Supersymmetry approach to delocalization transitions in a network model of the weak-field quantum Hall effect and related models

Bhardwaj, Shanthanu; Mkhitaryan, V. V.; Gruzberg, Ilya A.

doi:10.1103/physrevb.89.235305

Cited by 4 publications

(5 citation statements)

References 101 publications

(179 reference statements)

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“…To gain a deeper insight into the critical behaviour of matter, theoreticians often employ network models. Such is the case for the metal-insulator transition and also for the transition between different phases of topological insulator (TI) [19][20][21][22][23][24]. Critical phenomena related to the integer and fractional quantum Hall effects have been successfully described by a chiral Chalker-Coddingtonlike network representation of bulk transport in the high magnetic field limit [25].…”

Section: Introductionmentioning

confidence: 99%

“…Critical phenomena related to the integer and fractional quantum Hall effects have been successfully described by a chiral Chalker-Coddingtonlike network representation of bulk transport in the high magnetic field limit [25]. In contrast to the quantum Hall states, the 2D TI-metal transition could be represented by uncoupled counter propagating channels with opposite spin, the so called Z 2 network model [19,20,[22][23][24]26].…”

Section: Introductionmentioning

confidence: 99%

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Transport through the network of topological channels in HgTe based quantum well

Gusev¹,

Квон²,

Козлов³

et al. 2021

2D Mater.

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Topological insulators (TIs) represent a new quantum state of matter which is characterized by edge or surface states and an insulating band gap in the bulk. In a two-dimensional (2D) system based on the HgTe quantum well (QW) of critical width random deviations of the well width from its average value result in local crossovers from zero gap 2D Dirac fermion system to either the 2D TI or the ordinary insulator, forming a complicated in-plane network of helical channels along the zero-gap lines. We have studied experimentally the transport properties of the critical width HgTe QWs near the Dirac point, where the conductance is determined by a percolation along the zero-gap lines. The experimental results confirm the presence of percolating conducting channels of a finite width. Our work establishes the critical width HgTe QW as a promising platform for the study of the interplay between topology and localization.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Transport through the network of topological channels in HgTe based quantum well

Gusev¹,

Квон²,

Козлов³

et al. 2021

2D Mater.

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“…Using the SUSY method, in Ref. [35] we have provided a comparative study of the relevant networks and related models.…”

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confidence: 99%

Relevant perturbations at the spin quantum Hall transition

2015

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We study relevant perturbations at the spin quantum Hall critical point using a network model formulation. The model has been previously mapped to classical percolation on a square lattice, and we use the mapping to extract exact analytical values of the scaling dimensions of the relevant perturbations. We find that several perturbations that are distinct in the network model formulation correspond to the same operator in the percolation picture. We confirm our analytical results by comparing them with numerical simulations of the network model. PACS numbers: 72.15.Rn, 73.20.Fz, INTRODUCTIONAnderson localization of a quantum particle [1] or a classical wave in a random environment is a vibrant research field [2]. One of its central research directions is the physics of Anderson transitions [3], quantum critical points tuned by disorder. These include metal-insulator transitions and transitions of quantum Hall type separating distinct phases of topological insulators. While such transitions are conventionally observed in electronic (metallic and semiconductor) structures, there is also a considerable number of other experimental realizations actively studied in recent and current works. These include localization of light [4] and microwaves [5], cold atoms [6] (see a recent review [7]), ultrasound [8], and optically driven atomic systems [9].From the theoretical point of view, symmetries play a central role in determination of universality classes of critical phenomena. This idea was applied to Anderson localization by Altland and Zirnbaueer (AZ) [10] who identified ten distinct symmetry classes. In three of these classes, classes A, C, and D in AZ classification, the timereversal invariance is broken, and there is a possibility for a quantum Hall transition in two dimensions.The transition in class A is the usual integer quantum Hall (IQH) transition in a two-dimensional (2D) electronic system in a strong perpendicular magnetic field (see Ref.[11] for a review). Class A also includes the model of electrons in a random magnetic field, where all states are believed to be localized [12].Class C is one of the four Bogolyubov-de Gennes classes which describe transport of quasiparticles in disordered superconductors at a mean field level, and possess the particle-hole symmetry. In this class the spinrotation invariance is preserved, the quasiparticles have conserved spin, and one can study spin transport. The corresponding Hall transition is known as the spin quantum Hall (SQH) transition [13,14], at which the system exhibits a jump in the spin Hall conductance from 0 to 2 in appropriate units.In spite of tremendous efforts, most models of Anderson transitions have resisted analytical treatment. The IQH transition is one prominent example where only recently some analytical progress has been achieved [15]. On the other hand, the SQH transition enjoys a special status, since a network model of this transition was mapped exactly to classical percolation on a square lattice [16]. The original mapping used the supersymme...

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“…To gain a deeper insight into the critical behaviour of matter, theoreticians often employ network models. Such is the case for the metal-insulator transition and also for the transition between different phases of topological insulator [18][19][20][21][22][23]. Critical phenomena related to the integer and fractional quantum Hall effects have been successfully described by a chiral Chalker-Coddington-like network representation of bulk transport in the high magnetic field limit [24].…”

Section: Introductionmentioning

confidence: 99%

“…Critical phenomena related to the integer and fractional quantum Hall effects have been successfully described by a chiral Chalker-Coddington-like network representation of bulk transport in the high magnetic field limit [24]. In contrast to the quantum Hall states, the two-dimensional topological insulator-metal transition could be represented by uncoupled counter propagating channels with opposite spin, the so called Z 2 network model [18,19,[21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Transport through the network of topological channels in HgTe based quantum well

Gusev,

Kvon,

Kozlov

et al. 2021

Preprint

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Topological insulators represent a new quantum state of matter which is characterized by edge or surface states and an insulating band gap in the bulk. In a two dimensional (2D) system based on the HgTe quantum well (QW) of critical width random deviations of the well width from its average value result in local crossovers from zero gap 2D Dirac fermion system to either the 2D topological insulator or the ordinary insulator, forming a complicated in-plane network of helical channels along the zero-gap lines. We have studied experimentally the transport properties of the critical width HgTe quantum wells near the Dirac point, where the conductance is determined by a percolation along the zero-gap lines. The experimental results confirm the presence of percolating conducting channels of a finite width. Our work establishes the critical width HgTe QW as a promising platform for the study of the interplay between topology and localization.

show abstract

Supersymmetry approach to delocalization transitions in a network model of the weak-field quantum Hall effect and related models

Cited by 4 publications

References 101 publications

Transport through the network of topological channels in HgTe based quantum well

Transport through the network of topological channels in HgTe based quantum well

Relevant perturbations at the spin quantum Hall transition

Transport through the network of topological channels in HgTe based quantum well

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