2011/01/31 by J. T. Chalker, M. Ortuño, A. M. Somoza
Computer Science · Mathematics · Physics and Astronomy · #Condensed matter physics #Coupling (piping) #Geometry #Magnetic field #Materials science #Mathematics #Physics #Plateau (mathematics) #Quantum #Quantum Hall effect #Quantum Information and Cryptography #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Quantum spin Hall effect #Scaling #Spin (aerodynamics) #Symmetry (geometry) #Unitary state #cond-mat.dis-nn
paper · pdf · doi:10.1103/physrevb.83.115317
published as Phys. Rev. B 83, 115317 (2011) · 5 pages, 6 figures
arxiv created 2011/01/31 · openalex publication_date 2011/03/15 · arxiv updated 2015/03/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study the spin quantum Hall effect and transitions between Hall plateaus in quasi-two-dimensional network models consisting of several coupled layers. Systems exhibiting the spin quantum Hall effect belong to class C in the symmetry classification for Anderson localization, and for network models in this class there is an established mapping between the quantum problem and a classical one involving random walks. This mapping permits numerical studies of plateau transitions in much larger samples than for other symmetry classes, and we use it to examine localization in systems consisting of n weakly coupled layers. Standard scaling ideas lead one to expect n distinct plateau transitions, but in the case of the unitary symmetry class this conclusion has been questioned. Focusing on a two-layer model, we demonstrate that there are two separate plateau transitions, with the same critical properties as in a single-layer model, even for very weak interlayer coupling.