Integer and fractional quantum Hall effect in a strip of stripes

We study anisotropic stripe models of interacting electrons in the presence of magnetic fields in the quantum Hall regime with integer and fractional filling factors. The model consists of an infinite strip of finite width that contains periodically arranged stripes (forming supercells) to which the electrons are confined and between which they can hop with associated magnetic phases. The interacting electron system within the one-dimensional stripes are described by Luttinger liquids and shown to give rise to charge and spin density waves that lead to periodic structures within the stripe with a reciprocal wavevector 8k F in a mean field approximation. This wavevector gives rise to Umklapp scattering and resonant scattering that results in gaps and chiral edge states at all known integer and fractional filling factors ν. The integer and odd denominator filling factors arise for a uniform distribution of stripes, whereas the even denominator filling factors arise for a non-uniform stripe distribution. We focus on the ground state of the system, and identify the quantum Hall regime via the quantized Hall conductance. For this we calculate the Hall conductance via the Streda formula and show that it is given by σ H =νe 2 /h for all filling factors. In addition, we show that the composite fermion picture follows directly from the condition of the resonant Umklapp scattering. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2014