Primitive description for Hall oscillations in the extreme quantum limit of (TMTSF)₂ClO₄

(TMTSF)₂ClO₄ undergoes a cascade of Field Induced Spin Density Wave (FISDW) transitions as magnetic field are increased at low temperature. Each phase corresponds to a different integer quantum Hall state, ν, with ρ_{x y} = h / 2 ν e². However, after a "final" transition at ∼26 T there remain non quantized oscillations in transport and thermodynamic properties as particularly evident in recent Hall measurements. The nature of this high field state is unknown at present. In (TMTSF)₂ClO₄ an anion ordering transition leads to two Fermi surfaces. Here we introduce a simple description where one of the two Fermi surfaces is gapped by an FISDW at k_{F 1}, ν = 0 while the other Fermi surface lacks an FISDW gap. Satellite gaps (with index ν^′) at magnetic wave vectors G (G = e B b / h{stroke}, b the interchain lattice constant), i.e. at k_{F 1} + ν^′ G, gaps are swept past the second Fermi surface at k_{F 2}. This causes Hall sign changes at a frequency given by ν^′ G = k_{F 2} - k_{F 1} (or n h ω_c = 2 t_b: the transverse bandwidth) as observed.