Conductance fluctuations at the integer quantum Hall plateau transition

Cho, Sora; Fisher, Matthew P. A.

doi:10.1103/physrevb.55.1637

Cited by 63 publications

(76 citation statements)

References 12 publications

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“…2. However, a more detailed comparison is impossible, since the results of the simulations [65][66][67] do not obey the electron-hole symmetry condition P c (G) = P c (1 − G). On the other hand, within the RG approach, the latter condition is satisfied automatically.…”

Section: Comparison With Previous Simulationsmentioning

confidence: 99%

Integer quantum Hall transition in the presence of a long-range-correlated quenched disorder

et al. 2001

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We theoretically study the effect of long-ranged inhomogeneities on the critical properties of the integer quantum Hall transition. For this purpose we employ the real-space renormalization-group (RG) approach to the network model of the transition. We start by testing the accuracy of the RG approach in the absence of inhomogeneities, and infer the correlation length exponent ν = 2.39 from a broad conductance distribution. We then incorporate macroscopic inhomogeneities into the RG procedure. Inhomogeneities are modeled by a smooth random potential with a correlator which falls off with distance as a power law, r −α . Similar to the classical percolation, we observe an enhancement of ν with decreasing α. Although the attainable system sizes are large, they do not allow one to unambiguously identify a cusp in the ν(α) dependence at αc = 2/ν, as might be expected from the extended Harris criterion. We argue that the fundamental obstacle for the numerical detection of a cusp in the quantum percolation is the implicit randomness in the Aharonov-Bohm phases of the wave functions. This randomness emulates the presence of a short-range disorder alongside the smooth potential.

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Section: Comparison With Previous Simulationsmentioning

confidence: 99%

Integer quantum Hall transition in the presence of a long-range-correlated quenched disorder

et al. 2001

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“…We clearly see the expected renormalization flow of σ with the temperature, but the separatix is not a semicircle like at PIT in IQHE, but rather an ellipse. At the critical point, we find σ xy ≈ 1 2 e 2 h and, quite interestingly, σ xx ≈ e 2 h rather than 1 2 e 2 h (to be precise, the numerics place σ xy between 0.5 − 0.6 e 2 h at PIT 50,[92][93][94][95][96] ). The main surprise was, however, the absence of the Quantized Hall Insulator phase, characterized by σ = 0 but ρ xy = h e 2 .…”

Section: Introductionmentioning

confidence: 99%

Quantum criticality at the Chern-to-normal insulator transition

Xue

Prodan

2013

Phys. Rev. B

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Using the non-commutative Kubo formula for aperiodic solids and a recently developed numerical implementation, we study the conductivity σ and resistivity ρ tensors as functions of Fermi level E F and temperature T, for models of strongly disordered Chern insulators. The formalism enabled us to converge the transport coefficients at temperatures low enough to enter the quantum critical regime at the Chern-to-trivial insulator transition. We find that the ρ xx -curves at different temperatures intersect each other at one single critical point, and that they obey a single-parameter scaling law with an exponent close to the universally accepted value for the unitary symmetry class. However, when compared with the established experimental facts on the plateau-insulator transition in the Integer Quantum Hall Effect, we find a universal critical conductance σ c xx twice as large, an ellipse rather than a semi-circle law, and absence of the Quantized Hall Insulator phase.

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“…31. We did it by calculating the average G(ε) and fitting it to the curve in 31 . The agreement is again quite reasonable, especially taking into account some asymmetry of the numerical results.…”

Section: Conductance Fluctuationsmentioning

confidence: 99%