Universal Critical Exponent in Class D Superconductors

Kagalovsky, V.; Nemirovsky, D.

doi:10.1103/physrevlett.101.127001

Cited by 15 publications

(26 citation statements)

References 16 publications

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“…In a full agreement with the scenario suggested in Ref. [19] for W > W N , the critical exponent has a value distinctively different from W N = 0 1. The triritical fixed point was found at W T = 0 14.…”

Section: Novel Symmetry Classes C and Dsupporting

confidence: 81%

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Symmetry, Universality and Critical Transitions in the Network Models

Kagalovsky¹

2011

Jnl of Comp & Theo Nano

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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.

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Section: Novel Symmetry Classes C and Dsupporting

confidence: 81%

“…[17,19]. At low disorder W the critical line is at = 0 and it splits in two lines at the tricritical point W T .…”

Section: Novel Symmetry Classes C and Dmentioning

confidence: 96%

Symmetry, Universality and Critical Transitions in the Network Models

Kagalovsky¹

2011

Jnl of Comp & Theo Nano

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“…͑Here we disagree with Refs. 32 and 33, which maintain that the M-I transition exists in graphene as well.͒ Our lattice fermion model is different from the network model 9 used in previous investigations 10,11,15,16 but it falls in the same universality class so we expect the same critical conductivity and critical exponent. For the I-I transition analytical calculations 1,14 give c = G 0 / and = 1, in agreement with our numerics.…”

Section: Discussionmentioning

confidence: 99%

“…Earlier numerical investigations 10,11,15,16 of the class BD phase diagram were based on the Cho-Fisher network model. 9 Here we use a staggered-fermion model in the same symmetry class, originally developed in the context of lattice gauge theory 24,25 and recently adapted to the study of transport properties in graphene.…”

Section: Staggered Fermion Modelmentioning

confidence: 99%

Effective mass and tricritical point for lattice fermions localized by a random mass

2010

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This is a numerical study of quasiparticle localization in symmetry class BD ͑realized, for example, in chiral p-wave superconductors͒, by means of a staggered-fermion lattice model for two-dimensional Dirac fermions with a random mass. For sufficiently weak disorder, the system size dependence of the average ͑thermal͒ conductivity is well described by an effective mass M eff , dependent on the first two moments of the random mass M͑r͒. The effective mass vanishes linearly when the average mass M → 0, reproducing the known insulator-insulator phase boundary with a scale invariant dimensionless conductivity c =1/ and critical exponent = 1. For strong disorder a transition to a metallic phase appears, with larger c but the same . The intersection of the metal-insulator and insulator-insulator phase boundaries is identified as a repulsive tricritical point.

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“…For two other types of sign disorder: random-bond Ising model [5][6][7] and Cho-Fisher (CF) model [22], the metallic phase is either absent or emerges when W exceeds certain W c , correspondingly. The above two facts were also established numerically by studying transmission of finite-width (up to M = 256) stripes [12,[23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Localization Properties of Random-Mass Dirac Fermions from Real-Space Renormalization Group

Mkhitaryan

Raǐkh

2011

Phys. Rev. Lett.

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Localization properties of random-mass Dirac fermions for a realization of mass disorder, commonly referred to as the Cho-Fisher model, are studied on the D-class chiral network. We show that a simple renormalization group (RG) description captures accurately a rich phase diagram: thermal metal and two insulators with quantized σ(xy), as well as transitions (including critical exponents) between them. Our main finding is that, even with small transmission of nodes, the RG block exhibits a sizable portion of perfect resonances. Delocalization occurs by proliferation of these resonances to larger scales. Evolution of the thermal conductance distribution towards a metallic fixed point is synchronized with evolution of signs of transmission coefficients, so that delocalization is accompanied with sign percolation.

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Universal Critical Exponent in Class D Superconductors

Cited by 15 publications

References 16 publications

Symmetry, Universality and Critical Transitions in the Network Models

Symmetry, Universality and Critical Transitions in the Network Models

Effective mass and tricritical point for lattice fermions localized by a random mass

Localization Properties of Random-Mass Dirac Fermions from Real-Space Renormalization Group

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