2011/05/06 by M. Ortuño, A. M. Somoza, V. V. Mkhitaryan +2
Materials Science · Physics and Astronomy · Psychology · #Condensed matter physics #Graphene research and applications #Magnetic field #Percolation (cognitive psychology) #Phase (matter) #Phase diagram #Phase transition #Physics #Psychology #Quantum #Quantum Hall effect #Quantum and electron transport phenomena #Quantum mechanics #Quantum phase transition #Statistical physics #Topological Materials and Phenomena #cond-mat.dis-nn
paper · pdf · doi:10.1103/physrevb.84.165314
published as Phys. Rev. B 84, 165314 (2011) · 12 pages, 13 figures
arxiv created 2011/05/06 · openalex publication_date 2011/10/07 · arxiv updated 2012/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider magnetotransport in high-mobility two-dimensional electron gas \ensuremathσxx\ensuremath≫1 in a nonquantizing magnetic field. We employ a weakly chiral network model to test numerically the prediction of the scaling theory that the transition from an Anderson to a quantum Hall insulator takes place when the Drude value of the nondiagonal conductivity \ensuremathσxy is equal to 1/2 (in the units of e2/h). The weaker the magnetic field, the harder it is to locate a delocalization transition using quantum simulations. The main idea of this study is that the position of the transition does not change when a strong local inhomogeneity is introduced. Since the strong inhomogeneity suppresses interference, transport reduces to classical percolation. We show that the corresponding percolation problem is bond percolation over two sublattices coupled to each other by random bonds. Simulation of this percolation allows us to access the domain of very weak magnetic fields. Simulation results confirm the criterion \ensuremathσxy=1/2 for values \ensuremathσxx\ensuremath∼10, where they agree with earlier quantum simulation results. However, for larger \ensuremathσxx, we find that the transition boundary is described by \ensuremathσxy\ensuremath∼\ensuremathσxx^\ensuremathκ with \ensuremathκ\ensuremath≈0.5, i.e., the transition takes place at higher magnetic fields. The strong inhomogeneity limit of magnetotransport in the presence of a random magnetic field, pertinent to composite fermions, corresponds to a different percolation problem. In this limit, we find for the delocalization transition boundary \ensuremathσxy\ensuremath∼\ensuremathσxx0.6.