Abstract:
A theory of the Zeeman effect and fine structure of the energy spectrum of electron-hole complexes in highly symmetric quantum dots grown along the [111] direction from materials with a zinc blende lattice has been presented. In the studied quantum dots with $C_{3v}$ point symmetry, the Zeeman effect for a heavy hole in a magnetic field $\mathbf{B}$||[111] has an unusual form: in addition to the diagonal component $(g_{h1})$, the effective tensor of $g$-factors contains the off-diagonal element $(g_{h2})$. For $g_{h2}\ne$ 0, there is a magnetically induced mixing of heavy-hole states, which explains two additional lines observed in experimental photoluminescence spectra of excitons and trions. A microscopic theory of the effective $g$-factors $g_{h1}$ and $g_{h2}$ within the Luttinger Hamiltonian in the spherical approximation has been discussed, as well as additional contributions to the off-diagonal element $g_{h2}$ due to the warping of the spectrum of holes. The results of theoretical calculations of the $g$-factors $g_{h1}$ and $g_{h2}$ for quantum dots based on GaAs have been compared with the experimental data.
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