Spectroscopic access to single-hole energies in InAs/GaAs quantum dots

Abstract

We present a purely spectroscopic way to determine single-particle energy level splittings in individual InAs/GaAs QDs. The method is based on a combination of $\ensuremath{\mu}$-photoluminescence spectroscopy $(\ensuremath{\mu}\text{PL})$ with resonant excitation and $\ensuremath{\mu}$-photoluminescence excitation spectroscopy $(\ensuremath{\mu}\text{PLE})$ of charged QDs. The approach allows elimination of all contributions from few-particle interactions such that true single-particle energy level distances are determined. For the present InAs/GaAs QDs, showing ground-state recombination energies between 1.23 to 1.27 eV, the splitting between the hole ground state $({h}_{0})$ and first excited state $({h}_{1})$ is $\ensuremath{\Delta}({h}_{0}{h}_{1})=(27.1\ifmmode\pm\else\textpm\fi{}1.8)\text{ }\text{meV}$. The splitting between the first and second excited hole states is $\ensuremath{\Delta}({h}_{1}{h}_{2})=(10.8\ifmmode\pm\else\textpm\fi{}0.3)\text{ }\text{meV}$. These values are in good agreement with results from eight-band $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ calculations on lens-shaped InAs/GaAs QDs. Theoretical investigations identify unambiguously the heavy-hole-light-hole coupling as the decisive parameter leading to a nonzero ${h}_{1}\ensuremath{-}{h}_{2}$ splitting.