Coulomb correlations of charged excitons in semiconductor quantum dots

Abstract

The emission pattern of charged excitons in a semiconductor quantum dot ͑QD͒ is composed of a quadruplet of linearly polarized lines when a magnetic field is applied in a Voigt configuration. The orientation of the linear polarization of exciton emission is controlled by the orientation of the magnetic field in QDs with C 3v symmetry while for QDs with C 2v symmetry it is not. We demonstrate that the g factor of holes is very sensitive to the dot shape asymmetry but that of electrons is not. By comparing the effective g factors obtained for the neutral and charged excitons in the same quantum dot, we uncover the role of Coulomb correlations in these excitonic states. We show that the C 3v symmetry of pyramidal QDs makes them ideal candidates for implementing all-optical many-qubits gates based on electron spin as a quantum bit. DOI: 10.1103/PhysRevB.80.165312 PACS number͑s͒: 78.67.Hc, 71.70.Ej, 71.70.Gm, 78.55.Cr Spin degree of freedom of carriers in semiconductor quantum dots ͑QDs͒ could serve as quantum bits to store 1 and process 2,3 information in spin-based devices. Recent experiments demonstrated essential steps toward the implementation of these concepts. Effective initialization of a spin state was achieved for either an electron 4,5 or a hole 6,7 confined to a single quantum dot. Rapid rotation of an electron spin was accomplished by driving coherently the two spin states with short optical pulses by means of stimulated spinflip Raman scattering. 8 The coherent manipulation of a carrier spin 9 in a spin-flip Raman process involves the creation of two energetically different spin states by applying a magnetic field. A key property of an electron ͑or a hole͒ confined to a QD is the effective g factor that measures the Zeeman splitting of the ground state in an applied magnetic field and depends on the orientation of the field with respect to the symmetry axis of the QD. Even though the coherent manipulation of a single quantum dot spin was successively demonstrated, the extension of this scheme to quantum dot arrays seems to be a challenge as QDs must have a narrow distribution of emission energies and obey specific optical selection rules. It is thus necessary to investigate the homogeneity of the Zeeman splittings and the uniformity of the optical selection rules in QD arrays.Zeeman splittings in QDs have been investigated by capacitance spectroscopy, 10 by magnetophotoluminescence 11,12 and by transient nonlinear optical techniques.13 While transport techniques probe the g factors of electronic states, optical techniques probe the Zeeman splittings of excitonic states. The optical anisotropy of QDs was also studied by applying a magnetic field in the Voigt geometry, which revealed a complex behavior due to shape asymmetry and strain present in self-assembled quantum dots ͑SAQDs͒. 14-17In principle, probing different charged excitonic states in QDs could yield different values of the Zeeman splittings if the Coulomb correlations between carriers altered the singleparticle wave function of the strong...

Comparison of magneto-optical properties of various excitonic complexes in CdTe and CdSe self-assembled quantum dots

“…We particularly focus on differences between excitons of various charge states: their binding energy, g-factor and diamagnetic shift. These quantities have been already measured for single quantum dots [7][8][9][10][11][12][13][14][15][16][17] , but have not been analyzed in terms of variation across the QD population.…”

Intertwining of Zeeman and Coulomb interactions on excitons in highly symmetric semiconductor quantum dots

“…While the Zeeman energy splittings of the doublets vanish at zero magnetic field for both the charged and the neutral excitons, the energy separation between the doublets converges to zero for a charged exciton, whereas it takes a finite value for the neutral exciton. 14,20,27 In Fig. 1(b), we show the polarized photoluminescence spectra of the same QD that were recorded at a magnetic field of 6.5 T in the Voigt configuration.…”

“…The expression of this dependence can be easily obtained from the diagonalization of the Zeeman and e-h exchange Hamiltonian given in Ref. 27, taking into account that the anisotropic electron-hole exchange parameters (δ = δ * = 0) are equal to zero in the case of C 3v symmetry; it is then written as Eigenstates Eigenvalues where g e ⊥ and g h ⊥ are the transverse effective g factors for an electron and a hole, respectively.…”

“…All the quantum dots were measured from the same sample, which permitted the simultaneous observation of positively and negatively charged excitons in a single luminescence spectrum. 27 The sample was grown by low-pressure organometallic chemical vapor deposition on 2 • off-(111)B GaAs substrates prepatterned with a 5-μm pitch array of inverted tetrahedral recesses. 40 The growth on a (111)B-oriented substrate is perfectly suited to obtain semiconductor QDs possessing the symmetry properties of the C 3v point group because the growth axis is a threefold rotation axis of cubic crystals.…”

“…5 Most experimental studies of excitons confined in QDs were performed on self-assembled quantum dots (SAQDs) grown on {100} surfaces and were concerned with polarization anisotropy, [16][17][18] in-plane anisotropy of carrier effective g factors, 19,20 fine-structure splitting of neutral and charged exciton complexes, [21][22][23][24] which were induced by the shape asymmetry, and the existence of anisotropic strain and piezoelectric fields in these dots. Only recently, highly symmetric pyramidal QDs grown on {111} surfaces have emerged as interesting quantum structures in which zero fine-structure splitting of the neutral exciton was predicted 25,26 and eventually observed, [27][28][29][30] and for which the entanglement of polarized photon pairs was demonstrated. 31 It is our purpose in this paper to develop a general theoretical model of the Zeeman effects on the quantum states of excitons in highly symmetric QDs and to compare its predictions to experimental studies performed on magnetoexcitons confined in pyramidal QDs grown on (111)B GaAs substrates.…”