electronic branched flow in graphene: theory and machine ......aps march meeting 2018 los angeles,...
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Electronic Branched Flow in Graphene: Theory and Machine Learning Prediction
School of Engineering & Applied Sciences (SEAS)
Marios Mattheakis
Collaborators:G. P. TsironisE. Kaxiras
APS March Meeting 2018Los Angeles, CaliforniaF40.00006
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Dirac Solids Linear Energy Dispersion Relation of Dirac Solids
Quasi-classical dynamics: Ultra-relativistic Hamiltonian
Classical limit of Dirac equation
Small effective mass due to doping is neglected
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Charged impurities form disordered potential. Charge Puddles
Motivation Experiments
Martin et al.,Nature Phys 4, 2008
Ir(111)/graphenehBN/graphene
Samaddar et al. PRL 116, 2016 Martin et al. PRB 91, 2015
Branched Electronic Flow& Caustic Formationin parabolic 2DEGs Topinka et al., Nature 410, 2001
Jura et al., Nature Phys. 3, 2007
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Disordered PotentialRandom distributed charge puddles of radius R = 4 nm.
A bias potential along the direction of motion
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Simulations
As bias increases: (i) the passage to branched flow delays. (ii) the caustics disperse slower.
M.M., G.P. Tsironis, E. Kaxiras, arXiv: 1801.08217
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Theoretical ModelEffective Hamiltonian for
Local curvature u equation in the quasi-2D approach
Caustic is an area with high intensity occurs when
where
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The random potential acts as white noise with variance
Scaling of the First Caustic
Langevin equation for the local curvature
Solve approximately the first passage problem for
Conventional 2D metals: In the presence of bias the quasi-2D approach fails.
,
where
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First Caustic Time
Points & Dashed lines: Simulations
Solid lines:Theoretical Predictionup to
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Machine Learning Predicts CausticsThe Deep Learning method Reservoir Computing* is utilized for accurate prediction of Singular Events in wave dynamics.
*Lu et al., Chaos 27, 2017
Prediction
Prediction
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Conclusion
● Branched electronic flow in Dirac Solids focusing on graphene.
● A Langevin Eq. for the local curvature of an ultra-relativistic biased electronic flow is derived.
● Scaling-type relationship between the first caustic location and the statistical properties of disordered potential.
● Machine Learning prediction of singular events in wave dynamics.
[email protected]://scholar.harvard.edu/marios_matthaiakisarXiv: 1801.08217
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Acknowledgements
EFRI 2-DARE NSF Grant No. 1542807
ARO MURI Award No. W911NF-14-0247
NHQWAVE MSCA-RISE Project No. 691209
[email protected]://scholar.harvard.edu/marios_matthaiakis