  We study experimentally the dependence of dynamic nuclear spin polarization
on the power of non-resonant optical excitation in two types of individual
neutral semiconductor quantum dots: InGaAs/GaAs and GaAs/AlGaAs. We show that
the mechanism of nuclear spin pumping via second order recombination of
optically forbidden (''dark'') exciton states recently reported in InP/GaInP
quantum dots [Phys. Rev. B 83, 125318 (2011)] is relevant for material systems
considered in this work. In the InGaAs/GaAs dots this nuclear spin polarization
mechanism is particularly pronounced, resulting in Overhauser shifts up to ~80
micro-eV achieved at optical excitation power ~1000 times smaller than the
power required to saturate ground state excitons. The Overhauser shifts
observed at low-power optical pumping in the interface GaAs/AlGaAs dots are
generally found to be smaller (up to ~40 micro-eV). Furthermore in GaAs/AlGaAs
we observe dot-to-dot variation and even sign reversal of the Overhauser shift
which is attributed to dark-bright exciton mixing originating from
electron-hole exchange interaction in dots with reduced symmetry. Nuclear spin
polarization degrees reported in this work under ultra-low power optical
pumping are comparable to those achieved by techniques such as resonant optical
pumping or above-gap pumping with high power circularly polarized light.
Dynamic nuclear polarization via second-order recombination of ''dark''
excitons may become a useful tool in single quantum dot applications, where
manipulation of the nuclear spin environment or electron spin is required.
