Quantum site percolation on triangular lattice and the integer quantum Hall effect

Mkhitaryan, V. V.; Raǐkh, M. É.

doi:10.1103/physrevb.79.125401

Cited by 12 publications

(22 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this chapter we describe two network models proposed recently: the first one is a weakly chiral network p − q model, 26 27 constructed to study the levitation of extended states at low magnetic fields, and the second one is a triangular model, 28 proposed as an alternative to the quadratic CC model to describe inter-plateaux transitions in the IQHE. It was later generalized 27 to study the levitation scenario as p − q model.…”

Section: Weakly Chiral and Triangular Network Modelsmentioning

confidence: 99%

“…In Ref. [28] the critical exponent of the triangular model was inferred from the real space renormalization group analysis ≈ 2 3 ÷ 2 76. Later, in Ref.…”

Section: Weakly Chiral and Triangular Network Modelsmentioning

confidence: 99%

“…The triangular p − q model, 28 constructed to study the levitation scenario, allows backscattering on the links, described by the same matrix (Eq. (22)) as in the square p − q model.…”

Section: Weakly Chiral and Triangular Network Modelsmentioning

confidence: 99%

See 2 more Smart Citations

Symmetry, Universality and Critical Transitions in the Network Models

Kagalovsky¹

2011

Jnl of Comp & Theo Nano

View full text Add to dashboard Cite

We discuss various applications of the network models, starting with the original ChalkerCoddington (CC) network model, proposed to describe inter-plateaux transition in the integer quantum Hall effect (IQHE). We present a semi-classical picture which serves as a basis for the CC model. We then discuss various generalizations of the CC model: a two-channel per link, allowing to include spin or consider two lowest Landau levels; different symmetries of the transfer matrices corresponding to novel symmetry classes of the spin and thermal quantum Hall effects; quantum spin Hall effect with very nontrivial phase diagram. We proceed by presenting two recent network models: a weakly chiral network model constructed on the square lattices to describe levitation of extended states at low magnetic fields, and a triangular network model analogous to the original CC model, and its generalization, also supporting the levitation scenario. We discuss how the critical exponent of the transition depends on the existence of two critical energies. We conclude our review by discussing the generalization of the CC model, describing the effect of nuclear spin on the tunneling of electron, which allows spin-flip scattering.

show abstract

Section: Weakly Chiral and Triangular Network Modelsmentioning

confidence: 99%

“…In Ref. [28] the critical exponent of the triangular model was inferred from the real space renormalization group analysis ≈ 2 3 ÷ 2 76. Later, in Ref.…”

Section: Weakly Chiral and Triangular Network Modelsmentioning

confidence: 99%

See 1 more Smart Citation

Symmetry, Universality and Critical Transitions in the Network Models

Kagalovsky¹

2011

Jnl of Comp & Theo Nano

View full text Add to dashboard Cite

show abstract

“…In Ref. 76 it was demonstrated that these probabilities are equal to 4/9. Correspondingly, the probability of the forward scattering is 1/9.…”

Section: A Fully Chiral Triangular Modelmentioning

confidence: 99%

“…While for the square p-q model each chiral network was of CC type, here each chiral network represents a "triangular" model introduced in Ref. 76 …”

Section: Triangular P-q Modelmentioning

confidence: 99%

Weakly chiral networks and two-dimensional delocalized states in a weak magnetic field

2010

Self Cite

View full text Add to dashboard Cite

We study numerically the localization properties of two-dimensional electrons in a weak perpendicular magnetic field. For this purpose we construct weakly chiral network models on the square and triangular lattices. The prime idea is to separate in space the regions with phase action of magnetic field, where it affects interference in course of multiple disorder scattering, and the regions with orbital action of magnetic field, where it bends electron trajectories. In our models, the disorder mixes counter-propagating channels on the links, while scattering matrices at the nodes describe exclusively the bending of electron trajectories. By artificially introducing a strong spread in the scattering strengths on the links (but keeping the average strength constant), we eliminate the interference and reduce the electron propagation over a network to a classical percolation problem. In this limit we establish the form of the disorder -magnetic field phase diagram. This diagram contains the regions with and without edge states, i.e. the regions with zero and quantized Hall conductivities. Taking into account that, for a given disorder, the scattering strength scales as inverse electron energy, we find agreement of our phase diagram with levitation scenario: energy separating the Anderson and quantum Hall insulating phases floats up to infinity upon decreasing magnetic field. From numerical study, based on the analysis of quantum transmission of the network with random phases on the links, we conclude that the positions of the weak-field quantum Hall transitions on the phase diagram are very close to our classical-percolation results. We checked that, in accord with the Pruisken theory, presence or absence of time reversal symmetry on the links has no effect on the line of delocalization transitions. We also find that floating up of delocalized states in energy is accompanied by doubling of the critical exponent of the localization radius. We establish the origin of this doubling within classical-percolation analysis.

show abstract

Random network models with variable disorder of geometry

2019

View full text Add to dashboard Cite

Recently it was shown (I. A. Gruzberg, A. Klümper, W. Nuding and A. Sedrakyan, Phys. Rev. B 95, 125414 (2017)) that taking into account random positions of scattering nodes in the network model with U (1) phase disorder yields a localization length exponent 2.37 ± 0.011 for plateau transitions in the integer quantum Hall effect. This is in striking agreement with the experimental value of 2.38 ± 0.06. Randomness of the network was modeled by replacing standard scattering nodes of a regular network by pure tunneling resp. reflection with probability p where the particular value p = 1/3 was chosen. Here we investigate the role played by the strength of the geometric disorder, i.e. the value of p. We consider random networks with arbitrary probability 0 < p < 1/2 for extreme cases and show the presence of a line of critical points with varying localization length indices having a minimum located at p = 1/3.

show abstract

Quantum site percolation on triangular lattice and the integer quantum Hall effect

Cited by 12 publications

References 37 publications

Symmetry, Universality and Critical Transitions in the Network Models

Symmetry, Universality and Critical Transitions in the Network Models

Weakly chiral networks and two-dimensional delocalized states in a weak magnetic field

Random network models with variable disorder of geometry

Contact Info

Product

Resources

About