Dirac cones for graph models of multilayer AA-stacked graphene sheets

Oliveira, César R. de; Rocha, Vinícius L.

doi:10.1515/zna-2020-0330

Cited by 5 publications

(8 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Optimize generative model parameters θ to minimize either the feature preservation error or the reconstruction error. Various optimization techniques can be applied, including utilizing gradients [76], solving eigenvalue problems [77], or employing rewards [78]. Consider a classical dataset 𝑋 = {𝑥 1 , 𝑥 2 , .…”

Section: Qgms For Data Synthesismentioning

confidence: 99%

Utilising Dimensionality Reduction for Improved Data Analysis with Quantum Feature Learning

Sihare

2024

Preprint

View full text Add to dashboard Cite

This research explores the potential of quantum computing in data analysis, focusing on the efficient analysis of high-dimensional quantum datasets using dimensionality reduction techniques. The study aims to fill the knowledge gap by developing robust quantum dimensionality reduction techniques that can mitigate noise and errors. The research methodology involved a comprehensive review and analysis of existing quantum dimensionality reduction techniques, such as quantum principal component analysis, quantum linear discriminant analysis and quantum generative models. The study also explored the limitations imposed by NISQ devices and proposed strategies to adapt these techniques to work efficiently within these constraints. The key results demonstrate the potential of quantum dimensionality reduction techniques to effectively reduce the dimensionality of high-dimensional quantum datasets while preserving critical quantum information. The evaluation of quantum principal component analysis, quantum linear discriminant analysis and quantum generative models showed their effectiveness in improving quantum data analysis, particularly in improving simulation speed and predicting properties. Despite the challenges posed by noise and errors, robust quantum dimensionality reduction methods showed promise in mitigating these effects and preserving quantum information. Finally, this research contributes to the advancement of quantum data analysis by presenting a comprehensive analysis of quantum dimensionality reduction techniques and their applications. It highlights the importance of developing robust quantum feature learning methods that can operate efficiently in noisy quantum environments, especially in the NISQ era.

show abstract

Section: Qgms For Data Synthesismentioning

confidence: 99%

Utilising Dimensionality Reduction for Improved Data Analysis with Quantum Feature Learning

Sihare

2024

Preprint

View full text Add to dashboard Cite

show abstract

“…Another possibility is the so-called AA-stacked, in which all graphene sheets and carbon-carbon connections between consecutive sheets are alined. In another work [9], we discuss this possibility for many layers. Our main results here may be summarized as follows.…”

Section: Introductionmentioning

confidence: 97%

“…(d) Although the interlayer interaction parameter t 0 should be small to model the multilayer graphene, our results here hold for all t 0 > 0. On the other hand, in our study of multilayer AA-stacked graphene [9], the larger the number of layers the smaller t 0 is required.…”

Section: Introductionmentioning

confidence: 99%

Dirac cones for bi- and trilayer Bernal-stacked graphene in a quantum graph model

Oliveira¹,

Rocha²

2020

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

A quantum graph model for a single sheet of graphene is extended to bilayer and trilayer Bernal-stacked graphene; the spectra are characterized and the dispersion relations explicitly obtained; Dirac cones are then proven to be present only for trilayer graphene, although the bilayer has a gapless parabolic band component. Our model rigorously exhibits basic facts from tight-binding calculations, effective two-dimensional models and a π-orbital continuum model with nearestneighbour tunneling that have been discussed in the physics literature.

show abstract

“…The latter approach has two advantages: it is simpler then the previous one and permits an accurate spectral analysis including details of Dirac cones; however, this technique requires that all edges in the graph have the same length, that is, an equilateral graph. Recently, the present authors have proposed adaptations in the boundary conditions so that the AA-and AB-stacked graphene multilayer could (at least qualitatively) be modeled by QGMs [6,7]; there is a work that also covers a few layers of graphene combined with hexagonal boron nitride [8] (again with a QGM).…”

Section: Introductionmentioning

confidence: 99%

Effective Quantum Graph Models of Some Nonequilateral Graphyne Materials

Oliveira

Rocha

2023

Self Cite

View full text Add to dashboard Cite

It is shown that it is possible to adapt the quantum graph model of graphene to some types of nonequilateral graphynes considered in the literature; we also discuss the corresponding nanotubes. The proposed models are, in fact, effective models and are obtained through selected boundary conditions and an ad hoc prescription. We analytically recover some results from the literature, in particular, the presence of Dirac cones for α-, β- and (6,6,12)-graphynes; for γ-graphyne, our model presents a band gap (according to the literature), but only for a range of parameters, with a transition at a certain point with quadratic touch and then the presence of Dirac cones.

show abstract

Dirac cones for graph models of multilayer AA-stacked graphene sheets

Cited by 5 publications

References 39 publications

Utilising Dimensionality Reduction for Improved Data Analysis with Quantum Feature Learning

Utilising Dimensionality Reduction for Improved Data Analysis with Quantum Feature Learning

Dirac cones for bi- and trilayer Bernal-stacked graphene in a quantum graph model

Effective Quantum Graph Models of Some Nonequilateral Graphyne Materials

Contact Info

Product

Resources

About