Linear scaling quantum transport methodologies

Fan, Zheyong; García, Jose H.; Cummings, Aron W.; Vargas, José Eduardo Barrios; Panhans, Michel; Harju, Ari; Ortmann, Frank; Roche, Stephan

doi:10.1016/j.physrep.2020.12.001

Cited by 74 publications

(62 citation statements)

References 342 publications

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“…To determine possible experimental signatures of this phenomenon, we analyze the valley Hall conductivity σ v xy and nonlocal resistance R NL using both the Kubo and Landauer-Buttiker formalisms. We employ the Kubo-Bastin formula [26,[69][70][71][72][73][74][75][76] to calculate both the full and Fermi-surface contributions to σ v xy [66] for a R = 10 nm mass dot (V A/B = ±0.1|t|) placed into one of three different square supercells with side lengths W C = 5R, 10R, 20R. This allows us to examine the competition between scattering and Berry curvature effects, which can arise in periodic systems due to a finite concentration c of sites with mass , yielding an effective global mass ≈ c .…”

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confidence: 99%

Valley Hall effect and nonlocal resistance in locally gapped graphene

et al. 2021

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We report on the emergence of bulk, valley-polarized currents in graphene-based devices, driven by spatially varying regions of broken sublattice symmetry, and revealed by nonlocal resistance (R NL ) fingerprints. By using a combination of quantum transport formalisms, giving access to bulk properties as well as multiterminal device responses, the presence of a nonuniform local band gap is shown to give rise to valley-dependent scattering and a finite Fermi-surface contribution to the valley Hall conductivity, related to characteristics of R NL . These features are robust against disorder and provide a plausible interpretation of controversial experiments in graphene/hexagonal boron nitride superlattices. Our findings suggest both an alternative mechanism for the generation of valley Hall effect in graphene and a route towards valley-dependent electron optics, by materials and device engineering.

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confidence: 99%

Valley Hall effect and nonlocal resistance in locally gapped graphene

et al. 2021

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“…Several complementary models can support these enhancements. For example, the Kubo-Greenwood-Chester-Thellung formulation [65,142] is suitable for quantum transport investigations in disordered bulk materials. However, it may be incomplete to simulate nanoscale devices approaching the ballistic regime.…”

Section: Quantum Limitations and Ballistic Modelsmentioning

confidence: 99%

“…However, it may be incomplete to simulate nanoscale devices approaching the ballistic regime. An additional approach such as Landauer-Büttiker Formalism [142][143][144][145] is requested for contact effects and non-equilibrium transport properties. The quantum Hall Effect is not considerable if the magnetic field will be less then B < 0.5T [145].…”

Section: Quantum Limitations and Ballistic Modelsmentioning

confidence: 99%

A Comprehensive Review of Integrated Hall Effects in Macro-, Micro-, Nanoscales, and Quantum Devices

Karsenty

2020

Sensors

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A comprehensive review of the main existing devices, based on the classic and new related Hall Effects is hereby presented. The review is divided into sub-categories presenting existing macro-, micro-, nanoscales, and quantum-based components and circuitry applications. Since Hall Effect-based devices use current and magnetic field as an input and voltage as output. researchers and engineers looked for decades to take advantage and integrate these devices into tiny circuitry, aiming to enable new functions such as high-speed switches, in particular at the nanoscale technology. This review paper presents not only an historical overview of past endeavors, but also the remaining challenges to overcome. As part of these trials, one can mention complex design, fabrication, and characterization of smart nanoscale devices such as sensors and amplifiers, towards the next generations of circuitry and modules in nanotechnology. When compared to previous domain-limited text books, specialized technical manuals and focused scientific reviews, all published several decades ago, this up-to-date review paper presents important advantages and novelties: Large coverage of all domains and applications, clear orientation to the nanoscale dimensions, extended bibliography of almost one hundred fifty recent references, review of selected analytical models, summary tables and phenomena schematics. Moreover, the review includes a lateral examination of the integrated Hall Effect per sub-classification of subjects. Among others, the following sub-reviews are presented: Main existing macro/micro/nanoscale devices, materials and elements used for the fabrication, analytical models, numerical complementary models and tools used for simulations, and technological challenges to overcome in order to implement the effect in nanotechnology. Such an up-to-date review may serve the scientific community as a basis for novel research oriented to new nanoscale devices, modules, and Process Development Kit (PDK) markets.

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“…This new element in the equation of motion is what is usually called the collision term. Typical examples found in the literature following this strategy are Green function [3][4][5], the density matrix [6,7], Wigner distribution function [8][9][10][11][12][13][14], the master equation [15,16], Kubo formalism [17], conditional wave functions [20][21][22], etc.…”

Section: Introductionmentioning

confidence: 99%

Can Wigner distribution functions with collisions satisfy complete positivity and energy conservation?

Villani

Oriols

2021

J Comput Electron

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To avoid the computational burden of many-body quantum simulation, the interaction of an electron with a photon (phonon) is typically accounted for by disregarding the explicit simulation of the photon (phonon) degree of freedom and just modeling its effect on the electron dynamics. For quantum models developed from the (reduced) density matrix or its Wigner–Weyl transformation, the modeling of collisions may violate complete positivity (precluding the typical probabilistic interpretation). In this paper, we show that such quantum transport models can also strongly violate the energy conservation in the electron–photon (electron–phonon) interactions. After comparing collisions models to exact results for an electron interacting with a photon, we conclude that there is no fundamental restriction that prevents a collision model developed within the (reduced) density matrix or Wigner formalisms to satisfy simultaneously complete positivity and energy conservation. However, at the practical level, the development of such satisfactory collision model seems very complicated. Collision models with an explicit knowledge of the microscopic state ascribed to each electron seems recommendable (Bohmian conditional wavefunction), since they allow to model collisions of each electron individually in a controlled way satisfying both complete positivity and energy conservation.

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Linear scaling quantum transport methodologies

Cited by 74 publications

References 342 publications

Valley Hall effect and nonlocal resistance in locally gapped graphene

Valley Hall effect and nonlocal resistance in locally gapped graphene

A Comprehensive Review of Integrated Hall Effects in Macro-, Micro-, Nanoscales, and Quantum Devices

Can Wigner distribution functions with collisions satisfy complete positivity and energy conservation?

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