Spectroscopic study of dark excitons in ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ self-assembled quantum dots by a magnetic-field-induced symmetry breaking

The dark states of the heavy-hole ground-state exciton have been studied by photoluminescence spectroscopy of single self-assembled ${\mathrm{In}}_{0.60}{\mathrm{Ga}}_{0.40}\mathrm{As}$ quantum dots in magnetic fields of varying strengths and orientations. When tilting B out of the [001] crystal direction the exciton states with angular momenta $|m|=2\mathrm{}$ are mixed with the $|m|=1\mathrm{}$ states and become observable. In combination with a detailed analysis of the corresponding Hamiltonian a comprehensive picture of the exciton fine structure is obtained. This fine structure is characteristic for direct gap semiconductors with a twofold degenerate valence band.