Cubic anisotropy of hole Zeeman splitting in semiconductor nanocrystals

We study theoretically cubic anisotropy of Zeeman splitting of a hole localized in semiconductor nanocrystal. This anisotropy originates from three contributions: crystallographic cubically-symmetric spin and kinetic energy terms in the bulk Luttinger Hamiltonian and the spatial wave function distribution in a cube-shaped nanocrystal. From symmetry considerations, an effective Zeeman Hamiltonian for the hole lowest even state is introduced, containing a spherically symmetric and a cubically symmetric term. The values of these terms are calculated numerically for spherical and cube-shaped nanocrystals as functions of the Luttinger Hamiltonian parameters. We demonstrate that the cubic shape of the nanocrystal and the cubic anisotropy of hole kinetic energy (so called valence band warping) significantly affect effective $g$ factors of hole states. In both cases, the effect comes from the cubic symmetry of the hole wave functions in zero magnetic field. Estimations for the effective $g$ factor values in several semiconductors with zinc-blende crystal lattices are made. Possible experimental manifestations and potential methods of measurement of the cubic anisotropy of the hole Zeeman splitting are suggested.Comment: 17 pages, 7 figure

Quantum Oscillations of Photocurrents in HgTe Quantum Wells with Dirac and Parabolic Dispersions

We report on the observation of magneto-oscillations of terahertz radiation induced photocurrent in HgTe/HgCdTe quantum wells (QWs) of different widths, which are characterized by a Dirac-like, inverted and normal parabolic band structure. The photocurrent data are accompanied by measurements of photoresistance (photoconductivity), radiation transmission, as well as magneto-transport. We develop a microscopic model of a cyclotron-resonance assisted photogalvanic effect, which describes main experimental findings. We demonstrate that the quantum oscillations of the photocurrent are caused by the crossing of Fermi level by Landau levels resulting in the oscillations of spin polarization and electron mobilities in spin subbands. Theory explains a photocurrent direction reversal with the variation of magnetic field observed in experiment. We describe the photoconductivity oscillations related with the thermal suppression of the Shubnikov-de Haas effect.Comment: 16 pages, 13 figure

Statistics of excitons in quantum dots and the resulting microcavity emission spectra

A theoretical investigation is presented of the statistics of excitons in quantum dots (QDs) of different sizes. A formalism is developed to build the exciton creation operator in a dot from the single exciton wavefunction and it is shown how this operator evolves from purely fermionic, in case of a small QD, to purely bosonic, in case of large QDs. Nonlinear optical emission spectra of semiconductor microcavities containing single QDs are found to exhibit a peculiar multiplet structure which reduces to Mollow triplet and Rabi doublet in fermionic and bosonic limits, respectively.Comment: Extensively expanded revision, 14 pages, 12 figures, submitted to Phys. Rev.