Efficient linear scaling approach for computing the Kubo Hall conductivity

Ortmann, Frank; Leconte, Nicolás; Roche, Stephan

doi:10.1103/physrevb.91.165117

Cited by 21 publications

(20 citation statements)

References 47 publications

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“…The nondissipative Hall conductivity is calculated using a newly developed efficient real-space algorithm [49,50] (see also Ref. [51]) as follows:…”

Section: Model and Methodsmentioning

confidence: 99%

Unconventional features in the quantum Hall regime of disordered graphene: Percolating impurity states and Hall conductance quantization

et al. 2016

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We report on the formation of critical states in disordered graphene, at the origin of variable and unconventional transport properties in the quantum Hall regime, such as a zero-energy Hall conductance plateau in the absence of an energy band gap and Landau-level degeneracy breaking. By using efficient real-space transport methodologies, we compute both the dissipative and Hall conductivities of large-size graphene sheets with random distribution of model single and double vacancies. By analyzing the scaling of transport coefficients with defect density, system size, and magnetic length, we elucidate the origin of anomalous quantum Hall features as magnetic-fielddependent impurity states, which percolate at some critical energies. These findings shed light on unidentified states and quantum-transport anomalies reported experimentally.

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“…The nondissipative Hall conductivity is calculated using a newly developed efficient real-space algorithm [49,50] (see also Ref. [51]) as follows:…”

Section: Model and Methodsmentioning

confidence: 99%

Unconventional features in the quantum Hall regime of disordered graphene: Percolating impurity states and Hall conductance quantization

et al. 2016

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“…We further calculated the Hall conductivity from the Kubo-Bastin formula, 35 in the context of the kernel polynomial method. 36,37 We find that unbiased BP presents the characteristic integer quantum Hall effect with σ IQHE xy = 2n(e 2 /h), whereas biased semimetal BP presents a relativistic quantum Hall effect characteristic of Dirac materials, with σ RQHE xy = 4(n + 1/2)(e 2 /h).…”

Section: Introductionmentioning

confidence: 99%

“…For this aim, we use an efficient numerical approach, recently developed by García et al, 36 that is based on a real space implementation of the Kubo formalism where both diagonal and offdiagonal conductivities are treated in the same footing. In the limit ω → 0 and for non-interacting electrons, the so-called Kubo-Bastin formula for the conductivity can be used to obtain the elements of the static conductivity tensor [35][36][37] …”

Section: Hall Conductivitymentioning

confidence: 99%

Quantum Hall effect and semiconductor-to-semimetal transition in biased black phosphorus

Yuan¹,

Veen²,

Katsnelson³

et al. 2016

Phys. Rev. B

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We study the quantum Hall effect of 2D electron gas in black phosphorus in the presence of perpendicular electric and magnetic fields. In the absence of a bias voltage, the external magnetic field leads to a quantization of the energy spectrum into equidistant Landau levels, with different cyclotron frequencies for the electron and hole bands. The applied voltage reduces the band gap, and eventually a semiconductor to semimetal transition takes place. This nontrivial phase is characterized by the emergence of a pair of Dirac points in the spectrum. As a consequence, the Landau levels are not equidistant anymore, but follow the εn ∝ √ nB characteristic of Dirac crystals as graphene. By using the Kubo-Bastin formula in the context of the kernel polynomial method, we compute the Hall conductivity of the system. We obtain a σxy ∝ 2n quantization of the Hall conductivity in the gapped phase (standard quantum Hall effect regime), and a σxy ∝ 4(n + 1/2) quantization in the semimetalic phase, characteristic of Dirac systems with non-trivial topology.

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“…II. The core of this method lies in the approximation of the completeness relation by random-phase vectors (Ortmann et al, 2015;Ortmann and Roche, 2013),…”

Section: A Topological and Fermi Surface Contributionsmentioning

confidence: 99%

“…One of the main advantages of such approaches is the ability to identify different regimes of quantum transport -ballistic, diffusive, and localized -by following the time-dependent spatial spreading of quantum wavepackets. Similar types of methodology, as well as other algorithms using the KPM technique, have extended the capability of these methods to the study of other quantities such as the Hall conductivity (García et al, 2015;Ortmann et al, 2015;Ortmann and Roche, 2013), spin dynamics (Cummings et al, 2017;Van Tuan et al, 2014;Vierimaa et al, 2017), and lattice thermal conductivity in disordered systems (Sevinçli et al, 2011;Li et al, 2010Li et al, , 2011.…”

mentioning

confidence: 99%