Green’s functions on a renormalized lattice: An improved method for the integer quantum Hall transition

Puschmann, Martin; Vojta, Thomas

doi:10.1016/j.aop.2021.168485

Cited by 6 publications

(3 citation statements)

References 28 publications

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“…We also demonstrated how this is reflected in their finite-wavevector electromagnetic responses to an applied electric field. We introduced a transfer matrix and studied the electronic delocalization transition in the lowest level of the zeroquadratic model with quenched onsite disorder and found a localization-length critical exponent of 2.57(3), which is in close agreement that of the disordered Hofstadter model 2.58(3) [50], and in concurrence with localizationlength exponents for Landau levels and the IQHE [44][45][46][47][48][49][50][51][52][53][54][55]. This provides evidence that supports a broad universality of the IQHE localization-delocalization critical exponent independent of specific model parameters.…”

Section: Discussionsupporting

confidence: 57%

“…The value of this critical exponent has drawn much attention, with experimental values of approximately ν = 2.38 [42,43]. Theoretical values are less clear, with recent values between 2.37 and 2.62 being reported for different models [44][45][46][47][48][49][50][51][52][53][54][55]. A recent large-scale numerical study of the disordered Hofstadter model using the recursive Green's function method found ν = 2.58(3) [50].…”

Section: A Background Theorymentioning

confidence: 99%

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Fractional Chern insulators with a non-Landau level continuum limit

Bauer,

Talkington,

Harper

et al. 2021

Preprint

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Recent developments in fractional quantum Hall (FQH) physics highlight the importance of studying FQH phases of particles partially occupying energy bands that are not Landau levels. FQH phases in the regime of strong lattice effects, called fractional Chern insulators, provide one setting for such studies. As the strength of lattice effects vanishes, the bands of generic lattice models asymptotically approach Landau levels. In this article, we construct lattice models for single-particle bands that are distinct from Landau levels even in this continuum limit. We describe how the distinction between such bands and Landau levels is quantified by band geometry over the magnetic Brillouin zone and reflected in the electromagnetic response. We analyze the localization-delocalization transition in one such model and compute a localization length exponent of 2.57(3). Moreover, we study interactions projected to these bands and find signatures of bosonic and fermionic Laughlin states. Most pertinently, our models allow us to isolate conditions for optimal band geometry and gain further insight into the stability of FQH phases on lattices.

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Section: Discussionsupporting

confidence: 57%

Section: A Background Theorymentioning

confidence: 99%

Fractional Chern insulators with a non-Landau level continuum limit

Bauer,

Talkington,

Harper

et al. 2021

Preprint

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“…Quantum transport is a wide field of study [1][2][3][4] for which there exist plenty of recursive methods to study it within the tight-binding approximation [5][6][7][8][9][10][11][12][13][14]. These methods are useful to calculate the Green's function, the transfer matrix, or the scattering matrix (S-matrix) of the system, which then can be used to obtain the transmission function T(E) at energy E [5,6].…”

Section: Introductionmentioning

confidence: 99%

A divide-and-conquer method to improve performance in quantum transport calculations: conductance in rotated graphene nanoribbons side-contact junctions

Rodríguez¹,

García²

2022

Electron. Struct.

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We propose a divide-and-conquer algorithm to find recursively the Scattering matrix of general tight-binding structures. The Scattering matrix allows a direct calculation of transport properties in mesoscopic systems by using the Landauer formula. The method is exact, and by analyzing the performance of the algorithm in square, triangular and honeycomb lattices, we show a significant improvement in comparison to other state-of-the-art recursive and non-recursive methods. We utilize this algorithm to compute the conductance of a rotated graphene nanoribbon side-contact junction, revealing that for electrons with energies smaller than -2.7eV the transmission function depends negligibly on the angle of the junction, whereas for electrons with energies greater than -2.7eV, there exists a set of angles for the system that increase its conductance independently of the energy of the particles.

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Special Issue “Localisation 2020”: Editorial Summary

Bhatt

Kettemann

2021

Annals of Physics

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Green’s functions on a renormalized lattice: An improved method for the integer quantum Hall transition

Cited by 6 publications

References 28 publications

Fractional Chern insulators with a non-Landau level continuum limit

Fractional Chern insulators with a non-Landau level continuum limit

A divide-and-conquer method to improve performance in quantum transport calculations: conductance in rotated graphene nanoribbons side-contact junctions

Special Issue “Localisation 2020”: Editorial Summary

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