Critical level statistics of a quantum Hall system with Dirichlet boundary conditions

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The electronic properties of a bricklayer model, which shares the same topology as the hexagonal lattice of graphene, are investigated numerically. We study the influence of random magnetic-field disorder in addition to a strong perpendicular magnetic field. We found a disorder-driven splitting of the longitudinal conductance peak within the narrow lowest Landau band near the Dirac point. The energy splitting follows a relation which is proportional to the square root of the magnetic field and linear in the disorder strength. We calculate the scale invariant peaks of the two-terminal conductance and obtain the critical exponents as well as the multifractal properties of the chiral and quantum Hall states. We found approximate values Ϸ 2.5 for the quantum Hall states but = 0.33Ϯ 0.1 for the divergence of the correlation length of the chiral state at E = 0 in the presence of a strong magnetic field. Within the central n = 0 Landau band, the multifractal properties of both the chiral and the split quantum Hall states are the same, showing a parabolic f͓␣͑s͔͒ distribution with ␣͑0͒ = 2.27Ϯ 0.02. In the absence of the constant magnetic field, the chiral critical state is determined by ␣͑0͒ = 2.14Ϯ 0.02.

Section: E Multifractal Eigenstatessupporting

confidence: 73%

Disorder-driven splitting of the conductance peak at the Dirac point in graphene

Schweitzer

Markoš

2008

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“…Level statistics for the isotropic system have been extensively studied by Potempa et al 14,15 and Batsch et al, 16,17 proving the validity of the approach in distinguishing localized from extended states. In addition, the level number variance ⌺ 2 (͗N͘)ϭ͗N͘ has been numerically obtained for the isotropic system, 18 using the Chalker-Coddington network model, 19 and compared with analytical theories, 20 which give for the spectral compressibilty ϭ͓dϪD(2)͔/2d, where D(2) is the multifractal exponent of the wave function at the critical point.…”

Section: Resultsmentioning

confidence: 96%

Metal-insulator transitions in anisotropic two-dimensional systems

Ruhlander

Soukoulis

2001

Several phenomena related to the critical behavior of noninteracting electrons in a disordered twodimensional tight-binding system with a magnetic field are studied. Localization lengths, critical exponents, and density of states are computed using transfer-matrix techniques. Scaling functions of isotropic systems are recovered once the dimension of the system in each direction is chosen proportional to the localization length. It is also found that the critical point is independent of the propagation direction, and that the critical exponents for the localization length for both propagating directions are equal to that of the isotropic system, Ϸ 7 3 . We also calculate the critical value ⌳ c of the scaling function for both the isotropic and the anisotropic system. It is found that ⌳ c iso ϭͱ⌳ c x ⌳ c y . Detailed numerical studies of the density of states n(E) for the isotropic system reveal that for an appreciable amount of disorder, the critical energy is off the band center.

“…A consensus has been reached on the notion that all electronic states are localized for such systems where in addition to the random magnetic flux also random diagonal disorder is present. 3,21,22 However, in the absence of diagonal disorder, it has also been shown that the random flux model with Gaussian distributed and δ-correlated magnetic fields can be mapped onto a nonlinear σ model of unitary symmetry so that all electronic states should be localized. 23 The recognition of a special chiral symmetry that can emerge in systems with an underlying bi-partite lattice, so that the eigenvalues appear in pairs ±ε i , 24 has considerably augmented our view of the possible situations a random flux model can assume.…”

Section: Introductionmentioning

confidence: 99%

Critical conductance of two-dimensional chiral systems with random magnetic flux

Markoš

Schweitzer

2007

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The zero temperature transport properties of two-dimensional lattice systems with static random magnetic flux per plaquette and zero mean are investigated numerically. We study the localization properties and the two-terminal conductance and its dependence on energy, sample size, and magnetic flux strength. The influence of boundary conditions and of the oddness of the number of sites in the transverse direction is also studied. For very long strips of finite width, we find a diverging localization length in the middle of the energy band at E = 0 and determine its critical exponent ν = 0.35±0.03. A previously proposed crossover from a power-law to a logarithmic energy dependence can be excluded from our data, at least for energies |E| > 10 −10 . For square systems, the sample averaged scale independent critical conductance gc turns out to be a function of the amplitude of the flux fluctuations whereas the variance of the respective conductance distributions appears to be universal. We find a critical conductance gc ≃ 1.49 e 2 /h for the strongest possible disorder.