"Fractional" Quantized Hall Effect in a Quasi-One-Dimensional Conductor

When the magnetic field is not aligned along one of the crystallographic axes of a quasi-1D conductor, the electronic motion is periodic only for special values of the field orientation. For these values, a cascade of spin-density-wave subphases is expected as the field increases. In each subphase the Hall resistance per layer is ${\rho }_{\mathrm{xy}}=\frac{\mathrm{qh}}{p{e}^2}$. $q$ depends on the orientation of the field and $p$ on its amplitude. The electron motion involves large orbits which spread over $q$ unit cells. The integer quantization of these orbits implies a fractional quantization of the density of carriers.