Revision of the edge channel picture for the integer quantum Hall effect

Abstract

State of the art computing opens now a new window to the integer quantum Hall effect (IQHE) regime, which enforces a major revision of the common knowledge accumulated so far. In our record-breaking application of the Hartree–Fock method we use up to 3000 electrons distributed over up to 5000 states for almost macroscopic system size of 1000 × 1000 nm. In particular, the formation of compressible and in-compressible edge stripes turns out to develop essentially different from the common picture used so far. Oppositely to the theory of Chklovskii, Shklovskii and Glazman (CSG), the narrow channels, as assumed by the early models of the IQHE, do not widen up into wide compressible stripes. Instead, the wide compressible stripes of CSG transform into a mixture of clusters of full and empty spin-split LLs, while the cluster boundaries create a network of still narrow quantum channels sitting on top of the wide compressible stripes. On this background the early models based on narrow edge channels do not suffer from neglecting electron–electron interaction as falsely stated in the past. Quite oppositely, in contrast to the common believe, our modeling demonstrates that also the IQHE regime carries the hallmark of many-body physics which stabilizes narrow edge channels also in the presence of electron–electron interaction.