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The two-terminal conductance of a random flux model defined on a square lattice is investigated numerically at the band center using a transfer matrix method. Due to the chiral symmetry, there exists a critical point where the ensemble averaged mean conductance is scale independent. We also study the conductance distribution function which depends on the boundary conditions and on the number of lattice sites being even or odd. We derive a critical exponent $ u=0.42pm 0.05$ for square samples of even width using one-parameter scaling of the conductance. This result could not be obtained previously from the divergence of the localization length in quasi-one-dimensional systems due to pronounced finite-size effects.
The chiral surface electrons in the bulk quantum Hall effect probably form the first extended system in which conductance fluctuations can be calculated non-perturbatively in the presence of disorder. By use of the Kubo formula with appropriate bound
Bilayer graphene in a perpendicular electric field can host domain walls between regions of reversed field direction or interlayer stacking. The gapless modes propagating along these domain walls, while not strictly topological, nevertheless have int
We report experimental results on a quantum point contact (QPC) device formed in a wide AlAs quantum well where the two-dimensional electrons occupy two in-plane valleys with elliptical Fermi contours. To probe the closely-spaced, one-dimensional ele
We present first numerical studies of the disorder effect on the recently proposed intrinsic spin Hall conductance in a three dimensional (3D) lattice Luttinger model. The results show that the spin Hall conductance remains finite in a wide range of
We consider a clean two-dimensional interacting electron gas subject to a random perpendicular magnetic field, h({bf r}). The field is nonquantizing, in the sense, that {cal N}_h-a typical flux into the area lambda_{text{tiny F}}^2 in the units of th