A technique using layered wavelength shifting, scintillating and non-scintillating films is presented to achieve discrimination of surface $alpha$ events from low-energy nuclear recoils in liquid argon detectors. A discrimination power greater than $10^{8}$, similar to the discrimination possible for electronic recoils in argon, can be achieved by adding a 50 micron layer of scintillator with a suitably slow decay time, approximately 300 ns or greater, to a wavelength-shifter coated surface. The technique would allow suppression of surface $alpha$ events in a very large next-generation argon dark matter experiment (with hundreds of square meters of surface area) without the requirement for position reconstruction, thus allowing utilization of more of the instrumented mass in the dark matter search. The technique could also be used to suppress surface backgrounds in compact argon detectors of low-energy nuclear recoils, for example in measurements of coherent neutrino-nucleus scattering or for sensitive measurements of neutron fluxes.
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