Radiation-induced oscillatory Hall effect in high-mobility ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ devices

We examine the radiation induced modification of the Hall effect in high-mobility ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ devices that exhibit vanishing resistance under microwave excitation. The modification in the Hall effect upon irradiation is characterized by (a) a small reduction in the slope of the Hall resistance curve with respect to the dark value, (b) a periodic reduction in the magnitude of the Hall resistance $R_{\mathrm{xy}}$ that correlates with an increase in the diagonal resistance $R_{\mathrm{xx}},$ and (c) a Hall resistance correction that disappears as the diagonal resistance vanishes.