular momentum |m| have the form Ψm±(r) = ψm(r)e, where ψm can be chosen real. For the first excited state m = 1. The positions of energy levels ǫ±, split and shifted by random potential and by magnetic field, can be obtained as the eigenvalues of the secular matrix