Hayes specialised in crystals, and studied imperfections in crystals and defects in solids. He investigated the spectroscopic signatures of imperfections in alkali halides and semiconductors, using varied research techniques that included inelastic light scattering (Raman and Brillouin spectroscopy), magneto-optics (Zeeman effect), nuclear magnetic resonance (NMR), electron paramagnetic resonance (EPR) and muon spin resonance (mu-SR).