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, νν, with ρxy=h/2νe2ρxy=h/2νe2. 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 kF1,ν=0kF1,ν=0 while the other Fermi surface lacks an FISDW gap. Satellite gaps (with index ν′ν′) at magnetic wave vectors GG (G=eBb/ħG=eBb/ħ, bb the interchain lattice constant), i.e. at kF1+ν′GkF1+ν′G, gaps are swept past the second Fermi surface at kF2kF2. This causes Hall sign changes at a frequency given by ν′G=kF2−kF1ν′G=kF2−kF1 (or nhωc=2tbnhωc=2tb: the transverse bandwidth) as observed.