Treatment of Alzheimer's disease (AD) is impeded by the lack of effective early diagnostic methods. Small, soluble Aβ globulomers play a major role in AD neurotoxicity, and detecting their presence in aqueous fluids could lead to suitable sensors. We evaluate the adsorption behavior of small Aβ oligomers on the surface of a single walled carbon nanotube of high curvature. While the intrinsic self-assembly propensity of Aβ is markedly hindered by adsorption, the oligomeric units show high degrees of surface immobilization. Immobilized complexes are capable of oligomeric growth, but with a shifted monomer-oligomer equilibrium compared to the free states. In the presence of an ionic solution and suitable external electric fields, magnitudes of the current blockades are found to be sensitive to the oligomeric number of the adsorbed complex. However, this sensitivity gradually diminishes with increasing oligomeric size. The results provide a proof-of-concept basis for further investigations in the design of sensors for detecting the toxic small oligomers of Aβ.