The potential importance of Aitken mode particles (diameters similar to 25-80 nm) for stratiform mixed-phase clouds in the summertime high Arctic (> 80 degrees N) has been investigated using two large-eddy simulation models. We find that, in both models, Aitken mode particles significantly affect the simulated microphysical and radiative properties of the cloud and can help sustain the cloud when accumulation mode concentrations are low (< 10-20 cm^-3), even when the particles have low hygroscopicity (hygroscopicity parameter - kappa = 0.1). However, the influence of the Aitken mode decreases if the overall liquid water content of the cloud is low, either due to a higher ice fraction or due to low radiative cooling rates. An analysis of the simulated supersaturation (ss) statistics shows that the ss frequently reaches 0.5 % and sometimes even exceeds 1 %, which confirms that Aitken mode particles can be activated. The modelling results are in qualitative agreement with observations of the Hoppel minimum obtained from four different expeditions in the high Arctic. Our findings highlight the importance of better understanding Aitken mode particle formation, chemical properties and emissions, particularly in clean environments such as the high Arctic.